Programmes

Applied Mathematics

The Applied Mathematics Office, Department of Mathematics \& Statistics is located in Room 227 of the Petrie Science Building, telephone (416) 736-5248.

The Applied Mathematics Programme stresses areas 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 Science Faculty may pursue a course of study leading to either an Ordinary degree in three years or an Honours degree in four years. Students may combine their studies in Applied Mathematics with another subject, for example, physics, earth and atmospheric science, biology or computer science and thereby graduate with a Combined Honours degree in both subjects. Applied Mathematics students interested in economics, psychology, or any other subject offered by the Arts Faculty, may pursue a combined program by selecting a Major-Minor Honours programme in the Arts Factulty; the Major either in Applied Mathematics or in a subject of choice. For example, an Economics-Applied Mathematics Major-Minor degree would be a very natural combination. All our students are given ample opportunity to take electives in other areas of interest, such as in business administration. We encourage our students to specialize in at least one area of mathematics which has important applications; this is important for career selection.

All students take a common core of six full courses: two courses in Calculus and Differential Equations, one course in Linear Algebra, one 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.

All students entering Applied Mathematics are carefully advised concerning their course of study by a member of the programme. The lecturers in Applied Mathematics courses are available throughout the year for additional counselling and help with specific course-related problems.

If you wish further information, please contact the Programme Secretary, Gillian Moore, or the Director 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 CV. 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 with their colleagues. Cultivate a passion for Mathematics, find some like-minded classmates and you will find obtaining your degree in Mathematics to be a very rewarding experience. Mathematics is one of the oldest academic disciplines and yet continues to be ``new'' and at 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. toolong 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 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 in both our undergraduate programmes and graduate programmes. Several members of our department play a very active role in this area, among them is Professor Pat Rogers who is jointly-appointed with the Faculty of Education. Walter Whiteley has been designated as an advisor for concurrent education students until June 30, 1995. 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 Math2560.03/2570.03; Math2221.03/2222.03 or Math1025.03/2222.03; 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).

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 and are graded so as to be fair. In addition, students who wish to switch back to the ordinary stream will be accomodated 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. It also provides 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 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 program 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 program'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 programs:

(a) The Ordinary B.A. Program in Mathematics for Commerce,
(b) The Honours B.A. Program in Mathematics for Commerce.

(a) The Ordinary degree is usually completed in 3 years and requires a total of 90 credits, subject to Faculty and Department of Mathematics requirements listed in the end pages.

(b) The Honours degree is usually completed in 4 years and requires a total of 120 credits subject to Faculty and Department of Mathematics requirements listed in the end pages. The Honours degree is split into three streams:

(b1) the Actuarial Stream
(b2) the Operations Research Stream
(b3) the General Stream
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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 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. For additional information, please contact Professor Morton Abramson at 736-5250. par

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.

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.


Operations Research

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) offer 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 larger 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 agriculture 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 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 practioners 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 Prof. Neal Madras who will notify CORS to grant the diploma. For further information and membership forms for CORS, please contact Prof. Madras in N623 Ross.

Several events are planned for those students interested in this program. Details will be announced in class. par 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 program:par

The following are also recommended for consideration as elective courses in students' programs of study:
MGTS4710.03; MGTS4720.03.

Mathematics for Commerce:

Mathematics for Commerce students who wish to obtain the CORS Diploma must satisfy the following:

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: