YORK UNIVERSITY

               DEPARTMENT OF MATHEMATICS AND STATISTICS

                            FACULTY OF ARTS

                  FACULTY OF PURE AND APPLIED SCIENCE

                             MINI-CALENDAR

                              1996 - 1997



                          Applied Mathematics
                           Pure Mathematics
                              Statistics
                       Mathematics for Commerce
                         Actuarial Mathematics
                          Operations Research


Undergraduate Office - 416-736-5902

Undergraduate Coordinator:    Professor Morton Abramson
                              N505 Ross Building
                              (416)736-5250
                    e-mail:  abramson@mathstat.yorku.ca

World Wide Web Address:  http://www.math.yorku.ca


It's never too late!!!! If you have not taken OAC calculus or have minimal background in mathematics you can still pursue a career involving mathematics by taking our specially designed courses (MATH 1510.06 and MATH 1500.03)
DEPARTMENT OF MATHEMATICS AND STATISTICS FACULTY This list is subject to change. Please ask at N520R or phone the department number at 736-5250. Room Ext# G. O'Brien(Chair) N522R 22555 M. Abramson N505R 66087 G. Albright 540 AK 22479 J.C. Bouhenic 210 GL 66708 N. Bergeron S626R 33930 E. Brettler S508R 66321 J.M.N. Brown N509R 66084 R.L.W. Brown N515R 66085 K. Bugajska S514R 33956 R.G. Burns N615R 66086 J. Caldwell 332 PS 77721 S. Chamberlin N628R 22591 C. Czado N621BR 22596 J.W. Darewych 221 PS 33843 G.E. Denzel C130 WOB 55440 A. Dow N528R 22594 D.A.S. Fraser N630R 66099 H.S. Freedhoff 229 PS 77746 M. Friendly N601AR 33117 R. Ganong S625R 66088 T. Gannon S622R 66090 S. Guiasu N530R 33946 M. Horbatsch 230 PS 77747 S. Hou S512R 66092 C. Hruska N532R 66096 E. Janse vanRensburg 215 PS 33837 G. Janelidze N633R 66089 H.R.P. Joshi N621AR 66094 A. Karrass N517R 66091 I. Kleiner N618R 66095 S. Kochman N510R 22553 J. Laframboise 228 PS 55621 S.W. Lee N633R 66098 T. MacHenry S620R 33902 N. Madras N623R 66097 K. Maltman 222 PS 77741 H. Massam N626R 33903 R. McEachran 225 PS 77743 Y. Medvedev N520R 55250 A. Meir S519R 33994 G. Monette 263ASB 77164 M.E. Muldoon N513R 33911 P. Ng N601BR 77167 P. Olin S614R 22889 M. Ondrack N602R 66010 D.H. Pelletier N506R 33339 J.W. Pelletier N534R 22554 P. Peskun N634R 66089 A. Pietrowski N617R 33924 S.D. Promislow N518R 33497 N. Purzitsky N606R 33932 P. Rajagopal 508 ATK 22267 P. Rogers S834R 88802 T. Salisbury N625R 33938 S. Scull 534 ATK 66676 D. Smylie 109 PS 66438 A. Stauffer 223 PS 77742 J. Steprans S624R 33952 A. Szeto 110 PS 77703 D. Tanny N610R 22588 P. Taylor 112 PS 77707 W. Tholen N605R 33918 A. Trojan 532 ATK 66461 W. vanWijngaarden 247PS 77750 F. Vinette S511R 33936 M. Walker 528 ATK 20470 S. Watson N610R 22588 A. Weiss S618R 66672 W. Whiteley S616R 33971 A. Wong N630R 66099 M.W. Wong S518R 22598 J. Wu S619R 33968 Y. Wu N609R 88604 J. P. Zhu S621 44645
MESSAGE FROM THE DEPARTMENTAL CHAIR To All York Students, We in the Department of Mathematics and Statistics welcome you to the Department, whether it is to major in one of our programmes, to take a course required by another programme, or to take a course for general interest. The faculty members in the Department value both the beauty and the utility of their discipline. They are dedicated to exploring and developing new ideas in mathematics and statistics, and to helping you to explore, understand, appreciate and make use of those ideas. This Mini Calendar is intended to help you with the practical side of your studies, in particular to assist you to choose the programmes and courses best suited to your needs and interests. You should read it in conjunction with the York Undergraduate Programme Calendar, which contains the "official" legally binding University and Faculty regulations. However, there are some programme regulations which are new for this year and so are not in previous years' Calendars. Therefore, I urge you to fill out the updated check list for the programme of your choice before enrolling in courses. You will know that York University, like all Ontario universities, is coping with financial cutbacks. This Department, like all others, has been forced to reduce the number of courses it offers. This means you will have fewer courses to choose from, especially at the upper levels. The number of sections of the big courses is also being reduced. Some of you will not be able to get into your preferred section and may have a less attractive course schedule. Also, courses will be bigger on average, so i t may be harder for you to get individual attention when you need it. In spite of these difficulties, we have tried our best to make sure that you can fulfill all the requirements of your degree programmes. If timetable or other problems present you fro m doing so, please seek the help of one of the people named below. They will do their best to help you solve your problems. Programmes The department offers, in both the Faculty of Arts and the Faculty of Pure and Applied Science, a diversity of degree programmes to meet students' differing interests and career aspirations. These are described in detail near the back of the mini-calendar. Given the variety of choices it is of utmost importance to study all possibilities very carefully and to obtain advice on the programmes offered. Where to go for help The Department's faculty and staff members will be pleased to offer you their assistance. Any questions concerning your programme or the enrolment in or dropping of courses should be directed first to the staff members in the Departmental Undergraduate Programme Offices. Arts and Science students may contact Ms. Janice Grant or Ms. Angela De Gasperis in N502 Ross (736-5902), Monday - Friday 10:30 am - 12:00 noon and 1:30 - 3:30 pm (but 1:30 - 3:00 pm in July and August); Science students may also contact Ms. Gillian Moore in 227 Petrie (736-5248), Monday - Friday 8:30 am - 4:30 pm. Should you need further advice on academic matters, please ask for an appointment, through one of the Undergraduate Office staff, with one of the Undergraduate Programme Directors: Professor M. Abramson (Mathematics, Mathematics for Commerce) Professor M. Muldoon (Applied Mathematics) Professor P. Peskun (Statistics) Appointments with faculty members may be made through the Department's main office in N520 Ross (736-5250) or the Undergraduate Programme Office in 227 Petrie (736-5248). Please feel free to direct appropriate concerns also to me. Appointments can be ma de with the Secretary to the Chair in N522 Ross (ext. 22555). You will find that your course instructors and teaching assistants are eager to help when you encounter a problem in a course. If they can't resolve the problem you can approach one of the Undergraduate Programme Directors. Goals You may find that a variety of teaching methods are used in your mathematics and statistics courses. But whatever methods may be used, faculty members have some common goals. They want to help you. - learn the basic materials of the course and its application, - acquire "critical thinking skill" through problem solving, - pursue careers in areas where a sound understanding of mathematics or statistics is fundamental, - read mathematical literature with understanding and enjoyment, - develop the ability and desire to pursue knowledge independently, - understand the power and elegance of abstract reasoning, - appreciate the role of mathematics in human culture Prizes and awards The Department offers several attractive prizes and awards for outstanding achievements in mathematics and statistics courses. The Chair's Honour Roll was introduced in 1989-90 and is displayed in the halls of the Department. It shows the names of students with high grade point average over all Departmental courses taken in the year of the award (at least two full-course equivalents need to be taken, exclusive of courses with second digit 5). This year, a g.p.a. of at least 7.5 is required for students who take the equivalent of a least three full-courses in the Department, and 8.0 for those who take two or two and a half courses. Students on the Roll received a certificate and a copy of the Roll. The best student in each of the year-levels 2, 3, and 4 in a Departmental programme is selected by a Departmental Committee. Their names will be displayed permanently, as winners of the Irvine R. Pounder Award. Professor Pounder was one of the two founding members of the Department , and the award was established by the Department in 1990-91 on the occasion of the hundredth anniversary of his birth. The two Alice Turner Awards of $400 each, donated by Professor Alice W. Turner, the other founding member, and her friends, are awarded to outstanding Faculty of Arts majors in a Departmental degree programme, one to a third-year ordinary-degree candidate, and one to a fourth-year honours-degree or combined honours-degree candidate. The Moshe Shimrat Prizes are awarded from a fund established in memory of Dr. Moshe Shimrat, a former faculty member, by his family and friends. The fund is used to make awards to students in university and secondary school for interest and demonstrated ability in mathematical problem-solving. The G. R. Wallace Scholarship is named in honour of the late G. R. Wallace, who was Senior Vice-President and Chief Actuary of the Zurich Life Insurance Company at the time of his death, and is donated by his friends and family. This $1500 scholarship is awarded annually to an outstanding student in an honours programme in the Department of Mathematics and Statistics who has demonstrated an interest in pursuing an actuarial career. (The Department may decide not to give out all prizes and awards in some years.) Mathematics contests There are two international mathematics contests open to undergraduate students. One, called the Putnam Examination, involves attempting to solve a number of challenging mathematics problems during an all-day examination late in the fall term. The other, called The Mathematical Contest in Modelling, involves being on a team of students who have a weekend to develop a mathematical model for some applied problem. In both cases, practice sessions will be held under the guidance of a member of the faculty. Students who participate in the practice sessions and the examinations find the examinations to be hard but enjoyable. They get to work on the problems for the challenge without having to think about grades. Announcements about these contests will be made in classes at the appropriate times. We invite you to test your skills. I wish you success in your studies but above all I wish for you that you will share the excitement and enthusiasm that my colleagues feel for their subject. George L. O'Brien Chair of the Department
General Information The main York calendar will answer many questions that are not addressed in this booklet. Please remember in particular that the main calendar contains the "official", legally binding statements of all university and faculty regulations. Choice of courses. A student should take care to enrol in the mathematics courses most appropriate to her or his interests, needs, and background. In many cases, courses with similar titles may be intended for widely different audiences. Students should be guided by the information given in this booklet and should consult an advisor in case of doubt. When selecting courses, please note the following: 1. A student choosing university-level mathematics courses for the first time should consider speaking to either an advisor (either at the Advising Centre (Arts), the Office of Academic Services (Science), or the Department's Undergraduate Office) or a Department faculty member. 2. MATH1510.06 is intended for students who have a weak mathematical background, even those who may have one or more OACs in mathematics (or equivalents). MATH1510.06 can serve as preparation for MATH1500.03 and from there entrance to further calculus courses. 3. Note on calculus courses for first-year students. a) BBA students who wish to take only a minimum amount of mathematics should take both MATH1530.03 and MATH1540.03, or MATH1550.06. The prerequisite for these courses is MATH1500.03 or OAC Calculus or equivalent. b) Science students (particularly those majoring in Biology, Geography, Kinesiology and Health Science or Psychology) who do not require other specific calculus courses to satisfy degree requirements or as prerequisites for higher-level courses, may take SC/MATH1505.06 to satisfy the Faculty of Pure and Applied Science 1000-level mathematics requirement. Other students should be guided by paragraphs (c) and (d) below. c) A student with at least one OAC in mathematics or equivalent, but without previous calculus, must begin the study of calculus with MATH1500.03. d) A student with OAC Calculus or equivalent can begin with MATH1000.03 or MATH1013.03 or MATH1300.03 and then take MATH1010.03 or MATH1014.03 or MATH1310.03. Degree credit exclusions. Specific regulations governing "degree credit exclusions" appear in the York calendar. An exclusion occurs when two courses have overlapping material. As a general rule, you may not take both for degree credit. Department minicalendars do not contain all degree credit exclusions; when in doubt consult a departmental advisor. Club Infinity. This club is a student-run organization committed to providing visibility and a voice for mathematics and statistics students. It organizes and sponsors different activities at York which are aimed to help math and stats students in dealing with their studies. Copies of old math exams are also available through the club. The office of Club Infinity is located in S597 Ross. Please come in and get involved! WWW Department's Home Page. The Department of Mathematics and Statistics has general Undergraduate and Graduate information available on-line on the World Wide Web. In addition, the course descriptions in this minicalendar are also available on the web. Our internet WWW address is: "http://www.math.yorku.ca". Comments and/or questions can be e-mailed to webmaster@mathstat.yorku.ca. Problems The Faculty and Staff at York want to make all students feel comfortable while at York. If students have any problems they may wish to speak to the undergraduate coordinator, Professor Morton Abramson (736-5250). Of course, students are also encouraged to discuss with their instructors any difficulties they may have.
Information for Majors Degrees offered. The Department of Mathematics and Statistics offers degree programmes in four major subjects: I. Applied Mathematics (BA or BSc) II. Mathematics (BA or Bsc) III. Mathematics for Commerce (BA) IV. Statistics (BA or BSc) The degree programmes in each major are described in checklists near the back of this mini-calendar. A student should choose one of these majors based on interest and employment goals; but it is possible to change major provided the requirements of the desired major can be met. Course numbering. MATH-courses with second digit 5 _cannot_ be used to satisfy major or minor degree requirements in this Department, except in the Mathematics for Commerce programmes and in other programmes where specifically noted. Second digit 0 usually indicates that a course is required in an Honours programme. With the exception of MATH 1530.03, MATH courses with third digit 3 involve statistics. "In-department" credits. A student must complete a minimum number of credits within the (AS/SC) Department of Mathematics and Statistics. Those Atkinson courses which are cross-listed as AS/SC/MATH courses will count as In-department. The minimum required in-department credit are: for Ordinary Major or Honours Minor, 18; Honours or Double Honours Major (Arts), 24 (but 30 for Honours Mathematics for Commerce); Combined Honours (Science), 21; Specialized Honours, 30. (In Mathematics for Commerce degrees COSC1520.03/1530.03 is not counted as an "in-department" course.) Upper-level courses. In choosing courses students should bear in mind the prerequisites for courses which they may wish to take in later years. Also, students are cautioned that some courses may be given only in alternate years. The "Special topics" and "Topics in" courses (MATH4100.03, MATH4110.03, MATH4120.03, MATH4130.03, MATH4200.03, etc.) may be offered in both terms and may be repeated with different topics. The prerequisites for each course are usually the 3000-level course(s) in the appropriate subject area. In registrations for these courses a letter immediately preceding the decimal point in the course number will indicate the section of the course the student is taking. The same course letter may not be used again for credit.
