50 courses in the 1990–91 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
(See also Actuarial Science, Applied Mathematics, Combinatorics and Optimization, Computer Science, Mathematics Electives, Pure Mathematics, Statistics.)
Undergraduate Office MC 5115, ext. 3905
Introductory Notes
1. Courses with the following prefixes are offered by the Faculty of Mathematics: ACTSC (Actuarial Science), AM (Applied Mathematics), C&O (Combinatorics and Optimization), CS (Computer Science), MATH (non-departmental Faculty courses), MTHEL (Mathematics Elective), PMATH (Pure Mathematics), STAT (Statistics). The course descriptions appear in ascending order by course number within these groups. Unless otherwise indicated with the course description, and provided space is
available (see Section 6.3 on page _
13:38), these courses are normally open to students in any UW faculty, subject to stated prerequisite requirements (see Section 6.4 on page 13:38).
2. Anumber of mathematics courses are offered at three different levels for BMath degree credit to accommodate the wide variety of students interested in such courses. The most challenging level, Advanced, is intended for exceptionally gifted students in an Honours program. The second level, Honours, is intended for all Honours students not taking the Advanced courses. The third level, General, is intended for students registered in the threeyear General program. In some
Course Descriptions Management Sciences Mathematics
instances, there are also other versions of such courses designed for students in faculties-other than Mathematics.
Advanced courses may always be substituted in lieu of corresponding Honours courses to satisfy Honours BMath degree requirements. Neither the Advanced nor Honours courses listed in Tables If and iil, on pages 13:10 and 13:11, are open to students registered in the threeyear BMath General program. However, in cases where a student registers in the General program following registrations in an Honours program, any successfully completed Advanced or Honours courses may be substituted in lieu
of the corresponding General required courses to satisfy threeyear BMath General degree requirements. Honours Advanced General AM/PMATH PMATH MATH 331 351 322A AM/PMATH PMATH MATH 332 352 322B C&O C&O 230 220 MATH MATH MATH 130A/B 140A/B 113A/B MATH MATH MATH 134A/B ” 144A/B 111A/B MATH MATH MATH 135/136 145/146 111A/B MATH MATH MATH 137/138 147/148 113A/B MATH MATH - MATH 230A/B 240A4/B 220A/B MATH MATH MATH 234A/B 244A/B 224A/B MATH MATH MATH 235 245 225 MATH MATH MATH 237. 247 227 MATH PMATH PMATH 332B 352 322B PMATH PMATH MATH 334 344 324 STAT STAT STAT 230/231 240/241 220/221 STAT STAT 331/332 321/322
Prerequisites involving these core courses will normally be given in terms of the lowest hierarchy level acceptable (e.g. ‘Prereq: MATH 230B' implies that MATH 240B is also acceptable but MATH 220B is not).
3. Courses offered by the Faculty of Mathematics which have been designed with the academic needs
16:93
and backgrounds of students in. other faculties in mind are identified by a note following the course description. Courses in this category include: CS 100, 102, _ 212, 316; MATH 103, 104, 106, 111A/B, 113A/B, 114, 115A/B, 116, 118, 210, 211, 212, 213A/B, 215, 216; STAT 202, 204, 304, 311.
; Courses not offered in the current
academic year are listed at the end of this section.
All students enrolled in one or more of MATH 135, 136, 137, 138, 145, 146, 147, 148, and CS 131, 132 are automatically enrolled in a non-credit lab that is scheduled one evening each week from 7:00 to 9:00 p.m. This time slot appears as a MATH 010 entry on student timetables and is reserved for mid-term tests in the above courses. This time slot is used only on those evenings when mid-term tests are scheduled.
All students enrolled in any secondyear mathematics course offered by the Faculty of Mathematics, with the exception of various service courses ° designed for students in other faculties, are automatically enrolled in a noncredit lab that is scheduled from 4:30 to 6:30 p.m. Tuesday and Thursday each week. This time slot is used only on those days when mid-term tests are scheduled.
An introduction to applications of algebra to business, the behavioural sciences, and the social sciences. Topics will be chosen from set theory, permutations and combinations, binomial theorem, probability theory, systems of linear equations, vectors and matrices, mathematical induction.
Prereq: Grade 12 Mathematics or equivalent
Not open to students in the Faculties of Engineering, Mathematics or Science, or to other students who have credit in any one of Grade 13 Algebra, OAC Algebra, OAC Finite Mathematics, or the equivalent. Other students with two or more Grade 13/OAC math credits require consent of the instructor to enrol in MATH 103.
An introduction to applications of calculus in business, the behavioural sciences, and the social sciences. The models chosen will include the study of polynomial, rational, exponential and logarithmic functions; elementary analytic geometry; linear and quadratic systems of equations. The major concepts introduced to solve problems are: rate of change; optimization; growth and decay; and integration.
Prereq: Grade 12 Mathematics or equivalent
Not open to students in the Faculties of Engineering, Mathematics or Science, or to other students who have credit in Grade 13/OAC Calculus or the equivalent.
Algebraic functions and their graphs; exponential and logarithmic functions; elementary differential and integral calculus; applications and problems associated with kinesiology.
Antireq: MATH 113A, 115A, 116, 130A, 137, 140A, 147
Not open to students in the Faculty of Mathematics. .
Elementary number theory, number , systems, mathematical induction, binomial theorem, complex numbers, polynomiais.
Prereq: Grade 12 Mathematics or equivalent. Grade 13 or OAC Algebra is recommended but not required.
Antireq: MATH 134A, 135, 144A, 145
This course is designed for students in the Faculties of Arts and Science and students in the three-year BMath General program. It cannot be counted for credit toward a BMath Honours or four-year General degree.
Course Descriptions Mathematics
Determinants, vectors, matrices, elementary solid geometry, systems of linear equations.
Prereq: Grade 12 Mathematics or equivalent. Grade 13 or OAC Algebra is recommended but not required. MATH 111A is not a required prerequisite for MATH 1118.
Antireq: MATH 114, 134B, 136, 144B, 146
This course is designed for students in the Faculties of Arts and Science and students in the three-year BMath General program. It cannot be counted for credit toward a BMath Honours or . four-year General degree.
The derivative, differentiation, higher order derivatives, implicit functions, differentials, applications of the derivative. The definite integral. Differentiation and integration of the logarithmic, exponential and trigonometric functions. Prereq: Grade 13 or OAC Calculus Antireq: MATH 106, 115A, 116, 130A, 137, 140A, 147 This course is designed for students in the Faculties of Arts and Science and students in the three-year BMath General program. It cannot be counted for credit toward a BMath Honours or four-year General degree.
Techniques of integration. Indeterminate forms and L'H6pital's rule. Infinite series. Parametric equations, arc length, volumes and surfaces/of revolution. Polar co-ordinates. Elementary differential equations.
Prereq: MATH 113A or equivalent
Antireq: MATH 115B, 118, 130B, 138, 140B, 148
This course is designed for students in the Faculties of Arts and Science and students in the three-year BMath General program. It cannot be counted for credit toward a BMath Honours or four-year General degree.
Matrix algebra. Systems of linear equations. Determinants. Vectors in Euctidean space, lines, planes, spheres. Eigenvalues. Introduction to vector spaces.
Prereq: Grade 13 or OAC Algebra
Antireq: MATH 1118, 134B, 136, 144B, 146
Not open to students in the Faculty of Mathematics.
Real numbers, functions, trig functions. > Limits. The derivative, differentiation, higher order derivatives, implicit functions, differentials, applications of the derivative. The definite integral. Antidifferentiation. Logarithms and exponential functions, hyperbolic and inverse hyperbolic functions..
Prereq: Grade 13.ar OAC Calculus
Antireq: MATH 106, :113A, 116, 130A, 137, T40A:49R
Not open to students in the Faculty of Mathematics. 13.98 2
Techniques of integration. improper integrals. indeterminate forms and 1 L'HOpital's rule. Infinite series. Parametric equations and polar co-ordinates. Partial derivatives. Prereq: MATH 115A Antireq: MATH 113B, 118, 130B, 138, 140B, 148 % Not open to students in the Faculty of Mathematics.
Review of limits and sequences, and inverse functions; the definite integral; techniques and applications of integration; sequences and series of numbers, and convergence.
Prereq: Grade 13 or OAC Calculus
Antireq: MATH 106, 113A, 115A, 130A. 137, 140A, 147
Formerly MATH 110A
Not open to students in the Faculty of Mathematics.
Students) . Approximation and the mean value theorem; power series and applications of power series; functions of two variables and properties of surtaces in space.
Prereq: MATH 116 or equivalent
Antireq: MATH 1138, 1158, 130B, 138, 140B, 148
Formerly MATH 110B
Not open to students in the Faculty of Mathematics.
A study of the basic algebraic systems “of mathematics: the integers, the integers modulo n, the rational numbers, the real numbers, the complex numbers and polynomials.
Prereq: OAC Algebra or equivalent
Antireq: MATH 111A, 134A, 144A, 148
This course replaces MATH. 134A in the Faculty core effective Fall, 1989. MATH 135 is also offered at St. Jerome's College in‘the Rat! term.
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Systems of linear equations and matrices. Determinants. ‘Vector. spaces. Applications selected from graph theory, geometry, least squares problems and error-corracting codes.
Prereq: OAC Algebra or equivalent. MATH 1385 is recommended but not required. . .
Antireq: MATH 111B, 114, 1348, 144B, 146.
This course replaces MATH 134B in the Faculty core effective Winter, 1990. MATH 136 is also offered at St. Jerome's College in the Winter term.
Review of limits and inverse functions. Riemann sums and the definite integral. The fundamental theorem and applications of integration. Introduction to sequences and series; tests for convergence.
Prereq: OAC Calculus or equivalent
Antireq: MATH 106, 113A, 115A, 116, 130A, 140A, 147
This course replaces MATH 130A in the Faculty core effective Fall, 1989. MATH 137 is also offered at St. Jerome's College in the Fall term.
Mean value theorem. L'Hépital's rule. Polynomial approximations and power: series representations. Convergence. Taylor series. An introduction to functions of two variables.
Prereq: MATH 137
Antireq: MATH 1138, 115B, 118, 130B, 140B, 148
This course replaces MATH 130B in the Faculty core effective Winter, 1990. MATH 138 is also offered at St. Jerome's College in the Winter term.
Course Descriptions -
Mathematics
MATH 145 is an advanced-level, enriched version of MATH 135. Prereq: OAC Algebra (or equivalent} and an OAC math average of at least 85%, or consent of instructor Antireq: MATH 111A, 134A, 135, 144A This course replaces MATH 144A effective Fall, 1989.
MATH 146 is an advanced-level, enriched version of MATH 136. Prereaq: MATH 145 or consent of instructor Antireq: MATH 111B, 114, 134B, 136, 144B This course replaces MATH 144B effective Winter, 1990..
MATH 147 is an advanced-level, enriched version of MATH 137. Preraq: OAC Calculus (or equivalent) and an OAC math average of at least 85%, or consent of instructor Antireg: MATH 106, 113A, 115A, 116, 130A, 137, 140A This course replaces MATH 140A effective Fal! 1989.
MATH 148 is an advanced-level, enriched version of MATH 138.
Prereq: MATH 147 or consent of instructor
Antireq: MATH 113B, 115B, 118, 130B, 138, 140B
This course replaces MATH 140B effective Winter, 1990.
Partial differentiation, the gradient, multiple integrals with applications, line and surface integrals, divergence and curl, theorems of Green and Stokes. Applications to physical problems.
Prereq: MATH 118
Antireq: AM 231, MATH 212, 213B, 2208, 230B, 240B
Not open to students in the Faculty of Mathematics.
16:95
Fourier series; Ordinary differential equations; Laplace transform; applications to linear electrical systems.
Prereq: MATH 118
Antireq: MATH 213A, 220A, 227, 230A, 237, 240A, 247
Cross-listed as E&CE 205
Not open to students in the Faculty of Mathematics.
Vector differential calculus. Multiple Integrals. Line and Surface Integrals. Complex analysis: analytic functions, complex integrals, residues. Partial differential equations.
Prereq: MATH 211
Antireq: AM 231, MATH 210, 213B, 220B, 230B, 240B
Cross-listed as E&CE 206
Not open to students in the Faculty of Mathematics.
Infinite series. Partial derivatives, chain rule, total differential, Taylor's theorem, extreme values.
Prereq: MATH 113B or 115B
Coreq: MATH 111B
Antireq: MATH 211, 220A, 227, 230A, 237, 240A, 247
Not open to students in the Faculty of Mathematics.
Muitiple Integrals. Vector calculus: gradient, directional derivative, divergence, curl, line integrals and path independence. Green's theorem, Stokes’ theorem, and Gauss’ theorem. Prereq: MATH 213A or equivalent Antireq: AM 231, MATH 210, 212, 220B, 230B, 2408 Not open to students in the Faculty of Mathematics.
Complex numbers. Partial ditferentiation. Solution of ordinary differential equations with emphasis on special functions encountered in chemistry (Hermite and Legendre equations). Introduction to matrix algebra and eigenvalue problems.
Prereq: MATH 113B or 115B, or equivalent
Antireq: AM 250, MATH 216
Not open to students in the Faculty of Mathematics.
Standard methods of solution. Applications to physical engineering problems. Linear equations with constant coefficients. Systems of differential equations. Solution of differential equations by the Laplace Transformation.
Prereq: One of MATH 1138, 115B, 118, or equivalent
Antireq: AM 250, MATH 215
Not open to students in the Faculty of Mathematics.
Differential calculus for functions of several variables.
Prereq: MATH 130B
Coreq: MATH 134B
Antireq: MATH 211, 213A, 227, 230A, 237, 240A, 247
Not open to Honours Mathematics students.
This course is being replaced by MATH 227 effective Fall, 1990. MATH 220A will not be offered on campus after Fall, 1990.
Double integrals, triple integrals. Line integrals and Green's theorem. Ordinary differential equations.
Prereq: MATH 220A
Antireq: AM 231, MATH 210, 212, 213B, 230B, 240B
Not open to Honours Mathematics students.
This course will not be offered on campus after Winter, 1991.
Linear transformations, eigenvalues, characteristic polynomials, inner products.
Prereq: MATH 134B
Antireq: MATH 225, 234A, 235, 244A, 245
Not open to Honours Mathematics students.
This course is being replaced by MATH 225 effective Fall, 1990. MATH 224A will not be offered on campus after Fall, 1990.
Course Descriptions Mathematics
Elementary group and field theory and other topics in algebra.
Prereq: MATH 134A, 224A
Antireq: MATH 234B, 244B, PMATH 336
Not open to Honours Mathematics students.
This course will not be offered on campus after Winter, 1991.
Linear transformations, eigenvalues and eigenvectors. Applications selected from computer graphics, cryptography, differential equations, quadratic forms, conic sections.
Prereq: MATH 1118 or equivalent
Antireq: MATH 224A, 234A, 235, 244A, 245
Not open to Honours Mathematics students.
This course replaces MATH 224A effective Fall, 1990+
Calculus of functions of several variables. Limits, continuity, differentiability, the chain rule. Taylor's formula. Optimization problems, mappings, the Jacobian. Multiple integrals. Prereq: MATH 1138 or equivalent Coreq: MATH 1118 or equivalent Antireq: MATH 211, 213A, 220A, 230A, 237, 240A, 247 Not open to Honours Mathematics Students This course replaces MATH 220A effective Fall, 1990.
Differential caiculus of functions of several variables; limits and continuity, partial derivatives, differentiability, chain rule, Taylor's formula, extreme values, mappings and Jacobians.
Prereq: MATH 130B
-Goreq: MATH 134B
Antireq: MATH 211, 213A, 220A, 227, 237, 240A, 247
This course is being replaced in the Faculty core by MATH 237 effective Fall, 1990. MATH 230A will not be offered after Fall, 1990.
. 231 effective Wiatas
Integral calculus of.functions of several variables; multiple integrals, iterated integrals; change of variables, applica: tions to area and volume calculations. Line integrals, Green's Theorem and path independence. Sequences and series of functions; uniform convergence and power series.
Prereq: MATH 230A
Antireq: AM 231, MATH 210, 212, 213B, 220R, FOB bs
This co SE, ERR replaced by AL fae, 1991. MATH 2308 will not be offered after Fall, 1990.
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Groups, fields and other topics in abstract algebra.
Prereq: MATH 134A, 234A
Antireq: MATH 2248, 244B, PMATt 336
This course is being replaced by PMATH 336 effective Winter, 1997. MATH 2348 will nat | be offered after Fall, 1990..
Linear transformations, eigenvalues, and eigenvectors. Applications selected from computer graphics, cryptography, differential equations, quad-- ratic forms, conic sections. : Prereq: MATH 136 Antireg: MATH 224A, 225, 234A, 244A, 245 / This course replaces MATH 234<A ir the Faculty core effective Fall, 1990. MATH 235 is also offered at St. Jerome's College in the Fall and Winter ‘terms. '
Calculus of functions of several vari- : ables. Limits, continuity, differentiability the chain rule, Taylor's formula. Opti-. mization problems, mappings, the Jaccbian. Multiple integrals.
