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Applied Mathematics


Applied Mathematics is motivated mathematics, or mathematics to a purpose. It reflects the belief that there exists a basic order and harmony in the physical world which may be described by the logical structures of mathematics. Thus, it is no coincidence that some of the greatest mathematicians of the past were also interested in engineering and physics.

This rich, classical tradition of Applied Mathematics is typified by the ongoing work in Theoretical and Fluid Mechanics, General Relativity, and Quantum Theory, at the interface among Mathematics, Theoretical Physics, and Engineering, and covering such diverse areas as the study of supersonic flow, the behaviour of ocean waves, the structure of space-time and cosmology, and the fundamental symmetry properties of the world of atoms and molecules. In addition, newer areas, such as Control Theory and Information Theory, analyse processes ranging from optimal control of a space vehicle to the measuring, coding, and transmission of information. As scientists find out more and more about the mechanisms that make the world 'tick', we also find that more, often new, mathematics is necessary to systematize, digest, and take advantage of this wealth of knowledge in all scientific areas. This need is often reflected in a keen interest among applied mathematicians in ordinary and partial differential equations and their discretizations.

In their first two years, all Applied Mathematics students take the same core courses as are taken by other Mathematics students, in order to acquire a sound mathematical background. At the same time, since the application of analytical reasoning to a wide variety of problems is the essence of Applied Mathematics, there is room in the program for introductory courses in scientific disciplines which are heavy users of mathematics, such as Physics or Engineering. In the upper years, the focus is on courses more specifically related to their chosen area of specialization. It is our belief that graduates from any of our programs will find their career opportunities to be excellent and varied.

The Applied Mathematics Department offers four Honours programs, each consisting of the common requirements listed below, plus specific other requirements as given in the individual program descriptions following.

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Requirements Common to All Honours Applied Mathematics Programs

In conjunction with the common degree requirements in Table I in "Degree Requirements", all Honours Applied Mathematics programs must include the Faculty core courses outlined in Table II in "Degree Requirements" and the following courses:

All of
AM 231 Calculus 4
AM 261 Newtonian Mechanics
AM/PMATH 332 Complex Analysis
AM 351 Ordinary Differential Equations
AM 353 Partial Differential Equations 1

All of
PHYS 121 Mechanics, Wave Motion and Heat 1
PHYS 122 Mechanics, Wave Motion and Heat 2

Recommended
AM 251 Elementary Differential Equations and Applications
AM/PMATH 331 Real Analysis

Note
CS 370 may be counted as equivalent to an AM 3xx credit towards an Honours Applied Mathematics degree.

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Honours Applied Mathematics

In conjunction with the common degree requirements in Table I in "Degree Requirements", this program requires at least 26 math half-credits. These overall requirements must include the courses common to all Honours Applied Mathematics programs as given above and the following courses:

Three 400-level AM half-credits

Three additional 300- or 400-level AM half-credits

One additional half-credit chosen from:
CS 370 Numerical Computation
AM/PMATH 331 Real Analysis

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Joint Honours Applied Mathematics

See "Academic Programs" for a complete description of Joint program requirements.

All of
AM 231 Calculus 4
AM 261 Newtonian Mechanics
AM/PMATH 332 Complex Analysis
AM 351 Ordinary Differential Equations
AM 353 Partial Differential Equations 1
Three 400-level AM half-credits

One of
CS 370 Numerical Computation
AM/PMATH 331 Real Analysis
One additional 300- or 400-level AM half-credit

All of
PHYS 121 Mechanics, Wave Motion and Heat 1
PHYS 122 Mechanics, Wave Motion and Heat 2

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Honours Applied Mathematics with Engineering Electives (Co-operative only)

In conjunction with the common degree requirements in Table I in "Degree Requirements", this program requires at least 26 math half-credits. These overall requirements must include the courses common to all Honours Applied Mathematics programs as given above and the following courses:

Three 400-level AM half-credits

Three additional 300- or 400-level AM half-credits

All of
CS 230 Introduction to Computers and Computer Systems

One additional half-credit chosen from:
CS 370 Numerical Computation
AM/PMATH 331 Real Analysis

Two additional half-credits chosen from:
AM/PMATH 331 Real Analysis
CS 334 Data Types and Structures
CS 370 Numerical Computation
C&O 350 Linear Programming
C&O 370 Deterministic OR Models
PMATH 336 Introduction to Group Theory
STAT 333 Applied Probability
STAT 371 Stochastic OR Models
STAT 433 Stochastic Processes

Non-math courses required in Year One

Groups D and E require E&CE 100 in either term 1B or 2A. Group F requires CH E 100/101.

Non-math courses required in Years Two, Three and Four

One course per term from the chosen Engineering Group, normally selected from the following. (Consult the Applied Mathematics Undergraduate Handbook for more detailed listings, including course titles and terms in which the courses are normally taken.)


Group A      M E 219, 220;
             Four of M E 351, CIV E 303, 313, 403, 404, 405, 413, 414

Group B SY DE 252, 281, 372, 381 Two of SY DE 442, 444, 452, 533, 543
Group C M E 219, 250, 351 Three of M E 353, 354, 452, 456, 459, 469, 557, 563
Group D E&CE 100, 241 Four of E&CE 231, 241, 318, 332, 342, 371, 380, 411, 412, 435, 436, 438, 443
Group E E&CE 100, 241 Four of E&CE 261, 342, 362, 370, 380, 463, 465, 481, 482
Group F Six of CH E 100, 101, 021, 023, 025, 026, 030, 035, 036, 041 Optional Courses: CH E 033, 034, 038, 044, CHEM 026, 036

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Honours Applied Mathematics with Physics Electives

In conjunction with the common degree requirements in Table I in "Degree Requirements", this program has the same course requirements as Honours Applied Mathematics, with the following additional courses required in the non-math component of the program:

Six half-credits in the physical sciences, normally selected from:
PHYS 252 Electricity and Magnetism 1
PHYS 253 Electricity and Magnetism 2
PHYS 256 Geometrical and Physical Optics
PHYS 275 Astrophysics 1 - The Solar System
PHYS 358 Thermodynamics
PHYS 359 Statistical Mechanics
PHYS 375 Astrophysics 2 - Stellar Astronomy
PHYS 380 Molecular Biophysics
PHYS 480 Radiation Biophysics
CHEM 120 Physical and Chemical Properties of Matter
CHEM 123 Chemical Reactions, Equilibria, Kinetics

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Honours 'X' with Applied Mathematics Minor

See "Academic Programs" for a complete description of Minor program requirements.

All of
AM 231 Calculus 4
AM 251 Elementary Differential Equations and Applications
AM 343 Discrete Models in Applied Mathematics
AM 351 Ordinary Differential Equations
AM 353 Partial Differential Equations 1
AM 451 Introduction to Dynamical Systems
Two additional 300- or 400-level AM half-credits.

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