Programmes Applied Mathematics The Applied Mathematics Office, Department of Mathematics and Statistics is located in Room 227 of the Petrie Science Building, telephone (416-736-5248). The Applied Mathematics Programme aims to give students a solid base of knowledge of mathematics which have important applications in fields such as computer science, physics, earth and atmospheric science, chemistry, biology, psychology and also in economics and business. Our graduates have gone into a variety of careers including business, industry and government as well as teaching. In particular, many have found jobs in various aspects of fields relating to computing. Some students have continued their studies in graduate schools of mathematics, physics or other areas of application. Professional qualifications are obtainable by the award of a diploma in Operations Research or by writing the examinations of the Society of Actuaries. There are potential jobs for our students wherever mathematics is employed. Students in Applied Mathematics in the Faculty of Pure and Applied Science may pursue a course of study leading to either an Ordinary degree (usually three years) or an Honours degree (usually four years). Students may combine their studies in Applied Mathematics with another subject such as Physics, Earth and Atmospheric Science, Biology, or Computer Science and thereby graduate with a Combined Honours degree in two subjects. Applied Mathematics students interested in Economics, Psychology, or another subject offered by the Faculty of Arts, may pursue a combined programme by selecting a Double Major or Major-Minor Honours programme in the Faculty of Arts. For example, an Economics-Applied Mathematics Major-Minor degree would be a very natural combination. All of our students are given ample opportunity to take electives in other areas of interest, such as business administration. Applied Mathematics majors take a common core of six full courses: two courses in Calculus and Differential Equations, one course in Linear Algebra, or laboratory course in Symbolic Computing (Maple), one course in Numerical Analysis, and a half-course in each of a Programming Language and in Probability and Statistics. There is a wide choice of elective courses in Applied Mathematics including Graph Theory, Operations Research, Partial Differential Equations, Advanced Numerical Analysis, and Complex Variables. In addition, students can select a number of optional courses from outside the programme. Courses in the programme stress applications of mathematics and computing to the solution of problems arising in many facets of science, engineering and commerce. Some possible areas of concentration are: Numerical Analysis; Discrete Applied Math/Operations Research; Statistical Applied Mathematics. All students entering Applied Mathematics are carefully advised concerning their course of study by a member of the programme. The instructors in Applied Mathematics courses are available throughout the year for additional advice and help with specific course-related problems. If you wish further information, please contact the Programme Director, Martin Muldoon (e-mail: muldoon@mathstat.yorku.ca), or the Secretary, Gillian Moore, at (416-736-5248). Mathematics The Honours Programmes in Mathematics (BA and BSc) are suitable for students who have a special fondness for mathematics. They provide an excellent background for many occupations demanding skills in mathematical reasoning and techniques. Those who wish to go on to graduate studies in mathematics should probably be in one of these programmes. An Honours programme in Mathematics tends to emphasize understanding of concepts, abstraction and reasoning; these then become the tools, language and environment in which problems are solved ("proofs"). The majority of students who complete an Honours degree (with good grades) are routinely accepted (with financial support included!) into Graduate Schools across North America. For a career in Industry, Government, or Business taking mathematics in a combination with Computer Science, Statistics, or Economics makes for a very impressive curriculum vitae. A mathematician is known as one who has exceptional reasoning, critical thinking, and problem solving skills. These are the skills that you will develop but, it may surprise you to learn that most mathematicians do math because they love it. They also love to talk about it to their colleagues. Mathematics is one of the oldest academic disciplines. Yet, if you cultivate a passion for Mathematics, find some like minded classmates then you find that pursuing a degree in mathematics is a new, exciting adventure bringing you to the forefront of scientific discovery. The mathematics of the ancient Greeks will likely be, not only remembered, but vital, long after Greek literature is forgotten. The Ordinary Programme (BA and BSc) provides a three-year degree in mathematics that is much less demanding than the honours programme and is very flexible. It allows the student to select courses in a wide variety of pure and applied mathematical areas. It can also be part of a liberal arts education with a moderate emphasis on mathematics, for example, as a Minor of an Honours Major/Minor degree. Many students find that they are not yet ready to begin an Honours programme in Mathematics in first year The department has introduced the course MATH3110.03 for this reason. A student who completes the regular Calculus sequence MATH1300.03/1310.03/2310.03 may take MATH3110.03 and use these courses as a substitute for the Honours sequence MATH1000.03/1010.03/2010.03. There is a similar arrangement to allow a substitution for the first course in Algebra (MATH2021.03/2022.03). However a student considering an Honours degree in Mathematics should seriously consider the Honours courses since they are designed for those with a genuine interest in Mathematics. In addition, students who wish to switch back to the ordinary stream will be accommodated to the extent that the Registrar's Office will allow. Mathematics and Education Many students choose to co-register in the Faculty of Education and obtain a BA or BSc and a BEd with a concentration in mathematics. The Department is very keen to be of help to students interested in Mathematics Education or for concurrent education students. A student wishing to have Mathematics as a teaching area must complete the following course requirements. MATH1000.03/1010.03 or MATH1300.03/1310.03 or approved equivalent; MATH1131.03/1132.03 or MATH 2560.03/2570.0 3; MATH 2221.03/2222.03 or MATH 1025.03/2222.03; and a proof-based course such as MATH3020.06 or MATH3050.06 or MATH3140.06 (other upper level courses may be acceptable, consult with an Education Mathematics advisor). Statistics Statistics is an interdisciplinary field providing the foundations and techniques to collect, analyze and present information in an effective and efficient manner. Through its applications in almost every branch of modern professional life and research, statistics is a fast-growing discipline which provides as statistician with a variety of career opportunities. A programme in statistics is an exploration of the nature of measurement, relationships amongst measured variables, chance variation, probability, uncertainty, inductive logic and inference. The Honours and Ordinary BA and BSc programmes in Statistics provide both the mathematical foundations and the methods needed in applications. They also provide exposure to a variety of computing environments, an essential asset for nearly all careers today. Statistics combines naturally with studies in the life, physical or social sciences, economics, administrative studies or environmental studies. The Honours programmes also provide excellent preparation for subsequent graduate study in Statistics. Mathematics for Commerce Mathematics for Commerce is an ideal environment for students who wish to obtain a strong background in the type of Mathematics which can be applied in a business oriented career. Courses such as Accounting, Computer Science, Mathematics for Economists, Mathematics of Investment and Actuarial Science, Mathematics with Management Applications, Operations Research and Statistics, provide the student with the necessary mathematical skills, techniques and confidence to succeed in a very demanding business world. Graduates of this programme go on to various careers in business, industry, government, schools, colleges and universities. They became actuaries, investment managers, consultants, analysts, or statisticians. Quite often they become executives, senior managers and leaders in their chosen professions. Examples of activities in which they may be involved are: optimization problems, project management, inventory control, forecasting, analyzing data, investigating patterns and trends, creating mathematical models, evaluating pension funds, and determining premiums for life insurance policies. Of course, many of the programme's students also pursue graduate degrees in areas such as Business Administration, Communications, Economics, Education, Environmental Studies, and Law. There are two basic Mathematics for Commerce programmes. These programmes are only available through the Faculty of Arts. (a) The Ordinary B.A. Programme in Mathematics for Commerce: It is usually completed in 3 years and requires a total of 90 credits (15 full courses), subject to Faculty and Department of Mathematics requirements listed in the end pages. (b) The Honours B.A. Programme in Mathematics for Commerce: It is usually completed in 4 years and requires a total of 120 credits (20 full courses), subject to Faculty and Department of Mathematics requirements listed in the end pages. The Honours degree is split into the streams: (b1) the General Stream (b2) the Actuarial Stream (b3) the Operations Research Stream (b1) The General Stream is a new innovation which is designed for students who have followed the requirements of the Ordinary Mathematics for Commerce and have achieved sufficiently high grades that they have Honours Standing. After having fulfilled the requirements of the Ordinary Mathematics for Commerce Programme with honours standing, students can take fourth-year advanced courses that give extra depth in areas such as Applied Statistics, Applied Optimization and Accounting. (b2) Actuarial Stream: An Actuary is a professional concerned with the design and administration of insurance programmes, pension plans, government welfare plans, and similar financial programmes. The main responsibility of actuaries is to ensure that these programmes operate on a sound financial basis. To do this they use many areas of mathematics and statistics as well as general principles of economic and finance. In North America the standard way to become an Actuary is to pass the examinations set and administered by the Society of actuaries. No university courses can be accepted in place of these examinations, but university courses can do a great deal to prepare the student for them. For additional information, please contact Professor Morton Abramson at 736-5250. (b3) Operations Research is the scientific study of any problem relating to optimal management of a system. The system could be, for example, a shipping operation needing efficient shipping schedules, a company selecting a product mix to maximize profits, or a town trying to locate its fire stations so that maximum protection is available at minimum cost. A common element is the optimization (that is maximization or minimization) of some measurable criterion of the system's performance, subject to constraints under which the system operates. The programmes of study at York can provide the student with the diverse background needed to prepare for work in operations research. The initials CORS stand for the Canadian Operational Research Society. This Society offers a diploma to students who complete a certain selection of courses. At York it is possible to earn a CORS diploma and a York Honours degree simultaneously. See the next section for a more detailed description and for additional information, please contact Professor Neal Madras at 736-5250.
Career Information Co-registration in Education A student seeking a B.Ed. degree pursues this degree concurrently with her or his Arts or Science degree, beginning normally in the second year at York. For further information contact the Faculty of Education, N801R, phone 726-5001. Graduate Studies York offers several graduate programmes in mathematics and statistics; for details enquire at the Graduate Programme Office (N519 Ross, 736-5250 ext. 33974). Students who may wish to pursue graduate work at York or elsewhere should choose upper-level undergraduate courses with care. Advice on this can be sought from faculty members. Actuarial Mathematics For a student seeking a career as an actuary, and/or wishing to pursue the self-study courses administered by the Society of Actuaries, the Honours B.A. Programme in Mathematics for Commerce will be the best preparation. Further information can be found in a pamphlet available in N501R. Operations Research Diploma Operations Research (OR) deals with making the 'best' decision when confronted with numerous choices as well as a variety of constraints in a large scale problem. Some examples of typical problems would be minimizing operating costs in a large hospital while maintaining quality service to patients, finding the shortest route for a delivery truck which has a number of stops, or scheduling jobs on a large construction project to finish in the shortest possible time. The problems are represented by mathematical models and various algorithms are used to find the optimal solution. Because of the magnitude of these problems, computers are almost always needed to execute the algorithm. To encourage students to study OR and seek employment in this field, the Canadian Operational Research Society (CORS) offers a Diploma in Operational Research to those students who have completed a prescribed set of courses. To get some idea of the employment opportunities for someone with a CORS diploma, it is worthwhile to look through the CORS membership list. The nearly 1000 members of CORS are mainly from Canada and there are members from every Canadian province. There are also CORS members from 32 other countries. The CORS members work at 257 companies, institutions, and agencies of which 58 are colleges or universities. (Some of the large groups of CORS members in Canada are at various universities.) Outside of academia, some notable groups are at the Department of National Defence (20), CNR (11), Air Canada (8), Bell Canada (7) and Transport Canada (7). The remaining companies and institutions include government agencies, hydro utilities, oil and gas companies, transportation authorities, police departments, steel companies, forestry and agricultural firms and agencies, banks and trust companies, chemical suppliers, food companies, lottery agencies, and, of course, consulting firms. In the Department of Mathematics and Statistics one can satisfy the requirements for the CORS diploma while completing an honours degree in Applied Mathematics, Mathematics for Commerce, or Statistics. The courses required for the Diploma (which are in addition to the required courses for the degree) are listed below for the various programmes. Students are also encouraged to become student members of CORS and participate in their meetings. This is a very good way in which to meet practitioners in the field of OR and find out more about potential job opportunities. A membership in CORS listed on your resume will indicate to future employers your seriousness about a career in this field. Students who have completed the required courses for the Diploma should arrange to have a transcript sent to Professor Neal Madras who will notify CORS to grant the diploma. For further information and membership forms for CORS, please contact Professor Madras in N623 Ross. Course requirements for the CORS Diploma: (i) Applied Mathematics: Specialized honours or honour major students who wish to obtain the CORS diploma must choose the following courses as part of their degree programme. MATH3260.03; MATH3170.06; MATH4170.06 at least two of MATH3030.03; MATH3131.03; MATH3132.03; MATH3033.03 or MATH3330.03; MATH 3034.03 or MATH 3230.03; MATH4430.03; MATH4830.03; at least two of ECON1000.03; ECON1010.03; ECON3580.03 or MATH4501.03; ECON3590.03 or MATH4502.03; at least one of MGTS4000.03; MGTS4200.03; MGTS4500.03; MGTS4550.03; The following are also recommended for consideration as elective courses in students' programmes of study: MGTS4710.03; MGTS 4720.03. (ii) Mathematics for Commerce: Mathematics for Commerce students who wish to obtain the CORS Diploma must satisfy the following: all the requirements for the Operations Research stream in the Honours programme. (Students in the Actuarial stream will satisfy these requirements if they also take MATH4170.06.) at least one of MGTS4000.03; MGTS4200.03; MGTS4500.03; MGTS4550.03; either ECON1000.03/1010.03 or MATH4501.03/4502.03. (iii) Statistics: Specialized honours or honours major students who wish to obtain the CORS Diploma must choose the following courses as pert of their degree programme: MATH3170.06; MATH4170.06; COSC1520.03; COSC1530.03; at least one of MGTS4000.03; MGTS4200.03; MGTS4500.03; MGTS4550.03; at least two of ECON1000.03; ECON1010.03; ECON3580.03 or MATH4501.03; ECON3590.03 or MATH4502.03. Mathematics for Commerce Some graduates from Mathematics for Commerce will choose to go on to acquire a Master of Business Administration (MBA) degree. Others might consider programmes like those in the School of Legal and Public Administration at Seneca College. An example is the eight-month programme in Real Property Administration which involves substantial amounts of applied statistics, math of investment and computer usage. Another example is the one-year Mortgage Broker Post-Diploma Certificate Programme. Both of these programmes seek students with mathematical knowledge and ability. At present (1996), job opportunities after completing these programmes are excellent. Science, Technology, Culture and Society This is a new programme in the Faculty of Arts, which can be one component of an Honours Double Major leading to a B.A. The co-major can be any of several subjects, including Mathematics. Students of mathematics who co-major in the Science, Technology, Culture and Society programme will be exposed to literature exploring the cultural, intellectual and social context of mathematical ideas and their link to scientific developments. The programme offers an interdisciplinary study of science and society through the ages. Some courses treat topics drawn from the history and philosophy of specific sciences, while others address such topics as science and gender, and technology and values. Students are encouraged to draw connections across traditional disciplinary boundaries and to question conventional wisdom about scientific and technological progress. They will also develop a facility in, and appreciation for, the aims and methods of both the arts and sciences. Graduates o! f this programme should be well equipped for further studies in law, medicine, education, journalism, and environmental policy. For more information, consult the STCS mini- calendar, available at 261 Vanier College, or contact the programme secretary, Ms. Sue Parsram, 261 Vanier College, 726-5910, ext. 77389. Atkinson "Equivalent Courses" The Department of Computer Science and Mathematics at Atkinson College offers mathematics courses at night and during the summer. Certain courses, especially 3000-level and 4000-level, are not offered every year. Many Atkinson courses are considered equivalent (or are exemptions) to Faculty of Arts/Science courses and can be taken in place of the latter for degree credit. All Atkinson Math courses which have the same course number as a course offered by the Department are equivalent to the corresponding Arts/Science course. The following is a list of course equivalences where the numbers differ. AK/MATH1409.03C MATH1500.03 AK/MATH1710.06 MATH1510.06 AK/ECON2560.03/2570.03 MATH1530.03/1540.03 All Atkinson courses which are equivalent to an SC course count as Science credits. However until this year those that are equivalent to an Arts course have not counted as AS credit. The information is not available at this time whether some of the Atkinson courses will count as "In-faculty" courses in the Faculty of Arts. You should assume that they do NOT count as in-faculty and ask at the Undergraduate Office for the most up to date information.
