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Programmes



Applied Mathematics

The Applied Mathematics Office of the Department of Mathematics and Statistics is located in Room 122 of the Petrie Science Building (736-5248).

The Applied Mathematics Programme aims to give students a solid base of knowledge of mathematics which has 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 (see the section on Career Information). 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.

All students take a common core of courses in Calculus, Differential Equations, Linear Algebra, Symbolic Computing (Maple), and Numerical Analysis. The core of required courses is larger for Honours students. 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 and corresponding recommended courses are:

Numerical Analysis: MATH4141, MATH4142, MATH4470

Discrete Applied Math / Operations Research: MATH3170,
MATH3260, MATH4141, MATH4160, MATH4170,
MATH4430

Applied Math in Physical Sciences / Differential Equations:
MATH3271, MATH3272, MATH3410, MATH4141,
MATH4142, MATH4241, MATH4270, MATH4271,
MATH4470, MATH4830

Statistical Applied Math: MATH3131, MATH3132, MATH
3033, MATH3034, MATH3230, MATH3330, MATH3430,
MATH4230, MATH4430, MATH4630, MATH4730,
MATH4830, MATH4930.

(In all cases, you should make sure that you satisfy all your degree requirements, given in the checklists towards the back of this minicalendar.)
Applied Maths BA checklist
Applied Maths BSc checklist

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 would like further information, please contact
the Programme Director, Prof. Martin Muldoon
(e-mail: muldoon@mathstat.yorku.ca), or the
Programme Secretary, Gillian Moore (736-5248).


Mathematics

The Honours Programmes in Mathematics (BA and BSc) are suitable for students who have a special fondness for mathematics. These Programmes provide an excellent background for many occupations demanding skills in mathematical reasoning and techniques. They are ideal for students who intend to pursue graduate study in mathematics. An Honours programme in mathematics emphasizes the understanding of concepts, abstraction and reasoning; these then become the tools for problem-solving, as well as the language and environment in which problems are solved (``proofs''). Most students who creditably complete a York Honours degree in mathematics are routinely accepted (with financial support included!) into Graduate Schools across North America. Taking mathematics in combination with Computer Science, Statistics, or Economics makes for a very impressive curriculum vitae for a graduate seeking a career in Industry, Government, or Business.

Mathematics is one of the oldest academic disciplines. A mathematician is known as one who has exceptional reasoning, critical thinking, and problem-solving skills. While the public knows of the utility of mathematics, less well known is the fact that most mathematicians do math because they love it. The Honours programmes are designed to help you cultivate this same passion. You will meet like-minded classmates, and you will find that your studies are a rewarding and exciting adventure bringing you to the frontier of scientific discovery.

The Ordinary Programme (BA and BSc) provides a three-year degree in mathematics that is much less demanding than the honours program 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 in 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 for this reason. A student who completes the regular Calculus sequence MATH1300/1310/2310 may later take MATH3110, and use these four half-courses as a substitute for the Honours sequence MATH1000/1010/2010 (currently, 2310 replaces 2010). There is also an arrangement to allow a substitution for the first Honours course in Algebra (MATH2021/2022). However, a student considering an Honours degree in Mathematics should seriously consider enrolling in the Honours courses, since they are designed for those with a genuine interest in Mathematics. In addition, Honours students who wish to switch back, in mid-term, to the Ordinary stream will be accommodated to the extent that the Registrar's Office will allow.


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 a 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 studies in statistics.


Mathematics for Commerce

Mathematics for Commerce is an ideal environment for students who wish to obtain a background in the type of Mathematics that can be applied in a business oriented career. Courses such as Computer Science, 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 become actuaries, investment managers, consultants, analysts, or statisticians. Examples of activities in which they may be involved are: optimization problems, project management, inventory control, forecasting, analysing data, investigating patterns and trends, creating mathematical models, evaluating pension funds, and detemining premiums for life insurance policies. Of course, many of the programme's students also pursue graduate degrees in areas such as Business Administration, Education, Environmental Studies, and Law.

Mathematics for Commerce offers both an Ordinary B. A. Programme and an Honours B. A. Programme.

The Ordinary degree is usually completed in three years and requires a total of 90 credits, subject to both Faculty of Arts and Department of Mathematics and Statistics requirements listed on two separate pages toward the back of this minicalendar.

The Honours degree is usually completed in four years and requires a total of 120 credits, subject to both Faculty of Arts and Department of Mathematics and Statistics requirements listed on two separate pages toward the back of this minicalendar. The Honours degree is offered in two streams:

-
The Actuarial Stream.
An Actuary is a professional concerned with the design and administration of insurance policies, pension plans, government welfare plans, and similar 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 economics 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. Additional information can be found at both http://www.math.yorku.ca/Careers/actuary.html and http://www.soa.org/ , and can also be obtained from Professor David Promislow at 736-5250.

