York University

Undergraduate Minicalendar

Fall/Winter 1997/98

The Applied Mathematics Office, Department of Mathematics and Statistics is located in Room 227 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.

Applied Mathematics majors 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 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 and corresponding recommended courses are:

*Numerical Analysis:* MATH4141, MATH4142, MATH4430, MATH4470

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 (in 1996-98, 2310 replaces 2010). There is a similar arrangement to allow a substitution for the first 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 to the ordinary stream will be accommodated to the extent that the Registrar's Office will allow.

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 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 become 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: The Ordinary B.A. Programme and the Honours B.A. Programme.

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

The Honours degree is usually completed in four years, and requires a total of 120 credits, subject to Faculty and Departmental requirements (see preceding paragraph). The Honours degree is offered in each of three streams:

- The 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 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.
- 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. See the next section for a more detailed description. For additional information, please contact Prof. Neal Madras at 736-5250.
- The General Stream.
- This is a new option, designed for students who have followed the requirements of the Ordinary Mathematics for Commerce degree and have achieved sufficiently high grades to 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 and Applied Optimization.