1000 LEVEL COURSES AS/SC/MATH1000.03 F Differential Calculus (Honours Version) This course covers material similar to that in MATH 1300.03. The emphasis, however, is on covering a smaller variety of topics more carefully, and on developing the student's ability to think and write clearly, logically, and precisely, and to read a mathematical text with understanding. One goal of the course is learning how to write proofs. (Of course, we will not spend all our time proving things!) MATH1000 should be taken by all students planning an Honours degree in Mathematics or Statistics. The policy of the Mathematics Department is to be generous in the grading of MATH 1000 and MATH 1010, to encourage interested students to take these courses. Therefore, although the honours courses are more "theoretical", students who are willing to put a serious effort into them should find it neither easier nor harder to get a high mark (A+, A, B+) in MATH 1000/1010 than to get the same mark in MATH 1300/1310. The text will be announced later. The final grade may be based on homework/quizzes (15%), and class tests and a final examination, weighted so as to favour each student's best results. Prerequisite: AS/SC/MATH 1500.03 or OAC Calculus or equivalent. Exclusions: AS/SC/MATH1013.03, AS/SC/MATH1300.03, SC/MATH 1505.06, AS/MATH 1530.03, AS/MATH 1550.06, AS/ECON 1530.03. Course Coordinator: R. Ganong AS/SC/MATH 1010.03 W Integral Calculus (Honours Version) This course covers material similar to that in MATH1310.03. It bears much the same relationship to MATH1310.03 as MATH 1000.03 does to MATH1300.03. See the description of MATH1000.03 for comments and grading policy. The text will be announced later. The final grade may be determined just as it was in MATH1000.03F. Prerequisite: AS/SC/MATH1000.03 or permission of the instructor. Exclusions: AS/SC/MATH1014.03, AS/SC/MATH 1310.03, SC/MATH1505.06. Coordinator: R. Ganong AS/SC/MATH1013.03F Applied Calculus I The first half of this course deals with differentiation and the second half with integration. Topics include derivatives of algebraic and transcendental functions, indefinite integrals, techniques of integration, the definite integral and its interpretation as an area. Three lecture hours, one tutorial hour. The text will be Varberg, D. and Purcell, E., Calculus with Analytic Geometry, Prentice-Hall. Prerequisites: AS/SC/MATH1500.03 or OAC Calculus. Exclusions: AS/SC/MATH1000.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, AS/ECON1530.03. Coordinator: Peter Taylor, Fall; Anthony Szeto, Winter AS/SC/MATH1014.03W Applied Calculus II Applications of differential and integral calculus (e.g. maxima and minima, areas, volumes of revolution, etc.), indeterminate forms, improper integrals, Taylor series, simple ordinary differential equations and an introduction to multivariate calculus. Three lecture hours, one tutorial hour. The text will be the same as for MATH1013.03. Prerequisites: One of AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SCMATH1300.03, or, for non-Science students only, one of AS/MATH1530.03 and AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03 and AS/ECON1540.03. Exclusions: AS/SC/MATH1010.03, AS/SC/MATH1310.03, SC/MATH1505.06. Coordinator: Peter Taylor AS/SC/MATH1025.03W Applied Linear Algebra Topics include polar coordinates in R3, general matrix algebra, determinants, vector space concepts for Rn (e.g. linear dependence and independence, basis, dimension, linear transformations, an introduction to eigenvalues and eigenvectors). The text will be S. F. Grossman, Elementary Linear Algebra. [If you plan to take MATH 2222.03, you may want to use instead Anton-Rorres, Elementary Linear Algebra, Applications Version (7th ed).] Prerequisites: AS/SC/MATH1525.03 or OAC Algebra and Geometry. Exclusions: AS/SC/MATH2021.03, AS/SC/MATH2220.06, AS/SC/MATH2221.03. Coordinator: Y. Medvedev AS/SC/MATH1090.03 Introduction to Sets and Logic (formerly MATH1120.03) This course is an introduction to sets, functions, relations, logic, induction and proof techniques, and may include a smattering of basic combinatorics and graph theory. It should be of value to mathematics or computer science majors, and may also appeal to students wanting to apply mathematics to the social and management sciences. The text has not yet been chosen. The final grade will be based on class tests and a final examination (and possibly assignments). Prerequisite: One OAC in mathematics or equivalent. Exclusions: AS/SC/MATH1120.03. This course is not open to students who have taken or are taking any mathematics course (with second digit different from 5) at 3000 or higher level. Coordinator: T. MacHenry, Fall; W. Tholen, Winter AS/SC/MATH 1131.03F Introduction to Statistics I Testing a new drug, evaluating the effects of free trade, making sound investment decisions, predicting who will win the World Series, are all activities that have in common the need to make sense out of ambiguous data. The modern discipline of statistics serves as a guide to scientists, policy makers and business managers who need to draw inferences or make decisions on the basis of uncertain information. This pair of courses provides an introduction to the concepts of statistics with an emphasis on developing a critical attitude towards the use and misuse of statistics in science and business. Statistical techniques will include confidence intervals for means or comparing two means, contingency tables, simple regression and basic analysis of variance. It is recommended that students have at least one OAC in mathematics but the mathematical level of the course will be quite elementary. Although students will be making some use of the computer to calculate statistics, to create statistical plots, and to obtain a better appreciation of statistical concepts no previous experience in computing is required. Students will receive in class all the necessary instruction about how to use the statistical computer package Minitab. Although this course is recommended for students who wish to major in statistics, the concepts are broadly applicable and it should be interesting to students who do not plan to specialize in statistics. The text will be D. S. Moore and G. P. McCabe, Introduction to the Practice of Statistics, 2nd ed. (W.H. Freeman). The final grade may be based (in each term) on assignments and/or quizzes, class tests and a final examination. Prerequisites: At least one OAC in mathematics is recommended. Exclusions: AS/SC/MATH/2560.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON2500.03, AS/SC/GEOG2420.03, AS/SCPHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06.} Coordinator: H. Massam AS/SC/MATH1132.03W Introduction to Statistics II See above description (AS/SC/MATH1131.03). Prerequisite: AS/SC/MATH1131.03. Exclusions: AS/SC/MATH2570.03, SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON3210.03, AS/ECON3500.03, AS/SC/GEOG2420.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2022.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06.) Coordinator: S. R. Chamberlin AS/SC/MATH1300.03 Differential Calculus with Applications Topics include functions, limits, continuity, differentiation, mean-value theorem, curve sketching, maxima and minima, Riemann integration, antiderivatives, fundamental theorem of calculus. The text will be Calculus: One and several variables, Salas & Hille, 7th Edition, Wiley. The final grade may be based on assignments, quizzes, class tests and a final examination worth at least 40%. Prerequisites: AS/SC/MATH1500.03 or OAC Calculus or equivalent. Exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1550.06, AS/ECON1530.03. Coordinator: S. Kochman, Fall; A. Dow, Winter AS/SC/MATH1310.03 Integral Calculus with Applications This is the second in a series of introductory calculus courses. It is designed to follow MATH1300.03. Topics include fundamental theorem of calculus, logarithmic and exponential functions, trigonometric functions, techniques of integration, applications of integration theory, l'H“pital's rule, infinite sequences and numerical series. The text will be Calculus: One and several variables, Salas & Hille, 7th edition, Wiley. Exclusions: MATH1010.03, MATH1014.03. This course will be offered in both terms. The final grade may be based on assignments, quizzes, class tests, and a final examination worth at least 40%. Prerequisites: One of AS/SCMATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, or, for non-Science students only, one of AS/MATH1530.03 and AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03 and AS/ECON1540.03. Exclusions: AS/SC/MATH1010.03, AS/SC/MATH1014.03, SC/MATH1505.06. Coordinator: F. Vinette, Fall; S. Kochman, Winter AS/SC/MATH1500.03F Introduction to Calculus This course is intended for students who have not taken OAC Calculus or equivalent and is intended to prepare them for courses which have "OAC Calculus or equivalent" as a prerequisite. Calculus is the part of mathematics which deals with the concept of change. This makes it at once both difficult and useful. In this introductory course we will deal with functions of one variable and their derivatives and integrals. We will show how the derivative is useful in defining (and finding the equations of) tangents to curves, in problems concerning velocity, and in optimization (finding the value of the variable for which a function is largest or smallest). We will also study the connection between derivatives and integrals and describe the application of integrals to finding areas between curves. Fundamental to all of these notions is that of limiting processes. Topics to be discussed include: limits, derivatives, tangents, rate of change, maxima and minima, curve sketching, trigonometric functions, logarithmic and exponential functions, antiderivatives, fundamental theorem of calculus, areas. The text will be announced later. The final grade will be based on assignments, tests, and a final examination (40%). Prerequisites: AS/SC/MATH1510.06 or AS/MATH1520.06 or equivalent. This course may be taken at the same time as the second half of AS/SC/MATH1510.06. Exclusions: May not be taken by any student who has taken or is currently taking another university course in calculus. Coordinator: A. Pietrowski SC/MATH1505.06 Mathematics for the Life and Social Sciences A presentation of the elements of single variable calculus, linear algebra, and probability and statistics. Topics include derivatives of algebraic and transcendental functions with applications to maxima and minima and rates of growth, techniques of integration, applications of the integral, simple ordinary differential equations, vectors, matrices, systems of linear equations, sample spaces, discrete and continuous probability distributions. This course is designed to provide a comprehensive mathematical background for students of the biological sciences. Emphasis is placed on basic mathematical skills and their applications to the life sciences. Three lecture hours, one tutorial hour. The text will be announced later. Prerequisite: At least one OAC in mathematics or AS/SC/MATH1510.06 Exclusions: AS/SC/MATH1000.03, AS/SC/MATH1010.03, AS/SC/MATH1013.03, AS/SC/MATH1014.03, AS/SC/MATH1300.03, AS/SC/MATH1310.03, AS/MATH1530.03, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1530.03, AS/ECON1540.03. Coordinator: N. Purzitsky AS/SC/MATH1510.06 Fundamentals of Mathematics The course is designed for students whose mathematical background is weak and who wish to take further mathematics courses. Completion of this course with a good grade should provide students with suitable preparation for any level of introductory university calculus course. The goal of the course is to promote understanding rather than memorization. Therefore the concepts and ideas underlying the algebraic manipulations will be emphasized. The following topics will be included: algebraic identities, quadratic and some polynomial equations, inequalities, systems of linear and quadratic equations; analytic geometry; and functions: algebraic, exponential, logarithmic, and trigonometric. The textbook for the course has not been chosen yet. The final grade will be based on quizzes and/or tests and/or a December mid-year examination and a final examination held during the official examination period at the end of the term. Exclusions: AS/MATH1520.06. May not be taken by any student who has taken or is currently taking another university course in mathematics or statistics except for AS/SC/MATH1500.03 and AS/SC/MATH1525.03. Coordinator: J. M. N. Brown AS/MATH 1530.03 Introductory Mathematics for Economists I The pair MATH1530.03 and MATH1540.03 are designed to give the student an introduction to mathematics sufficient for a thorough understanding of modern textbooks in economic theory. The emphasis is on the acquisition of tools for later use rather than on a rigorous development of the mathematics involved. These courses (or MATH1300.03/1310.03, plus MATH2221.03/MATH2222.03) are required for specialized honours students in economics and are recommended for honours and ordinary students in economics. They are accepted by Administrative Studies as prerequisites. Students with strong interest or ability in mathematics should consider registering in MATH1300.03 and MATH1310.03. MATH1530.03 is an introduction to differential and integral calculus. Emphasis will be not on theoretical proofs but on an understanding of concepts and of techniques for applications. Topics will include single-variable differentiation, limits, continuity, series, exponential and logarithmic functions, single variable optimization, and integration. Applications to problems in economics involving supply and demand functions, maximization of profits, elasticity of demand and consumers' surplus will be considered. The text last year was, Mathematics for Economic Analysis, by Sydsaeter and Hammond, together with selected exercises from, Introductory Mathematical Analysis by Haeussler and Paul. Both of these texts are published by Prentice-Hall. Last year a "package" consisting of the first text together with the selected exercises from the second text was available from the York bookstore. It is anticipated that the same texts will be used this year although students should check with their section instructor at the start of classes. Note carefully that a student taking MATH1530.03 must have taken or be taking ECON1000.03 or ECON1010.03. The final grade may be based on term tests and/or assignments and a final examination. Instructors will announce details in class. Prerequisites: AS/SC/MATH1500.03 or OAC Calculus or equivalent. Corequisites: AS/ECON1000.03 or AS/ECON1010.03. Exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1550.06, AS/ECON1530.03. Coordinators: M. Abramson, Mathematics Department P. Rilstone, Economics Department AS/MATH1540.03 Introductory Mathematics for Economists II This course deals with matrix algebra and functions of many variables in a way that will be of interest to students in economics and business. The emphasis will be on the acquisition of tools rather than on a rigorous development of the tools. Applications will include solutions of linear equations, maxima and minima of functions of several variables with and without constraints. This is a required course for specialized honours students in economics and is recommended for honours and ordinary economics students. It is acceptable, together with MATH1530.03 or ECON1530.03, for admission to the Faculty of Administrative Studies. The text is anticipated to be the same as that for MATH1530.03. A student taking MATH1540.03 must have passed MATH1530.03 or equivalent, and must have taken or be taking ECON1000.03 or ECON1010.03. This course cannot be taken by students who have taken or are taking MATH2021.03/2022.03 MATH2221.03/2222.03, AK/ECON2570.03, AK/MATH2220.06. The final grade may be based on class tests and/or assignments and a final examination. Prerequisites: One of AS/MATH1530.03, AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, AS/ECON1530.03. Corequisites: AS/ECON1000.03 or AS/ECON1010.03. Exclusions: SC/MATH1505.06, AS/MATH1550.06, AS/ECON1540.03. May not be taken by any student who has taken or is taking AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/MATH2021.03, AS/SC/MATH2221.03, or equivalent. Coordinators: M. Abramson, Mathematics Department P. Rilstone, Economics Department AS/MATH1550.06 Mathematics with Management Applications This course is designed primarily for students interested in business programmes. It satisfies a requirement for entry to the B.B.A programme in the School of Business. It also satisfies a requirement in the three-year B.A. Ordinary programme, or the four-year Honours General Stream, in Mathematics for Commerce. One theme of the course is optimization -- how to maximize or minimize a function subject to certain constraints. Most of the course is a discussion of calculus and its applications; matrix theory and its applications are also discussed. The emphasis will be not on theory but rather on techniques and on applications to business and management problems. The content of this course is very similar to that of the two half-courses MATH1530.03 and MATH1540.03. These latter two half-courses will also satisfy the requirements for the programmes mentioned above, and they are suitable for those who plan to major in economics. Those who wish a stronger foundation in calculus or who wish to major in any Mathematics programme other than Mathematics for Commerce, Ordinary or Honours General Stream, should choose calculus courses without the second digit 5. The text has not yet been chosen. In 1995-96 it was Introductory Mathematical Analysis for business, economics and the life and social sciences; Seventh Edition; by E. F. Haeussler, Jr. and R. S. Paul; Prentice Hall 1993. The method for determining the final grade has not yet been decided. In 1995-96 it was: Four to six hours of term testing (60%); Final exam, three hours, covering the whole course and common to all sections (40%). Prerequisites: AS/SC/MATH1500.03 (may also be taken as a first-term corequisite) or OAC Calculus or equivalent. Exclusions: AS/SC/MATH1000.03, AS/SC/MATH1013.03, AS/SC/MATH1300.03, SC/MATH1505.06, AS/MATH1530.03, AS/MATH1540.03, AS/ECON1530.03, AS/ECON1540.03. This course may not be taken by any student who has taken or is taking AS/SC/MATH1025.03 or AS/SC/MATH2000.06 or AS/SC/MATH2021.03 or AS/SC/MATH2221.03 or equivalent. Coordinator: P. Olin AS/SC/MATH1580.03F The Nature of Mathematics I A main objective of this course is to provide opportunities for students to develop a positive attitude towards mathematics and to achieve success in thinking mathematically. The course is intended primarily for students concurrently enrolled in the Primary/Junior or Junior/Intermediate programmes in the Faculty of Education. Prospective students should not be discouraged from taking this course either because their backgrounds in mathematics are incomplete or because past experiences have caused them to fear mathematics. The course will examine some of the areas of mathematics which are relevant to the Primary, Junior and Intermediate curriculum and will focus on the role of language and critical thinking in the construction of mathematical ideas and concepts. An investigative, exploratory approach will be encouraged. Students will work in small groups on selected problems and attention will be given to developing students' reading, writing and speaking skills in communicating mathematics. The final grade will be based on a combination of assignments and projects. The breakdown will be decided upon at the start of the course. IMPORTANT. In 1996-97, this course will form part of the Programme "Better Math for Kids and Teachers" sponsored by the Department of Mathematics and Statistics, the Faculty of Education and the Metro Cooperative. This Programme will involve both teacher candidates and practising teachers and encourage interaction between them. While it is possible to take the course without taking the Programme, the involvement in the Programme will require some departure from the standard timetable format. For example, it will be necessary to attend two all-day sessions in a summer institute on August 19-20. Alternate classes during the regular term will meet off-campus at a central North York location for two hours, and the remainder will be held on campus for three hours. Full details of the timetable can be obtained from the course coordinator. Exclusions: Not open to any student who has taken or is taking another university mathematics course unless permission of the course coordinator is obtained. Coordinator: Martin Muldoon AS/SC/MATH1590.03W The Nature of Mathematics II This course will continue in the spirit of MATH1580.03. Please note the important announcement contained in the description of that course. Students who have taken or are taking any other university level mathematics course, with the exception of MATH1580.03, may not enrol in this course without the permission of the course coordinator. Prerequisites: AS/SC/MATH1580.03 or permission of the course coordinator. Coordinator: Martin Muldoon