-
The Operations Research Stream.
Operations Research is the scientific study of any problem relating to optimal management of a system. The programmes of study at York can provide the student with the diverse background needed to prepare for work in operations research. The Canadian Operational Research Society (CORS) offers a diploma to students who complete a prescribed array of courses. At York it is possible to earn a CORS diploma and an Honours degree simultaneously. For additional information, please consult http://www.cors.ca or inquire at the Undergraduate Office (N502 Ross).


Career Information



There are available, in both N537 Ross and S525 Ross, a massive ring binder of information on careers that use mathematics, and another, on how to apply for postgraduate studies. Some of this information is already on the Web, linked to the Department's home page; additional pages are under construction. We mention some of the career categories below.

Co-registration in Education

A student seeking a B.Ed. degree pursues this degree concurrently with her or his B.A. or B.Sc.\ degree, beginning normally in the second year at York. For further information contact the Faculty of Education in S835 Ross (736-5001). Note that there are Consecutive Education programmes at several Ontario universities.

The Department places great importance on encouraging and helping students interested in Mathematics Education, in both its undergraduate and its graduate programmes. Professor Pat Rogers, who is jointly appointed with the Faculty of Education, has played a very active role in this area for many years. Concurrent or Consecutive Education students considering mathematics as a teaching subject, and needing advice connected with their programmes, should get in touch with Professor Rogers or Professor Walter Whiteley.

Graduate Studies

York offers several graduate programmes in mathematics and statistics; for details enquire at the Graduate Programme Office in N519 Ross. (Dial 736-2100, extn. 33974, or, to leave a message, 736-5250.) 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. A ring binder of information on applying to graduate schools is available in N537 and S525 Ross.

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 is the best preparation. Further information can be found in a pamphlet available in the Undergraduate Office, N502 Ross.



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 of this programme should be well equipped for further studies in law, medicine, education, journalism, and environmental policy. For more information please consult the STCS minicalendar, available at 205 Bethune College, or contact the Programme Secretary, Ms. Nisa Haniff (736-5164, or extn. 55164 if calling from campus).

Operations Research Diploma

Operations Research (OR) deals with making the ``best'' decision when confronted with many choices as well as a variety of constraints in a large scale problem. Examples of typical problems are: minimizing operating costs in a large hospital while maintaining quality service to patients, finding the shortest route for a delivery truck which has many 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 usually needed to execute the algorithms.

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 students who complete a prescribed set of courses. To get an idea of the employment opportunities for someone with a CORS diploma, one may look through the CORS membership list. The nearly 500 members are from all across Canada as well as from 32 other countries. The CORS members work at 174 companies, institutions, and agencies, of which 64 are colleges or universities. (Some of the larger groups of CORS members in Canada are at various universities.) Outside of academia, some notable groups are at the Department of National Defence (8), CN Rail (7), Air Canada (5), and Ontario Hydro (4). CORS members also work for government agencies (federal, provincial and municipal), international agencies, utility companies, transportation authorities, manufacturing companies, banks and trust companies, and 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 programs. 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. You can find out more about CORS through its web page (http://www.cors.ca).

As we go to press, the faculty liaison for the CORS Diploma for 1998/99 is not known. Please inquire at N522 Ross to learn who will be liaison this year. Students who complete all courses for the diploma should arrange to have a transcript sent to this individual, who will notify CORS to grant the diploma. Further information and membership forms for CORS will also be available from this individual.

Course requirements for the CORS Diploma:

Applied Mathematics:

Specialized Honours or Honours Major students who wish to obtain the CORS Diploma must choose the following courses as part of their degree programme:

1.
MATH3260 3.0, MATH3170 6.0, MATH4170 6.0
2.
at least two of: MATH3131 3.0; MATH3132 3.0;
MATH3033 3.0 or MATH3330 3.0; MATH3034 3.0 or
MATH3230 3.0; MATH4430 3.0; MATH4830 3.0
3.
at least two of: ECON1000 3.0; ECON1010 3.0;
ECON3580 3.0 or MATH/CC4501 3.0* ;
ECON3590 3.0 or MATH/CC4502 3.0*
4.
at least one of MGTS4000 3.0, MGTS4200 3.0,
MGTS4500 3.0, MGTS4550 3.0 (footnote # below).
5.
The following are also recommended for consideration as elective courses in students' programs of study:
MGTS4710 3.0, MGTS4720 3.0.

Mathematics for Commerce:

Mathematics for Commerce students who wish to obtain the CORS Diploma must satisfy 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 6.0.) They must also choose

1.
Item 4. above.
2.
ECON1000 3.0/1010 3.0 or
MATH/CC4501 3.0/4502 3.0*.

Statistics:

Specialized Honours or Honours Major students who wish to obtain the CORS Diploma must choose the following courses as part of their degree program:

1.
MATH3170 6.0, MATH4170 6.0
2.
COSC1520 3.0, COSC1530 3.0
3.
Item 4. above.
4.
Item 3. under Applied Mathematics, above.

* 4501 and 4502 are no longer offered by either MATH or CC (Calumet College).
# Management Science, offered by the Schulich School of Business.



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