Prereq: MATH 138
Coreq: MATH 136
Antireq: MATH 211, 213A, 220A, 227, 230A, 240A, 247
This course replaces MATH 230A in the Faculty core effective Fall, 1990. MATH 237 is also offered at St. Jerome's College in the Fall and Winte, terms.
4ATH 240B F,W,S 3C .0.5 Advanced Calculus 2 MATH 240B is an advanced-level, anriched version of MATH 230B. Prereg: MATH 240A or consent of wtructor Antireg: AM 231, MATH 210, 212, 213B, 2208, 230B This course will not be offered after ‘all, 1990.
AATH 244A is an advanced-level, nriched version of MATH'234A. ° Prereq: MATH 144B or consent of instructor mos Antirag: MATH 224A, 225, 234A, 995, 245 This course is being replaced by MATH 245 effective Fall, 1990. MATH
244A will not be offered after Fall, 1990.
MATH 245 is an advanced-level, nriched version of MATH 235. Prereq: MATH 146 or consent of ~structor Antirag: MATH 224A, 225, 234A, 235, 244A This course replaces MATH 244A ‘active Fall, 1990.
4ATH 247 is an advanced-level, unriched version of MATH 237. Prereq: MATH 148 or consent of instructor Coreg: MATH 136 or 146 Antireaq: MATH 211, 213A, 220A, 227, 230A, 237, 240A This course replaces MATH 240A ‘active Fall, 1990.
-AATH 322A F 3C 0.5 Introduction to Real Analysis Sequences and series, functions and ‘ontinuity, Laplace transforms, Fourier eries, applications. Prereq: MATH 220A. MATH 220B is recommended but not required. Antireq: AM/PMATH 331, PMATH 351 Not open to Honours Mathematics Studenis. This course will not be offered on campus after Fall, 1991.
Course Descriptions Mathematics
Complex numbers; continuity, differentiability, analyticity of functions: the Cauchy-Riemann equations; solution of Laplace's equation; conformal mapping by elementary functions, and applica- - tions; the Cauchy and ailied theorems; Taylor and Laurent expansions, uniform convergence and power series; the residue calculus, and applications. The emphasis will be on applications.
Prereq: MATH 220B
Antireq: AM/PMATH 332, MATH 332B, PMATH 352
Not open to Honours Mathematics students.
This course will not be offered on campus after Winter, 1992.
Topics in abstract algebra: groups, rings, fields and applications. Prereq: MATH 224B Antireg: PMATH 334, 344 Not open to Honours Mathematics students. This course will not be offered on campus after Fall, 1991.
Not offered in 1990–91.
Not offered in 1990–91.
Groups, subgroups, normal subgroups, “uotient groups, morphisms. Products
f groups. Permutation groups.
ymmetry groups.
Prereq: MATH 135, 235
Antireq: MATH 2248, 234B, 244B
Formerly MATH 234B
This course replaces MATH 234B effective Winter, 1991.
» PMATH 340 W 3C 0.5 ‘lementary Number Theory .n elementary approach to the theory of numbers; the Euclidean algorithm, congruence equations, multiplicative anctions, solutions to Diophantine quations, continued fractions, and .ational approximations to real numbers. Preraq: MATH 224B of 225 Antireq: PMATH 440 This course will be of interest to all math students.
-bstract Algebra 1 ultroduction to group theory, permutations, homomorphisms, subgroups, and "ormal subgroups, factor groups, agrange’s theorem, finite Abelian roups. Rings, ideals, modules, domains, Principal Ideal Domains, Euclidean aigorithms, Unique Factoriation Domains, finitely generated yodules over Principal Ideal Domains, applications to finite Abelian groups and Jordan cancnical form. Prereq: MATH 235 Antireg: MATH 324, PMATH 336 PMATH 343 may be substituted for PMATH 336 whenever the Iatter is a requirement in an Honours program.
Groups, rings, fields and applications.
Prereq: MATH 134A, 234A or MATH
35, 235
Antireq: MATH 324, PMATH 334
PMATH 344 may be substituted for PMATH 334 whenever this is a requirenent in an Honours program.
This version of PMATH 344 will be
affared for the last time in Fall, 1990.
Course Descriptions ©