2000 LEVEL COURSES AS/SC/MATH2015.03F Applied Multivariate and Vector Calculus This course involves the differentiation and integration of scalar and vector functions of (up to) 3 independent variables, with applications. Topics include partial derivatives, Taylor series and extrema of multivariate functions; curves and surfaces in cartesian, cylindrical, and spherical polar coordinate systems; single, double, and triple integrals; grad, div, curl and laplacian operators; differential vector identities; line, surface, and volume integrals; Green's, Gauss' and Stokes' theorems. Text: Calculus and Analytic Geometry, D. Varberg and E. J. Purcell (5th or 6th Editions). Prerequisites: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03, or SC/MATH1505.06 plus permission of the Course Coordinator. Exclusions: AS/SC/MATH2010.03, AS/SC/MATH2310.03, AS/SC/MATH3010.03. Coordinator: R. P. McEachran AS/SC/MATH 2021.03F Linear Algebra I (Honours Version) Linear algebra is the study of vectors, matrices and linear transformations. These concepts are used in all areas of mathematics, in all branches of science and in the quantitative aspects of the social sciences. The content of this course is similar to that of MATH2221.03. This course, however, is more theoretical and covers additional topics in linear algebra and its applications. It therefore provides a solid background not only for courses in linear programming and statistics which use linear algebra but also for advanced theoretical mathematics courses such as abstract algebra and functional analysis. The course begins with concrete topics such as the solution of linear systems of equations by Gauss-Jordan reduction, matrices and determinants. Applications are made to graph theory, economics and polynomial interpolation. We then proceed to study the more abstract concepts of vector spaces, basis, dimension and inner products. This is a rigorous mathematics course in which all definitions and proofs are presented in class. In addition, all concepts will be illustrated with examples and reinforced through computational homework problems. Moreover, students are expected to learn to construct proofs as the course progresses. Theoretical homework problems will be assigned, graded and counted towards the final grade. Most exam questions, however, will be computational in nature. This is an honours course intended primarily for students intending to earn an honours degree in mathematics (other than Honours Mathematics for Commerce). However, all students who meet the prerequisites are welcome. The text has not yet been selected. The final mark will be based on two in-class tests (50%) and a final examination (50%). Prerequisites: As prerequisite, one of SC/MATH1505.06, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1540.03. Corequisites: AS/SC/MATH1000.03 or AS/SC/MATH1013.03 or AS/SC/MATH1300.03 or permission of the Course Coordinator. Exclusions: AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/MATH2221.03. Coordinator: S. O. Kochman AS/SC/MATH2022.03W Linear Algebra II (Honours Version) This course is a continuation of MATH2021.03. The content is similar to that of MATH2222.03 but is more theoretical and covers more topics and applications. We will study linear transformations and eigenvalues with applications to quadratic forms, Markov chains, least squares approximations and isometries. The high points of the course are the Cayley Hamilton Theorem and the orthogonal diagonalization of symmetric matrices. The text will be the same as for MATH2021.03. The final mark will be based on two in-class tests (50%) and a final examination (50%). Prerequisites: AS/SC/MATH2021.03 or permission of the course coordinator. Exclusions: AS/SC/MATH2000.06, AS/SC/MATH2222.03. Coordinator: S. O. Kochman AS/SC/MATH 2030.03W Elementary Probability (formerly part of MATH2030.06) This course provides an introduction to probability theory. It is designed for those students who do not want a "cookbook" approach to the subject, those who intend to take further courses in mathematical or applied probability and statistics, or those majoring in mathematics. Topics covered include probability spaces, conditional probability, independence, random variables, distribution functions, density functions, expectation and variance, joint distributions, conditional distributions and limit theorems. If a student uses AS/SC/MATH2010.03 as a prerequisite, AS/SC/MATH3010.03 must be taken as a corequisite. Prerequisites:One of AS/SC/MATH2015.03, AS/SC/MATH2310.03, AS/SC/MATH2010.03. Exclusions: AS/SC/MATH2030.06. Note: Section N is adapted specifically for students in Computer Science. Coordinator: T. Salisbury AS/SC/MATH2041.03 Symbolic Computation Laboratory This course introduces students to symbolic computational languages and uses these to illustrate and reinforce topics covered in first- and second-year courses in calculus and linear algebra. The course will be run on microcomputers using DERIVE and MAPLE. Topics may include matrices, inverses, determinants, eigenvalues, linear equations, quadratic forms, complex algebra, derivatives and integrals, graphing of functions, asymptotes, Taylor's series, ordinary differential equations, gradient, Laplacian, integral theorems. Enrollment is limited. The text will be announced later. The book Maple V Language Reference manual Springer-Verlag, is a good reference for MAPLE. Prerequisites: SC/AS/COSC1540.03; or equivalent computing experience; one of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03. Exclusions: MATH 2040.06. Coordinator: J. Steprans AS/SC/MATH2042.03 Symbolic Computation Laboratory This course introduces students to symbolic computational languages and uses these to illustrate and reinforce topics covered in first- and second-year courses in calculus and linear algebra. The course will be run on microcomputers using DERIVE and MAPLE. Topics may include matrices, inverses, determinants, eigenvalues, linear equations, quadratic forms, complex algebra, derivatives and integrals, graphing of functions, asymptotes, Taylor's series, ordinary differential equations, gradient, Laplacian, integral theorems. Enrollment is limited to 24 students per section. The text will be announced later. The book Maple V Language Reference manuel Springer-Verlag, is a good reference for MAPLE. Prerequisites: AS/SC/MATH2041.03; one of AS/SC/MATH1025.03, AS/SC/MATH2021.03, AS/SC/MATH2221.03; one of AS/SC/MATH2010.03, AS/SC/MATH2015.03 or AS/SC/MATH2310.03. Corequisites: AS/SC/MATH2270.03; one of AS/SC/MATH2220.03 or AS/SC/MATH2022.03. Coordinator: J. Steprans AS/SC/MATH2090.03W Introduction to Mathematical Logic Logic is the formal study of the language of mathematics and the deductive reasoning used in mathematics. It is essential in establishing the foundations of mathematics and in recent years has also come to play an important role in computer science. Knowledge of the language of logic and the ability to apply logic is a necessity for the computer professional. This course will introduce the student to the basics of symbolic logic and deductive reasoning. Our goals include both facility with formal proofs in symbolic logic and clarity of verbal reasoning about logic. The course will use a computer program for symbolic logic (probably SYMLOG) to practice the symbolic proofs and for assignments. The text may be F.D. Portoraro, Logic with SYMLOG. Prerequisites: AS/SC/MATH1090.03 (formerly AS/SC/MATH1120.03) or any 2000-level MATH course (without second digit 5) or permission of the course coordinator. Students who have not taken 1090 are advised that familiarity with truth tables will be assumed. Exclusions: MATH2120.06, MATH3290.06. This course is not open to students who have taken or are taking COSC3101.03/4101.03 (formerly COSC3090.06) or AK/COSC3431.03/3432.03 (formerly AK/COSC3430.06). Coordinator: Walter Whiteley AS/SC/MATH2221.03 Linear Algebra with Applications I Linear algebra is a branch of mathematics which is particularly useful in other fields and in other branches of mathematics. Its frequent application in the engineering and physical sciences rivals that of calculus. Computer scientists and economists have long recognized its relevance to their discipline. Moreover, linear algebra is fundamental in the rapidly increasing quantification that is taking place in the management and social sciences. Finally, ideas of linear algebra are essential to the development of algebra, analysis, probability and statistics, and geometry. This course and MATH2222.03 (see below) provide a standard full-year introduction to linear algebra. While our focus will not be excessively theoretical, students will be introduced to proofs and expected to develop skills in understanding and applying concepts as well as results. Applications will be left mainly for MATH2222.03. Topics to be studied include: systems of linear equations and matrices, determinants, linear dependence and independence of sets of vectors in Rn, vector spaces, inner product spaces, and the Gram-Schmidt process. The text has not yet been chosen. The final grade will be based on term work and a final examination (with possible weights of 60% and 40% respectively). Prerequisites: One of SC/MATH1505.06, AS/MATH1540.03, AS/MATH1550.06, AS/ECON1540.03. Corequisites: AS/SC/MATH1000.03 or AS/SC/MATH1013.03 or AS/SC/MATH1300.03. Exclusions: AS/SC/MATH1025.03, AS/SC/MATH2000.06, AS/SC/MATH2021.03. Coordinator: Pat Rogers, Fall; T. Gannon, Winter AS/SC/MATH 2222.03 Linear Algebra with Applications II This course is a continuation of either MATH1025.03W or MATH 2221.03 and requires knowledge of the topics discussed in those courses. In this course we continue the study of linear algebra with the study of inner product spaces, least squares approximation, eigenvalues, diagonalization of real and complex matrices and linear transformations. The emphasis in this course will be on those aspects of linear algebra which are important in applications. Text for the fall course will be Anton & Rorres, Elementary Linear Algebra: Applications Version, 7th ed. (Wiley). Text for the winter course will be the same as that for MATH2221.03. The prerequisite is MATH2221.03 or MATH1025.03. Exclusions: MATH2022.03, MATH2000.06, MATH2220.06, MATH2222.03. The final grade will be based on assignments, class tests, and a final examination. Prerequisites: AS/SC/MATH1025.03 or AS/SC/MATH2221.03. Exclusions: AS/SC/MATH2000.06, AS/SC/MATH2022.03. Coordinator: S. K. Kochman, Fall; R.G. Burns, Winter AS/SC/MATH2270.03W Differential Equations I Differential equations have played a central role in mathematics and its applications for the past three hundred years. Their importance in applications stems from the interpretation of the derivative as a rate of change, a familiar example being velocity. Many of the fundamental laws of physical science are best formulated as differential equations. In other areas, too, such as biology and economics, which involve the study of growth and change, such equations are of fundamental importance. In this course we will study some important types of linear differential equations and their solutions. Topics will include first- order (differential) equations; homogeneous second and higher order equations with constant coefficients; the particular solution of inhomogeneous second-order equations; series-form solutions of equations with variable coefficients; solutions by use of Laplace and Fourier transforms. Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/MATH2310.03; AS/SC/MATH1025.03 or AS/SC/MATH2021.03 or AS/SC/MATH2221.03. Coordinator: E. J. Janse van Rensburg NOTE: Mathematics students should be registering in section N of this course. AS/SC/MATH 2280.03W THE MATHEMATICAL THEORY OF INTEREST This course is intended for those in the actuarial stream of Honours Mathematics for Commerce. It will prepare the student for Examination 140 of the Society of Actuaries. Topics include: Measurement of interest, annuities, amortization schedules, bonds, yield rates, mortgages, depreciation. The text is S. G. Kellison, the Theory of Interest, Irwin Dorsey. The final grade will be based on 3 term tests (50%) and a final examination (50%). Prerequisites: AS/SC/MATH1010.03 or AS/SC/MATH1014.03 or AS/SC/MATH1310.03. Exclusions: AS/MATH2580.06. Coordinator: M. Abramson AS/SC/MATH2310.03 Calculus of Several Variables with Applications This course is the sequel to MATH1300-1310. It is a required course in the ordinary programme in Mathematics, and in certain of the honours programmes in Mathematics for Commerce. Just as MATH1300-1310 studied the calculus of functions of one variable, this course studies vectors and the calculus of functions of two or three variables. Topics from differential calculus include tangent lines to space curves, tangent planes to surfaces, partial derivatives, gradients, maxima and minima. Those from integral calculus include double and triple integrals, change of variables, line integrals and Green's theorem. Students wishing to pursue calculus further may follow this course with MATH3010.03. The text will be determined later. Prerequisites: One of AS/SC/MATH1010.03, AS/SC/MATH1014.03, AS/SC/MATH1310.03. Exclusions: AS/SC/MATH2010.03, AS/SC/MATH2015.03. Coordinator: S. Hou, Fall; K. Bugajska, Winter AS/SC/MATH2320.03F Discrete Mathematical Structures This course is intended primarily, but not exclusively, for Computer Science students. It aims to provide an intensive introduction to a variety of algebraic and combinatorial structures which are needed in computer science. A student of mathematics should enjoy being introduced to this variety of mathematical topics, many of which are not covered elsewhere. The course does not require a previous knowledge of computer science. In broad categories the topics to be covered include set theory (relations, functions,...), combinatorics, graph theory and abstract algebra (posets, lattices, Boolean algebra, groups,...). The emphasis will be on examples and on extracting common properties. This course is a prerequisite for COSC3101.03, COCS3402.03, COCS4101.03, COCS4111.03. The text will be announced later. The final grade may be based on two class tests (25% each), and a final examination (50%). Prerequisites:: AS/SC/MATH1090.03 or AS/SC/MATH1120.03 or permission of the Course Coordinator. Coordinator: A. Dow AS/SC/MATH2560.03 Elementary Statistics I Statistics is a collection of methods for observing and analyzing numerical data in order to make sensible decisions about them. In these courses the basic ideas of the analysis of data and of statistical inference will be introduced. Little mathematical background is required; high school algebra is sufficient. Mathematical proofs will be minimal; reasoning and explanations will be based mostly on intuition, verbal arguments, figures, or numerical examples. Most of the examples will be taken from or daily life; many deal with the behavioural sciences, while others come from business, the life sciences, the physical sciences, and engineering. Although students will be making some use of the computer to calculate statistics, to create statistical plots, and to obtain a better appreciation of statistical concepts, no previous experience in computing is required. Students will receive in class all the necessary instruction about how to use the statistical computer package Minitab. Students who have taken MATH2560.03 will normally take MATH2570.03 in the second semester, where they will continue to investigate many basic statistical methods. The text has not yet been chosen. The final grade may be based on assignments and quizzes (10-30%), class tests (20-40%) and a final examination (50%). Prerequisites: Ontario Grade 12 Advanced Mathematics. Exclusions: AS/SC/MATH1131.03 SC/BIOL3080.03, SC/BIOL3090.03, AS/ECON2500.03, AS/SC/GEOG2420.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06. Coordinator: C. Hruska AS/SC/MATH2570.03 Elementary Statistics II See description for MATH2560.03. Prerequisite: MATH2560.03 Exclusions: AS/SC/MATH1132.03, SC/BIOL3090.03, AS/SC/GEOG2420.03, AS/SC/PHED2050.03, AS/SC/PSYC2020.06, AS/SC/PSYC2021.03, AS/SOCI3030.06. Not open to any student who has successfully completed AS/SC/MATH2030.06. Coordinator: C. Hruska AS/MATH2580.06 Mathematics of Investment and Actuarial Science The first four-fifths of the course deal with simple and compound interest, with applications to simple and general annuities, perpetuities, loan and mortgage payments, sinking funds, bonds, capital budgeting, depreciation, and internal rates of return. In the last few weeks of the course, the theory of interest is applied to life annuities and life insurance. Students will use EXCEL, a spreadsheet available in the micro-computer laboratory in the Steacie building. This spreadsheet operates on both the Macintosh and IBM-compatible platforms. EXCEL will be used to simplify and illuminate equation-solving, amortization of loans and mortgages, bond schedules, depreciation tables, and mortality tables. No previous computer experience is assumed. With the help of notes and class instruction students will be introduced to the spreadsheet and to its use in mathematics of finance. Students will receive individual computer accounts on the APOLLO server. Each student will also need a hand-held calculator which has power and logarithm functions. Specifically, it must be able, given values of x and y, to compute x^y. The course should be especially interesting to students of business and economics. The emphasis will be on practical problems. Although the mathematical background required is minimal, it is preferred that students will have taken one other mathematics course at university before taking this one. The required text for the course will be P. Zima and R. Brown, Mathematics of Finance 4th edition (McGraw-Hill Ryerson Ltd. 1993). The manuals for EXCEL will be on reserve at the desk in Steacie library. Students who wish a more advanced treatment of the material should not take this course but enrol instead in MATH2280.03. In particular, this includes: 1. Honours Mathematics for Commerce Students. MATH2280.03 is a required course for this programme. 2. Students who are contemplating a career in the actuarial profession. They should take MATH2280.03, followed by MATH3280.06. In past years the final grade has been based on class testing (60%) and a final examination (40%). In 1996-97 there will likely be some spreadsheet-based homework assignments. Prerequisites: One full university mathematics course. Exclusions: AS/SC/MATH2280.03. Coordinator: Donald H. Pelletier
3000 LEVEL COURSES AS/SC/MATH3010.03 (Vector Integral Calculus) This course covers the integral calculus of functions of several variables. It is a required course for the honours programmes in Mathematics. It is also a natural continuation of MATH2310.03. Though that course has some topics in common, here they will be treated in greater depth. Topics include multiple integrals, Jacobian determinants, change of variables, vector fields, curl and divergence, line and surface integrals, theorems of Gauss-Green-Stokes, differential forms. The text will be announced later. Prerequisites: AS/SC/MATH2010.03, or AS/SC/MATH2310.03, or AS/SC/MATH2015.03 and written permission of the Mathematics Undergraduate Director (normally granted only to students proceeding in Honours programmes in Mathematics or in the Specialized Honours Programme in Statistics). Corequisites: AS/SC/MATH2022.03 or AS/SC/MATH2222.03. Coordinator: N. Purzitsky AS/SC/MATH3020.06 Algebra I Algebra is the study of algebraic systems, that is, sets of elements endowed with certain operations. A familiar example is the set of integers with the operations of addition and multiplication. Algebra is used in almost every branch of mathematics; indeed it has simplified the study of mathematics by indicating connections between seemingly unrelated topics. In addition the success of the methods of algebra in unravelling the structure of complicated systems has led to its use in many fields outside of mathematics. One aim of this course is to introduce students to the basic concepts and methods of abstract algebra through the study of groups, rings, and fields. Motivation will come from number theory and geometry. A second aim of this course is to help students learn to write clear and concise proofs, read the mathematical literature, and communicate mathematical ideas effectively, both orally and in writing. The textbook has not yet been chosen. The prerequisite is MATH2021.03/2022.03 or MATH2221.03/MATH2222.03 or permission of the instructor. The final grade will be based on assignments, class participation, class tests and quizzes, and a final examination. The grade breakdown has not yet been determined. Prerequisites: AS/SC/MATH2022.03 or AS/SC/MATH2222.03. Coordinator: A. Trojan AS/SC/MATH3033.03F Classical Regression Analysis This course is closely linked with MATH3034.03W, Modern Regression Analysis, for which it is a prerequisite. The emphasis, in contrast to MATH3330.03 and MATH3230.03, will be a more mathematical development of linear models including modern regression techniques. To develop a solid knowledge of regression models, it is strongly advised that you take both MATH3033.03 and MATH3034.03. The first term will cover matrix formulation of multiple regression, properties and geometry of least square estimation, general linear hypothesis, confidence intervals and regions, multicollinearity, relationship between ANOVA and regression as well as residual analysis. The second term (MATH3034.03) will cover modern regression techniques like diagnostics, crossvalidation, transformations, logistic and Poisson regression, generalized linear models and nonlinear regression models. Students will use the computer for some exercises. No previous courses in computing are required. The statistical software package SPLUS in a UNIX environment will be used and instructions will be given in class. The text is R. H. Myers ed., Classical and Modern Regression with Applications (Duxbury). The final grade may be based (in each term) on assignments, quizzes, a project, one midterm, and a final examination. It is advisable that students have taken AS/SC/MATH1132.03 or AS/SC/MATH2570.03 before taking this course. Prerequisites: AS/SC/MATH1132.03; AS/SC/MATH2022.03 or AS/SC/MATH2222.03. Corequisites: AS/SC/MATH3131.03 or permission of the course coordinator. Exclusions: AS/SC/MATH3330.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. Coordinator: C. Czado AS/SC/MATH3034.03 Modern Regression Analysis For course description see AS/SC/MATH3033.03F. Prerequisites: AS/SC/MATH3033.03. Exclusions: AS/SC/MATH3230.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. Coordinator: C. Czado AS/SC/MATH 3050.06 Introduction to Geometries Geometry has an important classical side: Euclidean Geometry from the Greeks moving, in the last two centuries, to non-Euclidean geometries (which differ by their assumptions about parallel lines), including spherical, hyperbolic and projective geometries. This transition is one of the critical "paradigm shifts" in the history of mathematics. In modern geometry, the interplay of abstraction, axiomatics, synthetic geometry, analytic methods, and groups of transformations presents a rich mix of mathematical methods and problems to be explored. Geometry also has important modern applications, to such areas as Computer Aided Geometric Design, computer graphics, computational geometry, robotics, modern physics and engineering. Even how we practice Euclidean geometry (and teach geometry) is being changed by computer programmes, both symbolic (such as Maple) and visual (such as Geometer's Sketchpad). In this course we will introduce these plane geometries in their classical and their modern settings. This course is designed to prepare the student for further work in pure mathematics, in applied geometry, or for teaching geometry in the high schools. The formal prerequisites are minimal: we will assume familiarity with linear algebra and some mathematical maturity and all other background will be developed as needed. We will expect students to join in group work in class and out of class, to work with and build physical models in class (such as spheres for spherical geometry, plastic polydrons for polyhedral models, kaleidoscopes), to work with a dynamic plane geometry programme called Geometer's Sketchpad (which is installed in the Steacie Labs and can be purchased for Windows or the Macintosh for about $55.00) and to develop their own geometric questions and projects. The texts for the course may include: David Henderson: Experiencing Geometry on Plan and Sphere (Prentice Hall); or Istvan Lenart: Non-Euclidean Adventures on the Lenart Sphere (Key Curriculum Press) George A. Jennings, Modern Geometry with Applications (Springer-Verlag). Graded work will include: regular assignments including proofs, conjectures and open ended problems, oral presentations, written projects and quizzes. There may also be several unit tests. Prerequisites: AS/SC/MATH2021.03/2022.03 or AS/SC/MATH 2221.03/2222.03 or permission of the course coordinator. Exclusions: AK/MATH3550.06. Coordinator: Walter Whiteley NOTE: MATH3050.06 will probably not be offered in 1997-98. Instead, MATH3140.06 (Number Theory and Theory of Equations) will probably be offered that year. AS/SC/MATH3110.03F Introduction to Mathematical Analysis This course provides a path towards an honours degree for those students who have not taken the honours first year calculus course MATH1010.03. The course MATH3210.03, which is required for several honours programmes, has this course as an alternative to MATH1010.03 as a prerequisite. Some of the topics that will be discussed in this course are functions, the real numbers, least upper bounds, sequences, and limits of sequences and functions. The course will emphasize the theoretical aspects of the subject. A principal objective of the course is that students learn to understand the various definitions and to use them to prove basic properties of the objects being defined. The structure of proofs and the basic logic underlying these proofs will be carefully considered. Relatively little effort will be devoted to problems involving calculations, except when they are useful for explaining the concepts. The text has not yet been selected. The grading will be based on homework, one or two tests and a final examination. Prerequisite: AS/SC/MATH1310.03 or AS/SC/MATH1014.03. Corequisite: AS/SC/MATH2310.03 or AS/SC/MATH2010.03; AS/SC/MATH2021.03 or AS/SC/MATH2221.03. Exclusions: AS/SC/MATH1010.03. Coordinator: G. L. O'Brien AS/SC/MATH3140.06 Number Theory and Theory of Equations See note under AS/SC/MATH3050.06. AS/SC/MATH3131.03F Mathematical Statistics (formerly MATH3030). This course is intended for students who need a theoretical foundation in mathematical statistics. Students who have taken this course normally take MATH3132.03 in the second term. This course continues where Math2030.03 left off while providing a theoretical foundation for many of the statistical procedures learned in Math1131.03 and Math1132.03. Topics will include some aspects of probability theory including change of variables, common distributions, principle of likelihood, the method of maximum likelihood, likelihood regions, tests of significance, tests of hypotheses, likelihood ratio tests, goodness of fit tests, conditional tests and confidence sets. Prerequisites: AS/SC/MATH2030.03 or permission of the course coordinator. Exclusions: former AS/SC/MATH3030.03. Coordinator: S. R Chamberlin AS/SC/MATH3132.03W Mathematical Statistics II former MATH3031 This course is a continuation of MATH3131.03. The basic nature of statistical inference will be studied. Topics include sufficiency, ancillarity, and the intimate connection between the mathematical structure of important classes of probability models and the inferential process for unknown parameters that flows from these structures. Prerequisites: AS/SC/MATH3131.03. Exclusions: former AS/SC/MATH3031.03 and AS/SC/MATH3130.03. Coordinator: S. R. Chamberlin AS/SC/MATH3170.06 OPERATIONS RESEARCH I This course deals with a number of the standard techniques used in Operations Research. The main topics include: Linear Programming: the theory and applications of linear programming including the simplex algorithm, duality theorem, postoptimality analysis and a discussion of the types of problems that lead to linear programming problems. Transportation Problems the transportation algorithm with application to network flows, assignment problems, shortest-route problems and critical path scheduling Integer Programming: a study of the situations leading to integer-programming problems; branch and bound algorithm for solving such problems. Dynamic Programming: an introduction to the concepts of dynamic programming with a discussion of typical problems and their solutions The text will be Wayne L. Winston, Operations Research, 3rd ed. (Duxbury Press). The final grade may be based on class tests, computer assignments, problem assignments and a final examination. Prerequisite: AS/SC/MATH2022.03 or AS/SC/MATH2222.03 and SC/AS/COSC1530.03 or SC/AS/COSC1540.03 or equivalent. Coordinator: R.L.W. Brown AS/SC/MATH3190.03 Set Theory and Foundations of Mathematics Set theory was created almost single-handedly by Cantor in the latter part of the 19th century. Cantor's motivation came from analysis, in particular the problem of representability of functions by Fourier series. Set Theory maintained its close connection with analysis but in time became an autonomous subject. Paradoxes in set theory appeared in the early 20th century, leading in due course to the subject's axiomatization. Set theory began to serve as the foundation and language for much of mathematics. (For example, the fundamental concepts of relation and function are rigorously defined in terms of sets.) But it has also evolved into a flourishing discipline in its own right. Moreover, some of the groundbreaking results it has established in this century e.g., Godel's Incompleteness Theorems and Cohen's Independence results have had far-reaching philosophical implications. The main points in the historical account of set theory sketched above will serve as guideposts around which to structure the course. Thus, the origins of set theory will be touched on, followed by the "naive" development of some of its main notions, including cardinal and ordinal arithmetic, well ordering, and the axiom of choice. Several paradoxes in set theory will be noted, followed by an outline of the axiomatization of set theory. It will then be shown how this leads to a rigorous development of some of the basic notions of mathematics such as function and the natural numbers. Issues in the philosophy of mathematics, including formalism, intuitionism, and logicism, the problems of consistency, and Godel's theorems will also be discussed. The final grade will be based on assignments and tests (60%) and a final exam (40%). The text for the course has not yet been determined. Prerequisites: MATH2222.03, or MATH2022.03, or both MATH2090.03 and MATH2320.03. Coordinator: J. P. Zhu AS/SC/MATH3210.03W Principles of Mathematical Analysis The origins of some ideas of mathematical analysis are lost in antiquity. 300 years ago, Newton and Leibniz independently created what we call the calculus. This was used with great success, but for the most part uncritically, for nearly two hundred years. In the 19th century mathematicians began to examine the foundations of analysis, giving such concepts as "function", "continuity", "convergence", "derivative" and "integral" the firm basis they required. These developments continue today. For example, one of the major themes in 20th century mathematics has been the study of "functional analysis", or calculus in infinite dimensional spaces. The course is a prerequisite, or at least a good background, for several 4000-level courses,including MATH4010.06, MATH4030.06, MATH4080.06, and MATH4210.06. The topics of the course will include limits, continuity, derivatives and integrals, picking up where calculus courses leave off. Notions such as uniform continuity and uniform convergence will play a central role. The emphasis will be on rigorous mathematical argument, proofs and examples, and the development of the skills required in the study of advanced mathematics. The course is a natural continuation of the first and second year honours calculus courses. An alternate route into the course is to take the ordinary calculus courses, and follow them by MATH3110. The latter will not cover all topics in the same depth as the honours calculus courses, but it does provide sufficient background and exposure to rigorous mathematical argument to prepare students for MATH3210. The text has not yet been chosen. Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH3110.03. Coordinator: T. Salisbury AS/SC/MATH3230.03W ANALYSIS OF VARIANCE For course description see MATH3330.03. Prerequisites: AS/SC/MATH3330.03. Exclusions: AS/SC/MATH3034.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. Coordinator: A. Wong AS/SC/MATH3241.03F Numerical Methods I (same as COSC3121.03) The course begins with a general discussion of computer arithmetic and computational errors. Examples of ill-conditioned problems and unstable algorithms will be given. The first class of numerical methods we introduce are those for nonlinear equations, i.e., the solution of a single equation in one variable. We then turn to a discussion of the most basic problem of numerical linear algebra: the solution of a linear system of n equations in n unknowns. The Gaussian elimination algorithm will be discussed as well as the concepts of error analysis, condition number and iterative refinement. We then turn to the least squares methods for solving overdetermined systems of linear equations. Finally we discuss polynomial interpolations. The emphasis in the course is on the development of numerical algorithms, the use of mathematical software, and the interpretation of the results obtained on some assigned problems. A possible textbook is (Applied Numerical Analysis) by Burden and Faires. The final grade will be based on assignments (including computer assignments), tests and a final examination. Details will be announced. (Same as SC/AS/COSC3121.03.) Prerequisites: SC/AS/COSC1030.03 or SC/AS/COSC1530.03 or SC/AS/COSC1540.03; AS/SC/MATH1025.03 or AS/SC/MATH2221.03 or AS/SC/MATH2021.03; AS/MATH1010.03 or AS/MATH1014.03 or AS/MATH1310.03. Exclusions: SC/AS/COSC3121.03. Coordinator: S. Hou AS/SC/MATH3242.03W Numerical Methods II (same as COSC3122.03) This course is a continuation of the material in MATH3241.03 (COSC3121.03). The topics to be discussed include algorithms and numerical methods for solving problems of differentiation, integration, differential equations, non-linear equations and unconstrained optimization. The textbook will be announced later. The final grade will be based on assignments (including computer assignments), tests and a final examination. Details will be announced. Prerequisites: AS/SC/MATH2270.03; AS/SC/MATH3241.03 or SC/AS/COSC3121.03. Exclusions: SC/AS/COSC3122.03. Coordinator: A. D. Stauffer AS/SC/MATH3260.03W Introduction to Graph Theory A graph is a pair of sets (V,E), where V is non-empty, and E is a set of unordered pairs of the elements of V. We call the elements of V vertices, and of E, edges. A graph can be drawn by representing the vertices by points, and the edges by lines between the vertices. One can think of a road map or a diagrammatic representation of a molecule as graphs. The curriculum of this course covers graphs and digraphs, trees, planarity, graph colourings, an introduction to extremal graph theory and the counting of graphs. In addition, we will study graph algorithms and some applications to the physical sciences. A possible text is the book by Hartsfield and Ringel entitled "Pearls in Graph Theory". Prerequisite: Completion of any 2000-level MATH course (without second digit 5), or permission of the instructor. Coordinator: E. J. Janse van Rensburg AS/SC/MATH3270.03AF Dynamical Systems Dynamical systems is a branch of mathematics which studies processes which change. Such processes occur in all branches of science and examples of dynamical systems include the motion of stars, the change of stock markets, the variation of the world's weather, the rise and fall of populations, the reaction of chemicals and the motion of a simple pendulum. The central goal of the study of dynamical systems is to predict where the system under consideration is heading and where it will ultimately go (for example, one would like to know when the market goes up or down, whether it will be rainy or sunny, or if interacting populations become extinct). The study of dynamical systems, originated from differential or difference equations arising from many applied fields, has been one of the most fruitful fields of mathematical research in this century. Many profound results have been uncovered and applied to other branches of mathematics as well as to physics, chemistry, biology and economics. In this course, we will utilize scalar maps and low-dimensional ordinary differential equations to demonstrate the main contents, methods and applications of dynamical systems. The course will be structured so that students are gradually introduced to more and more sophisticated ideas from analysis as the course proceeds. It starts with only a few elementary notions that can be explained using graphical methods or simple differential calculus. The contents of the course include phase portraits, orbits, stability and bifurcations, fixed points, periodic solutions, homoclinic orbits, periodic doubling and transition to chaos. Examples and applications include interacting populations, reaction kinetics, forced Van der Pol equation, damped Duffing and Lorenz equations. The text is Dynamics and Bifurcations, by J. Hale and H. Kocak, Springer-Verlag, New York, 1991. Prerequisites: AS/SC/MATH2270.03; AS/SC/MATH1025.03. The final grade may be based on assignments, two tests and a final exam. Coordinator: M. W. Wong AS/SC/MATH3271.03F Partial Differential Equations A study of the partial differential equations of the mathematical sciences, their solution by separation of variables in Cartesian, cylindrical, and spherical coordinates and their application to boundary value problems. Topics include generalized curvilinear coordinates; the gamma and beta functions; Sturm-Liouville theory; Bessel, Legendre, Laguerre, Hermite, Chebyshev, hypergeometric, and confluent hypergeometric equations and functions and their properties. The principal reference text will be G. Arfken, Mathematical Methods for Physicists, Academic Press. Exclusions are MATH4200A.06, AK/MATH4040.06. Prerequisites: AS/SC/MATH2270.03; one of AS/SC/MATH2010.03, AS/SC/MATH2015.03, AS/SC/MATH2310.03; AS/SC/MATH3010.03 is also desirable, though not essential, as prerequisite for students presenting AS/SC/MATH2010.03 or AS/SC/MATH2310.03. Exclusions: AS/MATH4200A.06. Coordinator: H. Freedhoff AS/SC/MATH3280.06Y Actuarial Mathematics This course is intended for those students contemplating careers in the actuarial profession. It will help to prepare a student for Examination 150 of the Society of Actuaries. We will cover most of the material in Chapters 3-9 of the official textbook, N. L. Bowers et. al., Actuarial Mathematics (Society of Actuaries). There is not sufficient time in a one-year course to cover Chapters 10, 14 and 15, the remaining material needed for Exam 150. However, students who complete this course should acquire sufficient background to enable them to study the omitted chapters on their own. The prerequisites are a sound knowledge of both interest theory and probability theory. For the probability prerequisite, students should have completed MATH2030.03. For interest theory the preferred prerequisite is MATH2280.03. Those who have completed MATH2580.06 with a grade of B+ or better may be allowed to enroll, but such students should note that MATH3280.06 is considerably more advanced, and requires much more mathematical ability, than MATH2580.06. The final grade will probably be based on assignments (5%), four class tests (55%), and a final examination (40%). Prerequisites: AS/SC/MATH2280.03; AS/SC/MATH2030.03. Coordinator: S. D. Promislow AS/SC/MATH3330.03F Regression Analysis This course is closely linked with MATH3230.03W, Analysis of Variance, for which it is a prerequisite. Students will use the computer heavily in these courses, but no previous courses in computing are required. MATH3330.03 will focus on linear models for the analysis of data on several predictor variables and a single response. The emphasis will be on understanding the different models and statistical concepts used for these models and on practical applications rather than on the formal derivations of the models. The approach will require the use of matrix representations of the data, and the geometry of vector spaces, which will be reviewed in the course. The first term (MATH3330.03) will cover the basic ideas of multiple regression, having reviewed in depth the elements of simple linear regression. The second term (MATH3230.03) will have a major focus on models with categorical variables as predictors (classical ANOVA, or Analysis Of Variance). The nature of the course requires that students be involved on a constant basis with the material, and not fall behind. The text will be announced at a later date. The prerequisites are (i) a course in basic statistics with coverage of t- and F-statistics, as well as an introduction to simple linear regression (examples are MATH1131.03/1132.03, MATH2030.06, MATH2560.03/2570.03, PSYC2020.06); and (ii) some facility with linear algebra (including the idea of vectors), such as provided in MATH2021.03/2022.03 (formerly MATH2000.06), MATH2221.03/2222.03 (formerly MATH2220.06), or MATH1550.06, MATH1025.03, MATH1505.06. The final grade may be based (in each term) on assignments, quizzes, one or more midterms, and a final examination which will be common to all sections. Prerequisites: One of AS/SC/MATH1132.03, AS/SC/MATH2030.06, AS/SC/MATH2570.03, AS/SC/PSYC2020.06, or equivalent; some acquaintance with matrix algebra (such as is provided in AS/SC/MATH1025.03, SC/MATH1505.06, AS/MATH1550.06, AS/SC/MATH2021.03, or AS/SC/MATH2221.03). Exclusions: AS/SC/MATH3033.03, AS/ECON4210.03, AS/SC/GEOG3421.03, AS/SC/PSYC3030.06. Coordinator: H. Massam AS/SC/MATH3410.03F Complex Variables Some polynomials, such as x^2+ 1, have no roots if we confine ourselves to the real number system. The complex numbers can be defined as the set of all numbers of the form a + ib, where a and b are real, i is a new kind of number satisfying i^2= -1, and the operations of arithmetic are carried out in a fairly obvious way. The complex numbers include the reals (case b = 0), and the extended system has the desirable property that not only x^2 + 1 but every polynomial now has a root. In the system of complex numbers certain connections are seen between otherwise apparently unconnected real numbers. A striking example is Euler's formula e^(i * pi) + 1 = 0. This is actually a very simple consequence of the extension to complex variables of the familiar exponential and trigonometric functions. The concepts and operations of calculus (differentiation, integration, power series, etc.) find their most natural setting in complex (rather than real) variables. In addition, some physical problems such as those involving electrical circuits and certain two-dimensional potential problems (arising in fluid dynamics, airfoil theory, electrostatics, etc.) are most easily analyzed in the context of complex numbers and functions. The present course is intended to give the student a basic knowledge of complex numbers and functions and a basic facility in their use. The subject is a vast one, however, and its study can be continued in MATH 4210.03 (Complex Analysis). Topics include: Complex numbers and their representations; functions of a complex variable; mapping of elementary functions; complex differentiation; Cauchy-Riemann equations, complex integration; Cauchy's theorem; Cauchy's integral formula and its applications; complex power series; the residue theorem and its applications. The final grade may be based on assignments, a midterm examination and a final examination. Prerequisites: AS/SC/MATH2015.03 or AS/SC/MATH3010.03 or permission of the Course Coordinator. Exclusions: MATH4210.06. Coordinator: K. Maltman AS/SC/MATH3430.03W Sample Survey Design This course deals with the peculiarities of sampling and inference commonly encountered in sample surveys in medicine, business, the social sciences, political science, natural resource management, and market research. Attention will be focused on the economics of purchasing a specific quantity of information. That is, methods for designing surveys that capitalize on characteristics of the population under study will be presented, along with associated estimators to reduce the cost of acquiring an estimate of specified accuracy. Topics include the principal steps in planning and conducting a sample survey; sampling techniques including simple random sampling, stratified random sampling, systematic sampling, cluster sampling, and sampling with probabilities proportional to size; estimation techniques including difference, ratio, and regression estimation. The emphasis will be on the practical applications of theoretical results. The text will be R. L. Scheaffer, W. Mendenhall, and L. Ott, Elementary Survey Sampling, 5th ed. (PWS-Kent). The prerequisite is a second course in statistics such as MATH2030.03 or MATH3330.03 or PSYC3030.06. The final grade may be based on assignments (15%), a class test (35%) and a final examination (50%). Prerequisites: AS/SC/MATH3033.03 or AS/SC/MATH3131.03 or AS/SC/MATH3330.03. Exclusions: AS/SC/MATH4330.03. Coordinator: P. Peskun
4000 LEVEL COURSES AS/SC/MATH 4000.03/06 Individual Project This course is open to students in Honours Programmes in Applied Mathematics, Mathematics, Mathematics for Commerce or Statistics. The student works under supervision of a faculty member, who is selected by the course director and the student. The project allows the student to apply mathematical or statistical knowledge to problems of current interest. A report is required at the conclusion of the project. Students in the Applied Mathematics Honours Programmes are particularly encouraged to take this course. The procedure is as follows: Each year, faculty members who are interested in supervising projects will submit project descriptions to the Course Director for Applied Mathematics. Students will meet with the Course Director for Applied Mathematics, and they will jointly decide on a faculty member to supervise the project, taking into account the background and interest of the student, as well as the availability and interests of faculty members. For this year, there is an opening for a group project by two or three undergraduates in pure or applied mathematics. Interested students are encouraged to contact Walter Whiteley, with a project proposal or to seek suggested topics. The amount of work expected of the student is approximately 10 hours per week, that is, the equivalent of a standard full-year (for 4000.06) or half-year (for 4000.03) course. The supervisor is expected to spend about 1 or 2 hours per week with the student(s), averaged over the duration of the project. In addition to the final report, regular short progress reports will expected at definite times during the course. The final grade will be based upon the final report as well as the interim progress reports. Prerequisites: Open to students in Honours Programmes in Applied Mathematics, Mathematics for Commerce, Mathematics and Statistics. Permission of the Course Director is required. Applied Mathematics Coordinator: Martin Muldoon Mathematics for Commerce Coordinator: Morton Abramson Pure Mathematics Coordinator: Walter Whiteley Statistics Coordinator: Peter Peskun AS/SC/MATH4010.06 Real Analysis This course provides a rigorous treatment of real analysis. All students should have completed an introductory analysis course, MATH 3210.03. Students contemplating graduate work in mathematics are strongly advised to take this course. Specific topics include: Metric spaces; limits and continuity; sequences and serious of functions; Fourier series; functions of several variables; Lebesgue measure and integration. The text is W. Rudin, Principles of Mathematical Analysis, (McGraw-Hill). The final grade may be based on assignments (20%), two class tests (40%) and a final examination (40%). Prerequisites: AS/SC/MATH3210.03 or permission of the course coordinator. Coordinator: N. Madras AS/SC/MATH4020.06 Algebra II This course aims to broaden and deepen the student's knowledge and understanding of abstract algebra by building on the material of MATH3020.06 (or a comparable course which the student may have taken). The algebraic structures to be discussed in some detail are groups, rings, fields and (possibly) Boolean algebras. Topics will be chosen from the following: Group theory: finitely generated abelian groups, permutation groups, simple groups, symmetry groups, Sylow's theorems. Ring theory: divisibility in integral domains with applications to diophantine equations, elements of algebraic number theory, rings with chain conditions. Field theory: field extensions with applications to constructions with straight edge and compass, finite fields, elements of Galois theory. Boolean algebra: Boolean algebras with application to circuitry and logic, Boolean rings, finite boolean algebras, lattices. The text will be announced later. The grade will be based on assignments (20%), class tests (40%) and a final examination (40%). Prerequisites: AS/SC/MATH3020.06 or permission of the course coordinator. NOTE: Class hours for this course could be changed in order to accommodate students interested in taking the course. If applicable, please contact the Coordinator prior to the beginning of term. Coordinator: W. Tholen AS/SC/MATH4080.06 Topology Topology is one of the pillars of modern mathematics (along with geometry, algebra and analysis); in fact, it can be viewed as a synthesis of geometry and analysis, strongly influenced by algebraic methods. Its study clarifies the nature of concepts learned in analysis and geometry such as proximity, continuity and distance. It studies objects called topological spaces by studying the maps (functions) that they support, and their invariants. This is a basic course covering such topics as topological spaces, continuity, connectedness, compactness, fixed-point theory, metric spaces, nets, filters, metrization theorems, complete metric spaces, function spaces, fundamental group, and covering spaces. More advanced topics in topology that this course leads to are point set topology, algebraic topology (homology theory, homotopy theory) and differential topology (manifold theory). Topology has many applications within mathematics, but nowadays it also is used in physics and physical astronomy (e.g. cosmology) as well as in catastrophe theory and physiology, economics and sociology. The text is has not yet been chosen. The course can be used to fulfill the Pure Mathematics Honours requirement. The final grade will be based on assignments/class tests and a final examination. Prerequisites: AS/SC/MATH3480.03 or AS/SC/MATH3210.03 or permission of the course coordinator. Coordinator: A. Dow AS/SC/MATH4110H.03F Topics In Analysis: Summation of Series In this course, we will consider series which are convergent, slowly convergent or divergent. A number of methods will be presented which may be used to approximate the sum of a series, for example, the Shanks Transformation, Pade' Approximants and Borel Summation. The emphasis of this course will be on illustrating the summation methods rather than on theoretical proofs. Knowledge of Fortran or symbolic computational language (Maple or Mathematica) is useful but not required: however, examples using Maple will be given in class. The final mark in this course will be determined by two tests (40%) and a project (60%). Prerequisite: Permission of the Department. Coordinator: F. Vinette AS/SC/MATH4110N.03W Topics in Analysis: Ordinary Differential Equations This is an advanced introduction to a number of topics in ordinary differential equations. The topics will be chosen from the following: existence and uniqueness theorems, qualitative theory, oscillation and comparison theory, stability theory, bifurcation, dynamical systems, boundary value problems, asymptotic methods. Students will be expected to attend the lectures in MATH 6340.03F ORDINARY DIFFERENTIAL EQUATIONS (T/R 1:00 - 2:30). The lectures will survey the above topics and students will be expected to make an in-depth study of some of them by doing assignments and projects. Students should have a thorough knowledge of undergraduate analysis and linear algebra to the level of MATH 2220 and MATH 3210. It would be desirable but not essential that they have taken an undergraduate course in differential equations. Some exposure to real analysis, complex analysis and topology would be desirable also. The probably textbook is J. K. Hale, Ordinary Differential Equations, Krieger, Malabar, Florida, 1980. References: H. Amann, Ordinary Differential Equations, 3rd. ed., Springer, 1992. G. Birkhoff, and G. -C Rota, Ordinary Differential Equations, 4th ed. Wiley, 1988. F. Brauer and J. A. Nohel, The Qualitative Theory of Ordinary Differential Equations, Dover. J. K. Hale and H. Kocak, Dynamics and Bifurcations, Springer 1991. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems and Linear Algebra, Academic Press, 1974. Prerequisite: Permission of the Department. Coordinator: M. Muldoon AS/SC/MATH4130D.03F Topics in Probability and Statistics: Methods of Statistical Analysis A survey of methods for analyzing data with emphasis on the application of the methods: Least Squares; Minimum variance linear unbiased; Likelihood and first order methods; Maximum likelihood, Rao and Likelihood ratio tests; Sufficiency and exponential models; Conditioning and location models; Measures of departure; Bayes; Bootstrap; Minimum variance unbiased; Tests and power; Data analysis. Further topics may be covered depending on the background of the students: conditional methods; Quasi-likelihood; third order asymptotic methods; component model selection. The course will be evaluated with 3 assignments for 25%, 1 test for 30% and a final examination for 45%. The possible text may be, Probability and Statistics, D. A. S. Fraser. Prerequisite MATH3132.03 Coordinator: D. A. S. Fraser AS/SC/MATH4141.03F Advanced Numerical Methods Systems of nonlinear equations: Newton-Raphson iteration, quasi- Newton methods; optimization problems: steepest descents, conjugate gradient methods; linear and nonlinear approximation theory. Least squares, singular value decomposition, orthogonal polynomials, Chebyshev and Fourier approximation, Pade approximation; matrix eigenvalues: power method, Householder, QL and QR algorithms. The text will be announced later. The mark will be based on a combination of computer-based assignments, tests and a final exam. Prerequisites: AS/SC/MATH3242.03 or SC/AS/COSC3122.03. Coordinator: A.D. Stauffer AS/SC/MATH4142.03W Numerical Solutions to Partial Differential Equations Review of linear and nonlinear partial differential equations; boundary conditions; finite-difference approximations; solution of parabolic equations; boundary-value problems for elliptic equations; iterative methods for solution; direct methods; finite-element approximations of elliptic equations; solution of hyperbolic equations; error analysis. The most important reference for this course is: Numerical Recipes, Second Edition, by W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Cambridge, 1992. Prerequisites: AS/SC/MATH2270.03; AS/SC/MATH3242.03 or SC/AS/COSC3122.03; AS/SC/MATH3272.03 is strongly recommended. Coordinator: J. Laframboise AS/SC/MATH4170.06 Operations Research II This course deals with deterministic and probabilistic models based on optimization. The following topics will be discussed: 1) game theory (how to find the best strategies in a confrontation between two players with opposite interests); 2) decision theory (how to act in order to minimize the loss subject to the available data); 3) simulation (how to sample from a probability distribution and accurately approximate multiple integrals using random numbers); 4) reliability theory (how to evaluate the lifetime of a system consisting of many interacting subsystems); 5) queuing theory (how to assess what may happen in a system where the customers arrive randomly, wait in line, and then get served); 6) measures of uncertainty and nonlinear optimization (how to measure uncertainty in probabilistic modelling, applications to pattern-recognition and classification, nonlinear optimization techniques). Each chapter contains specific optimization problems and methods and algorithms for solving them. The course is rich in examples. There is no textbook and the lecture notes are essential. Useful books are: (a) F. S. Hillier and G. J. Liberman, Introduction to Operations Research, 4th ed. (Holden-Day); (b) H. A. Taha, Operations Research, An Introduction, 4th ed. (MacMillan). There are three prerequisites: (i) some background in probability and statistics such as MATH2030.06 or MATH1132.03 or MATH2030.03; (ii) some background in calculus of several variables such as MATH2010.03, MATH2310.03 or MATH2015.03; and (iii) some knowledge of linear programming, preferably from MATH3170.06. Students who have not taken these courses need the permission of the course coordinator. The final grade is based on four one-hour tests worth 15% each and a final examination worth 40%. Prerequisites: AS/SC/MATH2010.03 or AS/SC/MATH2015.03 or AS/SC/MATH2310.03; AS/SC/MATH1132.03 or AS/SC/MATH2030.06 or AS/SC/MATH2030.03; AS/SC/MATH3170.06; or permission of the course coordinator. Exclusion: AS/MATH4570.06. Coordinator: S. Guiasu AS/SC/MATH4250.06Y Differential Geometry This course is a natural continuation of MATH3010.03. It treats calculus on curves, surfaces and their higher dimensional generalizations, and uses this calculus to study the geometry of these objects. Differential geometry is basic to modern mathematics, and is the natural language of many areas of physics, especially mechanics, gauge field theory and general relativity. The course will focus initially on the geometry of hypersurfaces in Euclidean space, using vector fields to study parallelism, geodesics and curvature. In the second part of the course, we show how parametrized surfaces lead to the concept of a differentiable manifold. Riemannian metrics and the relation between local geometry and global topological properties will be studied. Most likely the textbook will be Thorpe, J.A., Elementary Topics in Differential Geometry, Springer-Verlag, but a final decision has not yet been made. Prerequisites: 13 courses including AS/SC/MATH2222.03 and AS/SC/MATH3010.03. The grading scheme for this course will be: Assignments, 20%; Term Tests, 40% and a Final Examination, 40%. Coordinator: M. Walker AS/SC/MATH4280.03F Risk Theory A study of the stochastic aspects of risk with emphasis on insurance applications. Topics include: an introduction to utility theory; individual and collective risk theory; compound Poisson processes; ruin theory; non-proportional reinsurance. This course is intended mainly for those students contemplating a career in the actuarial profession. It will cover the complete course of reading for Examination 151 of the Society of Actuaries, which is Chapters 1, 2, 11, 12 and 13 of the book N. L. Bowers et al, Actuarial Mathematics (Society of Actuaries). Note that this is the same text as for MATH3280.06. MATH3280.06 is not absolutely necessary as background but the student is advised to take it, at least concurrently. On the other hand, a reasonably advanced knowledge of probability theory is essential. Students should have MATH2030.03. The final grade will probably be based on assignments (20%), two tests (20% each) and a final examination (40%). Prerequisite: AS/SC/MATH2030.03, or AS/SC/MATH3030.03 (taken before 1993/94); AS/SC/MATH3280.06 is recommended but not required. Coordinator: N. Madras AS/SC/MATH4430.03W Stochastic Processes II This course is an introduction to stochastic, or random, processes. Stochastic processes are models which represent phenomena that change in a random way over time. Simple examples are: the amount of money a gambler has after each play of a game; and the number of people waiting for service at a bank at various times. This course studies some of the most basic stochastic processes, including Markov chains, Poisson processes, and renewal processes. A Markov chain is a stochastic process in which predictions for the future depend only on the present state of affairs, but not on knowledge of the past behaviour of the process. Markov chains are relatively easy to analyze, and they have been used as models in many areas of science, management, and social science. A Poisson process is a model for the occurrence of random events (such as oil spills in the Atlantic Ocean). A renewal process is a process that ''starts over'' whenever a certain kind of random event occurs (such as a computer starting up after a crash). Thus course will treat both the theory and applications of these stochastic processes. The text will probably be Introduction to Probability Models by Sheldon M. Ross (Academic Press). The final grade is likely to be based on assignments (20%), a test (30%) and a final examination (50%). Prerequisite: AS/SC/AK/MATH2030.03 or AS/SC/AK/MATH3030.03. Coordinator: N. Madras AS/MATH4501.03F Financial Accounting This introduction to financial accounting takes a conceptual approach with heavy emphasis on concepts and on case analysis. It examines the concepts, principles, and practices of financial accounting from the perspective of the users of financial statements. (Same as AS/CC4501.03). Exclusions AS/CC4501.03, AS/ECON3580.03, AD/ACTG2010.03, AD/ACTG2011.03, AD/ACTG3000.03, AD/ACTG5010.03. Coordinator: T.B.A. Please Note: Registration is only available by manual enrolment. Please see Janice Grant - N503 Ross. AS/MATH4502.03W Managerial Accounting This course focuses on the basic accounting concepts that form the foundation for management decisions. Performance appraisal, pricing, financing, output, investment, and other similar managerial decisions are examined and applied in case situations. Technical aspects of management accounting are not emphasized. (Same as AS/CC4502.03). Prerequisite: AS/MATH4501.03 or AS/CC4501.03. Exclusions: AS/CC4502.03, AS/ECON3590.03, AD/ACTG3020.03, AD/ACTG5020.03. Coordinator: TBA Please Note: Registration is only available by manual enrolment. Please see Janice Grant - N503 Ross. AS/SC/MATH4570.06 Applied Optimization Two-person zero-sum games, non-zero-sum games, N-person cooperative games, decision theory, nonlinear programming, interior methods of linear programming, Markov decision processes, dynamic programming, queuing theory. This course is designed primarily for students in the General Stream of Honours Mathematics for Commerce. The text will be H. A. Taha, Operations Research, An Introduction, 5th ed. (MacMillan). Prerequisite: AS/SC/MATH3170.06; AS/SC/MATH3330.03; AS/SC/MATH3230.03 or AS/SC/MATH3430.03. Exclusions: AS/SC/MATH4170.06. Coordinator: R.L.W. Brown AS/SC/MATH4730.03F Experimental Design "Designing" an experiment simply means planning it so that information will be collected which is relevant to the problem under investigation. All too often data are collected which turn out to be of little or no value in any attempted solution of the problem. The design of an experiment is, then, the complete sequence of steps taken ahead of time to insure that the appropriate data will be obtained in a way which permits an objective analysis leading to valid inferences about the stated problem. Prerequisites: A second full-course equivalent in statistics; including either AS/SC/MATH3033.03, or both AS/SC/MATH3230.03 and AS/SC/MATH3330.03, or permission of the Course Coordinator. Coordinator: S. R. Chamberlin AS/SC/MATH4830.03 Time Series and Spectral Analysis same as (EATS4020.03 and PHYS4060.03) Treatment of discrete sampled data by linear optimum Wiener filtering, minimum error energy deconvolution, autocorrelation and spectral density estimation, discrete Fourier transforms and frequency domain filtering and the Fast Fourier Transform Algorithm. Power and energy signals, wavelets convolution and the transform, expected value, autocorrelation and cross-correlation impulse, white noise and Wold decomposition, time reverse, properties of wavelets linear, optimum filtering deconvolution, shaping and spiking filters. Finite Fourier transforms, Fourier transform effects of sampling and record length, digital frequency filtering, the power spectrum, Fast Fourier transform. References will be E. R. Kanasewich, Time Sequence Analysis in Geophysics, 3rd ed., (University of Alberta Press, 1981), A. Robinson Enders and Sven Treital, Geophysical Signal Analysis, (Prentice-Hall, 1980), and A. Robinson Enders, Multichannel Time Series Analysis with Digital Computer Programs, rev. ed. (Holden-Day, 1978). Prerequisites: SC/AS/COSC1540.03 or FORTRAN programming experience; AS/SC/MATH2270.03; one of AS/SC/MATH2010.03 (before FW92), AS/SC/MATH2015.03, AS/SC/MATH2310.03 (before FW92), AS/SC/MATH3010.03.) Exclusions: SC/AS/COSC4010B.03, SC/AS/COSC4242.03, SC/EATS4020.03, SC/PHYS4060.03. Coordinator: D. E. Smylie AS/SC/MATH4930A.03W Topics in Applied Statistics: Statistical Quality Control This course will attempt to provide the student with a comprehensive coverage of the modern practice of statistical quality control from basic principles to state-of-the-art concepts and applications. An introduction to quality improvement in the modern business environment will deal with the facts that quality has become a major business strategy and that organizations with successful quality-improvement programmes can increase their productivity, enhance their market penetration, and achieve greater profitability and a strong competitive advantage. While the entire range of statistical process-control tools will be extensively discussed, the primary focus will be on the control chart whose use in modern-day business and industry is of tremendous value. Various control charts will be discussed, including cumulative sum procedures and multivariate charts. Commonly used process capability indices will be discussed and compared. The important interrelationship between statistical process control and experimental design for process improvement will be emphasised. In recent years, there has been much interest and discussion regarding a set of statistical and nonstatistical tools referred to as "Taguchi methods". These will be critically examined. The text will be D. C. Montgomery, Introduction to Statistical Quality Control, 2nd ed. (Wiley). The final grade may be based on assignments (15%), a class test (35%) and a final examination (50%). Prerequisites: AS/SC/MATH3330.03; AS/SC/MATH3230.03 or AS/SC/MATH3430.03. Corequisite: AS/SC/MATH 4730.03. Course Coordinator: P. Peskun
DEGREE CHECKLISTS (ARTS) FACULTY OF ARTS Faculty Requirements Checklist All Students in the Faculty of Arts must fulfill each of the following requirements: 1.General Education Requirements _______NATS 1000-level course. _______HUMA/SOSC 1000-level course. _______HUMA/SOSC 2000-level (or higher) course. _______Breadth (this requirement is fulfilled if at least one course is taken from both HUMA and SOSC). 2. Elective Courses: All students majoring in a programme from the Department of Mathematics and Statistics must take at least 3 additional full courses outside the department which are not required in the specific departmental programme (e.g. some programs require a COSC course). 1. __________ 2. _________ 3. _________ 3. Degree Programme selection: A student must choose Departmental program(s) in order to complete one of the following degrees: Specialized Honours (Choose 1 such program); Double Honours (choose 2 different Honours programmes, e.g. Mathematics and Economics or Mathematics and Statistics) Honours Major/Minor (Choose 1 Honours Major and a distinct Honours Minor) Honours Single Major (Choose 1 Honours Major Programme). Ordinary Major (Choose 1 Ordinary Programme). 4. Residence Requirement, Number of Courses, GPA and Upper Level course requirements: Ordinary: OVERALL REQUIREMENT: 15 full courses (90 credits) with a minimum of FIVE full York University courses (30) credits including Four full in-faculty courses (24 credits). MAJOR REQUIREMENT: A minimum of 50% (half) of the MAJOR course requirement must be in-faculty. At least three full courses at the 3000-level or higher must be completed (two of which must be in the Major). 15 full courses are required with a 4.0 grade point average. At most 2 more courses (above the 1000-level) may be taken if needed to raise the grade point average to above 4.0. Honours: OVERALL REQUIREMENT: 20 full courses (120 credits) with a minimum of FIVE full York University courses (30) credits) including FOUR full in-faculty courses (24 credits). MAJOR REQUIREMENT: A minimum of 50% (HALF) for each MAJOR'S or MINOR's course requirement must be in faculty. At least 3 full courses at the 4000-level (two of which must be in the Major) and at least 3 more full courses at the 3000-level or higher. A total of 20 courses must be completed and an overall grade point average of 5.0 must be maintained.
Faculty of Arts Applied Mathematics BA Programmes I: Specialized Honours, Honours Major/Double Honours, Ordinary: Programme Core: MATH1013.03/1014.03 or MATH1000.03/1010.03, COSC1540.03, MATH1025.03/2222.03 MATH2015.03/2270.03, MATH2041.03/2042.03, MATH2030.03, MATH3241.03/3242.03 Select additional courses from List 1 below, as indicated by your programme: A: Specialized Honours: Programme Core, MATH3260.03, MATH3410.03 and, if MATH1010.03 has not been completed, MATH3110.03. Select an additional 21 credits from major AS/SC/MATH courses (without second digit 5) at the 3000-level or higher, with at least 15 credits from List 1 of which 12 credits are at the 4000-level or higher. Students are encouraged to enroll in MATH4000.03/06. B: Honours Major/Double Honours: Programme Core and 12 credits (with 6 credits from List 1) at the 4000-level. C: Ordinary: Programme Core. Select an additional 9 credits from major AS/SC/MATH courses (without second digit 5) at the 3000-level or higher, with at least 6 credits from List 1. II: Honours Minor: This programme is pursued jointly with any 7 course Honours programme in Arts, including Economics, Psychology, Geography, Sociology and Physical Education. Curriculum: MATH1013.03/1014.03 or MATH1000.03/1010.03 or MATH1300.03/1310.03 AND COSC1540.03 MATH1025.03 or MATH2221.03 AND MATH2015.03 Any 2 from MATH2041.03, MATH2270.03 or MATH2222.03 9 credits from List 1, including one of MATH3170.06, MATH3241.03, MATH3260.03 ******************************** LIST 1 MATH3110.03 MATH3131.03 MATH3170.06 MATH3260.03 MATH3270.03 MATH3271.03 MATH3272.03 MATH4141.03 MATH4142.03 MATH4160.03 MATH4170.06 MATH4241.03 MATH4270.03 MATH4430.03 MATH4470.03 MATH4000.03/06 ******************************** Areas of Concentration: You can concentrate your area of study by selecting courses from one of the following areas (You should make sure that you satisfy all your degree requirements as set out above.) Numerical Analysis: MATH4141, MATH4142, MATH4430, MATH4470 Discrete Applied Math/ Operations Research: MATH3170, MATH3260, MATH4141, MATH4160, MATH4170, MATH4430, MATH4570 Applied Math in Physical Sciences/ Differential Equations: MATH3270, MATH3271, MATH3272, MATH3410, MATH4141, MATH4142, MATH4241, MATH4270, MATH4470, MATH4830 Statistical Applied Math: MATH3131, MATH3132, MATH3033, MATH3034, MATH3230, MATH3330, MATH3430, MATH4230, MATH4430, MATH4630, MATH4730, MATH4830, MATH4930
Faculty of Arts Mathematics BA Programmes Important: For a summary of Faculty degree requirements see previous pages. Please note that unless otherwise stated a slash ("/") between course numbers means "and" which means that all the stated courses must be taken to satisfy degree requirements. ********************************* ORDINARY or HONOURS MINOR __________MATH1300/1310/2310* __________one of MATH1090.03**/2090.03/2320.03 __________MATH2221.03/2222.03 __________ _________12 credits Major MATH 3000-level * or the corresponding Honours versions ** Note that MATH1090.03 may not be taken if any 3000-level MATH course is being (or has been) taken. *************************************** HONOURS (Specialized or Major) CORE All Honours candidates must complete the following Honours CORE plus additional courses as indicated below: ______ MATH1000.03/1010.03/2010.03* ______ one of MATH1090.03**/2090.03/2320.03 ______ MATH2021.03/2022.03*** ______ MATH3010.03 ______ MATH3210.03 ______ Either MATH3020.06 or MATH3131.03/3132.03. ______ 6 credits from 4000.06, 4000.03, 4010.06, 4020.06 4030.03 4050.06, 4080.06, 4110.03, 4120.03, 4130.03, 4140.03, 4150.03, 4160.03, 4170.06, 4210.03, 4230.03, 4250.06, 4280.03, 4290.03, 4430.03, 4630.03, 4730.03 * Courses from the sequences MATH1300/1310/2310 or MATH1013/1014/2015 may be substituted for the corresponding courses in the sequence MATH1000/1010/2010, BUT any student who has not completed MATH1010.03 will have to take MATH3110.03 over and above the other program requirements. ** Note that MATH1090.03 may not be taken if any 3000-level MATH course is being (or has been) taken. *** or MATH2221.03/2222.03 with an A in both; if less than A in either then add an additional one of MATH2090.03 or MATH2320.03. *********************************************** ADDITIONAL Specialized Honours ______ MATH4010.06 or MATH4020.06 credits in addition to CORE 24 more major MATH credits ______ ______ ______ ______ ______ ______ ______ ______ Honours or Double Honours _____6 major MATH 4000-level credits in addition to CORE.
Faculty of Arts Mathematics for Commerce BA Programmes May not be pursued jointly in a Double Major or Major/Minor with another subject. Important: For a summary of Faculty degree requirements please see previous pages. ********************************************* Honours Actuarial and Operations Research Common Core: ______ MATH1300.03/1310.03 ______ MATH1131.03/1132.03* ______ COSC1520.03/1530.03 ______ MATH2221.03/2222.03 ______ MATH2310.03 ______MATH3170.06 ______MATH3330.03 *or MATH2560.03/2570.03 ********************************************* Actuarial Stream (In addition to the Common Core) ______ MATH2280.03 ______MATH2030.03 ______MATH3131.03 ______MATH3230.03 ______ MATH3280.06 ______MATH4280.0 ____________ 9 additional 4000-level MATH credits *********************************************** Operations Research Stream (In addition to the Common Core) ______ one of MATH3230.03/3430.03 ______ MATH4170.06 ______ 6 additional 4,000 level MATH credits ************************************************ Ordinary and Honours General Stream Ordinary ______ COSC1520.03/1530.03 _____ MATH1550.06 or MATH1530/1540 ______ MATH2221.03/2222.03 ______ MATH2560.03/2570.03 _____ MATH2580.06 ______ MATH3170.06 ______ MATH3330.03 ______ one of MATH 3230.03/3430.03 HONOURS GENERAL STREAM in addition to Ordinary programme ______ The "other" of MATH3230.03/3430.03 _______ MATH4570.06 _______ MATH4730.03/4930.03 ______ MATH4501.03/4502.03 Notes: MATH1131.03/1132.03 and MATH2560.03/2570.03 are presently interchangeable. MATH2580.06 may be replaced by MATH2280.03 and another half-course in mathematics. MATH3033.03/3034.03 may be taken instead of MATH3330.03/3230.03. MATH4170.06 may be taken instead of MATH4570.06.
Faculty of Arts Statistics BA Programmes Specialized Honours or Honours Major of Double Honours or Honours Major/Minor Important: For a summary of Faculty degree requirements see previous pages. Programme Core: MATH 1000.03/1010.03 ______ MATH 1131.03/1132.03 ______ MATH 2021.02/2022.03 ______ MATH 2010.03/3010.03 ______ MATH 2030.03/3033.03 ______ MATH 3131.03/3132.03 ______ Specialized Honours: Students must take the Programme Core, listed above, plus the following: MATH 3210.03 ______ MATH 3034.03 ______ MATH 3430.03 ______ Twelve credits from 4000-level AS/MATH courses with third digit 3. _______ Nine additional credits from any major (second digit not 5) AS/MATH courses for a total of at least 66 major AS/MATH credits. _______ (Substitutions: MATH3033.03/3034.03 may be replaced by MATH3330.03/3230.03 if taken before September 1993.). Honours Major or Double Honours: Students must take the Programme Core, listed above, plus the following: One of MATH 3034.03 or MATH 3430.04 ______ Twelve credits from 4000-level AS/MATH courses with third digit 3 for a total of at least 51 major AS/MATH credits (48 with the AS/MATH 2015.03 or the AS/MATH 2310.03 option). ______ (Substitutions: In Honours Major or Double Honours it is permitted but not recommended to make the following substitutions. MATH 1300/1310 or MATH 1013/1014 for MATH 1000/1010. MATH 1025 or MATH 2221 for MATH 2021. MATH 2222 for MATH 2022. MATH 2010/3010 can be replaced by MATH 2015.03 or MATH 2310.03. Also, MATH 3033.03 and MATH 3034.03 may be replaced by MATH 3330.03 and MATH 3230.03 if taken before September 1993.)
Faculty of Arts Statistics BA Programmes Honours Minor or Ordinary Major Important: For a summary of Faculty degree requirements see previous pages. *********************************** Honours Minor: First year Calculus (two half courses without second digit 5) ______ MATH 1131.03/1132.03 ______ MATH 2221.03/2222.03 ______ Twelve credits from 2000-level or higher AS/MATH courses with third digit 3. (Substitutions: The requirement MATH 1131.03/1132.03 may be replaced by MATH 2560.03/2570.03 provided an average of at least B was attained.) *********************************************** Ordinary: First-year Calculus (two half courses without second digit 5)______ MATH 1131.03/1132.03 _______ MATH 2310.03 ________ MATH 2030.03_______ MATH 2221.03/2222.03 _______ MATH 3033.03 ________ MATH 3131.03_______ Three additional credits from 3000- or 4000-level AS/MATH courses with the third digit 3 (excluding AS/MATH3230.03 an AS/MATH3330.03). ******************************************** (Substitutions: The requirement MATH 1131.03/1132.03 may be replaced by MATH 2560.03/MATH 2570.03 provided an average of at least B was attained. MATH 2310.03 may be replaced by MATH 2015.03. A student who may wish subsequently to pursue an Honours degree should consider taking MATH 2021.03/MATH 2022.03 rather than MATH 2221.03/2222.03 and MATH 2010.03 instead of MATH 2310.03. If MATH 2010.03 is taken then MATH 3010.03 must be taken as a corequisite with MATH 2030.03.)
FACULTY OF PURE AND APPLIED SCIENCE Faculty Requirements Checklist All candidates must complete the following (in addition to 1000-level MATH requirements): --- 12 credits from SC/BIOL1010.06, SC/CHEM1010.06, SC/EATS1010.06, SC/MATH2041.03 and SC/MATH 2042.03*, SC/PHYS1410.06 or SC/PHYS1010.06; --- 6 credits in each of Humanities and Social Science (no substitutions permitted). ---- at least 3 credits in a COSC course; specifically COSC1540.03 for the Applied Mathematics programmes; COSC1520.03/1530.03 for the Mathematics programmes; one of COSC1020.03-1030.03; COSC1520.03-1530.03; or COSC1540.03 for the Statistics programmes. Degree Programme selection: A student must choose Departmental program(s) in order to complete one of the following degrees: Specialized Honours (Choose 1 such programme) Combined Honours (choose 2 different Honours programmes, e.g. Mathematics and Physics or Applied Mathematics and Statistics) Ordinary Major (Choose 1 Ordinary Programme) Departmental Programs are listed below Total Credit and GPA requirements: Ordinary: a minimum of 90 credits must be completed a minimum of 66 credits must be earned in Science courses, a minimum of 18 credits must be earned in courses at the 3000 or higher level Honours: To declare Honours requires successful completion of at least 24 credits and a minimum cumulative credit-weighted grade-point average of 5.0 over all Science (SC) courses completed. To proceed in each year of an Honours BSc programme requires a minimum cumulative credit-weighted grade-point average of 5.0 over all Science (SC) courses completed. To graduate in an Honours BSc programme requires successful completion of all Faculty requirements and departmental required courses and a minimum cumulative credit-weighted grade-point average of 5.0 over all Science (SC) courses completed. -- at least 120 passed credits must be completed -- a minimum of 90 must be earned in Science courses, -- a minimum of 42 must be earned in courses at the 3000 or higher level; 1. A maximum of 6 credits from 1000-level College courses may be counted towards a BSc degree. 2. All candidates beyond the 1000 level must obtain written approval of their study lists from an authorized member of the Department of Mathematics and Statistics. 3. For the purpose of satisfying departmental degree requirements, the following minimum numbers of credits must be completed within the Department of Mathematics and Statistics: 18 for the Ordinary Programme, 21 for the Combined Honours Programme, 30 for the Specialized Honours Programme. * NOTE: If SC/MATH2041.03 and SC/MATH2042.03 are taken, additional 1000-level Science credits (excluding SC/CHEM1520.04, SC/MATH1500.03, SC/MATH1510.06, SC/MATH1525.03, SC/PHYS1510.04 and all Natural Science courses) must be also taken - as required for total of at least 24 1000-level science credits.
Faculty of Pure and Applied Science Applied Mathematics BSc Programmes I: Specialized Honours, Combined Honours, Ordinary: Programme Core: MATH1013.03/1014.03 or MATH1000.03/1010.03, COSC1540.03, MATH1025.03/2222.03, MATH2015.03/2270.03, MATH2041.03/2042.03, MATH2030.03, MATH3241.03/3242.03 Select additional courses from List 1 below, as indicated by your programme: A: Specialized Honours: Programme Core, MATH3260.03, MATH3410.03 and, if MATH1010.03 has not been completed, MATH3110.03. Select an additional 24 credits from major AS/SC/MATH courses (without second digit 5) at the 3000-level or higher, with at least 15 credits from List 1 of which 12 credits are at the 4000-level or higher. Students are encouraged to enroll in MATH4000.03/06. B: Combined Honours/Ordinary: Programme Core and at least 9 additional credits from major AS/SC/MATH courses (without second digit 5) at the 3000-level or higher, including at least 6 credits selected from List 1. ************************************* LIST 1 MATH3110.03, MATH3131.03, MATH3170.06, MATH3260.03, MATH3270.03, MATH3271.03, MATH3272.03, MATH4141.03, MATH4142.03, MATH4160.03, MATH4170.06, MATH4241.03, MATH4270.03, MATH4430.03, MATH4470.03, MATH4000.03/06 ***************************************** Areas of Concentration: You can concentrate your area of study by selecting courses from one of the following areas (You should make sure that you satisfy all your degree requirements as set out above.) Numerical Analysis: MATH4141, MATH4142, MATH4430, MATH4470 Discrete Applied Math/ Operations Research: MATH3170, MATH3260, MATH4141, MATH4160, MATH4170, MATH4430, MATH4570 Applied Math in Physical Sciences/ Differential Equations: MATH3270, MATH3271, MATH3272, MATH3410, MATH4141, MATH4142, MATH4241, MATH4270, MATH4470, MATH4830 Statistical Applied Math: MATH3131, MATH3132, MATH3033, MATH3034, MATH3230, MATH3330, MATH3430, MATH4230, MATH4430, MATH4630, MATH4730, MATH4830, MATH4930 ************************************** Combined Honours Degrees: Applied Mathematics can be combined with degree programmes in Physics, Chemistry, EATS, Computer Science, Physical Education, Biology, Psychology, Statistics or Pure Mathematics. Students should consult the undergraduate programme directors for details. For example, here are suggested course selections for Combined Honours degrees with Computer Science and with Physics: Computer Science and Applied Mathematics: year1: MATH1013/1014/1025/1090, COSC1020/1030, PHYS1010, SOSC.06 year 2: MATH2015/2270/2090, COSC2001/2011/2021, EATS1010, HUMA.06 year 3: MATH2222/2030/2041/2042/3241/3242, COSC32XX,33XX,34XX plus3 credits from List 1 year 4: 6 credits from List 1, 12 credits in COSC at the 4000-level plus additional credits to satisfy faculty regulations. Physics and Applied Mathematics: year 1: MATH1013/1014/1025, COSC1540, PHYS1010, CHEM1010, SOSC.06 year 2: MATH2015/2222/2041/2042/2270, PHYS2010/2020/2040/2210, HUMA.06 year 3: MATH2030/3241/3242/3271/3410,PHYS2060/3010/3040 year 4: PHYS3210/3020/4010/4020. Select 15 additional credits with at least 3 from List 1.
Faculty of Pure and Applied Science Mathematics BSc Programmes Important: For a summary of Faculty degree requirements please see previous pages. ******************************** Ordinary Programme MATH1300/1310/2310* ______ one of MATH1090.03+/2090.03/2320.03 ______ MATH2221.02/2222.03 ______ 12 Major MATH 3000-level credits _____ ______ * or the corresponding Honours versions + Note that MATH1090.03 may not be taken if any 3000-level MATH course is being (or has been) taken. ************************************* HONOURS (Specialized or Combined) All Honours candidates must complete the following Honours CORE. Additional course requirements for specialized Honours students are indicated below. MATH1000.03/1010.03** ______ one of MATH1090.03+/2090.03/2320.03 ______ MATH2010.03** ______ MATH2021.03/2022.03*** ______ MATH3010.03 ______ MATH3210.03 ______ either MATH3020.06 or both of MATH3131.03/3132.03 _____ ______ 6 4000-level credits from 4000.06/03, 4010.06, 4020.06, 4030.03, 4050.06, 4080.06, 4110.03, 4120.03, 4130.03, 4140.03, 4150.03, 4160.03, 4170.06, 4210.03, 4230.03, 4250.06, 4280.03, 4290.03, 4430.03, 4630.03, 4730.03. + Note that MATH 1090.03 may not be taken if any 3000-level MATH course is being (or has been) taken. ** Courses from the sequences MATH1300/1310/2310 or MATH1013/1014/2015 may be substituted for the corresponding curses in the sequence MATH1000/1010/2010, BUT any student who has not completed MATH1010.03 will have to take MATH3110.03 over and above other programme requirements. *** or MATH2221.03/2222.03 with an A in both; if less than A in either then add an additional one of MATH2090.03 or MATH2320.03. Specialized Honours ______ MATH4010.06 or MATH4020.06 in addition to what was taken as part of Honours CORE. ______ 24 additional major MATH credits. For Combined Honours degrees, careful planning is necessary to ensure that MATH and OTHER prerequisites are met. Consult the undergraduate programme directors.
Faculty of Pure and Applied Science Statistics BSc Programmes Specialized Honours, Combined Honours or Ordinary Important: For a summary of _Faculty_ degree requirements please see previous pages. Specialized Honours: MATH 1000.03/1010.03 ______ MATH 1131.03/1132.03_____ MATH 2021.03/2022.03 ______ MATH 2010.03/3010.03 ______ MATH 2030.03 ______ MATH 3131.03/3132.03 ______ MATH 3210.03 ______ MATH 3033.03/3034.03 ______ MATH 3430.03 _______ 12 credits from 4000-level SC/MATH courses with third digit 3. 9 additional credits from any major (second digit not 5) MATH courses for a total of at least 66 credits in major MATH courses. Combined Honours: First-year calculus (6 credits without second digit 5) ______ MATH 1131.03/1132.03 ______ MATH 2310.03/2030.03 ______ MATH 2221.03/2222.03 ______ MATH 3131.03 ______ MATH 3033.03 ______ 9 additional credits from 3000- or 4000-level SC/MATH courses with third digit 3 (excluding SC/MATH 3230.03 and SC/MATH 3330.03). (Substitutions: Same as for Ordinary programme). NOTES: 1. For Combined Honours degrees, careful planning is necessary to ensure that MATH and OTHER prerequisites are met. Consult the undergraduate programme directors. 2. SC/MATH 3033.03 is strongly recommended but not required for students who enrolled in the Combined Honours Programme in Statistics before 1996/97 and complete 12 credits from 3000- or 4000-level SC/MATH courses with third digit 3 (excluding SC/MATH 3??0.03 and SC/MATH 3330.03) before January, 1999. Ordinary Major: First year calculus (6 credits without second digit 5) ______ MATH 1131.03/1132.03 _____ MATH 2221.03/2222.03 ______ MATH 2030.03 ______ MATH 2310.03 ______ MATH 3131.03 ______ MATH 3033.03 ______ At least 3 additional credits from 3000-or 4000-level SC/MATH courses with third digit 3 (excluding SC/MATH 3230.03 and SC/MATH 3330.03) (Substitutions: MATH 2221.03/MATH 2222.03 may be replaced by either MATH 1025.03/2222.03 or MATH 2021.03/2022.03. MATH 2310.03 may be replaced by either MATH 2010.03 or MATH 2015.03. If MATH 2010.03 is taken then MATH 3010.03 must be taken as a corequisite with MATH 2030.03. MATH 1131.03/1132.03 may be replaced by MATH 2560.03/2570.03 provided an average of B was obtained.)
ADDED Jun 3, 1996 From: "Janice Grant" Date: Mon, 3 Jun 1996 16:10:49 -0400 To: Teachers@mathstat.yorku.ca Subject: 1996-97 sessional dates The following are some of the sessional dates for the next academic session. Monday, September 9, 1996 - First day of classes Saturday and Sunday, September 14 and 15 - Rosh Hashannah - no classes Saturday, September 21, 1996 - last day to enrol in Terms F or Y courses and make changes without the approval of the course director Monday, September 23, 1996 - Yom Kippur - no classes, but University Open Friday, October 4, 1996 - last day to enrol in Term F courses WITH PERMISSION OF THE COURSE DIRECTOR. Monday, October 14, 1996 - Thanksgiving - University Closed Friday, October 18, 1996 - last day to enrol in Term Y courses with the written permission of the Course Director Saturday, November 9, 1996 - last day to withdraw from Term F courses without receiving a grade Wednesday, December 4th - last day of regularly scheduled classes Thursday, December 5th - classes normally scheduled for Mondays will be offered Friday, December 6th - Women's Remembrance Day - no classes will be held between 11:30 and 1:30 Monday, December 9, 1996 - December 23, 1996 - Mid-Term and Final Examinations happen in this period. 1997 Monday, January 6, 1997 - Term Y classes resume and Term W classes begin. Saturday, February 8, 1997 - last day to withdrawn from a Term Y course without receiving a grade. Saturday, March 8, 1997 - last day to withdraw from a Term W course without receiving a grade. Friday, March 28, 1997 - Good Friday - University Closed Monday, April 7, 1997 - Term W and Y classes end. Wednesday, April 9, 1997 - Friday, May 2, 1997 - Final Examinations happen Monday, April 28 - Tuesday, April 29 - Passover - no exams can be held I note in the sessional dates which I have there are separate dates for Atkinson College courses (exams, withdrawal, etc.) - I don't know what to do about them - if you have questions, please ask me. There are other dates which are not sessional - like grades due in, I will let you know closer to the time but the rule of thumb is that grades are due on my desk, 5 days after classes end if you don't have a final exam or 5 days after your final examination.