MATH 100 Commercial Law for Mathematics Students
Contract law. Agency. The law of banking. Real estate law. Insurance law. Partnership law. Company law. The law of intellectual property.
Computer Science (MATH)
179 courses in the 1975–76 Undergraduate Calendar, read from the scanned original. The text comes from OCR, so check the scanned page before relying on a detail.
Notes
® Statistics and Computer Science
* Pure Mathematics
* Chemistry
Course Descriptions 357 Mathematics “.
Department of Combinatorics and Optimization
Faculty listed in 1975–76
Professor, Chairman of the Department R.C. Mullin, B.A.(Western), Ph.D.(Waterloo)
Distinguished Professor W.T. Tutte, Ph.D.(Cantab.), F.R.S.C.
Professors
Faculty listed in 1975–76
G. Berman, M.A., Ph.D.(Toronto)
HLF. Davis, Ph.D.(M.1.T.)
Faculty listed in 1975–76
J. Edmonds, B.A.(Geo. Washington),.M.S.(Maryland) K.D. Fryer, B.A.(Western), Ph.D.(Toronto)
P.L. Hammer, Ph.D.Math.(Bucharest)
Faculty listed in 1975–76
R.C. Read, M.A.(Cantab.), Ph.D{London)
Associate Professors
J.A. Bondy, D.Phil.(Oxon.)
C.E. Haff, B.S.(Stanford), Ph.D.(Waterloo)
Faculty listed in 1975–76
R.A. Honsberger, B.A.(Toronto), M.A.(Waterloo)
U.S.R. Murty, M.A (Osmania), Ph.D(Indian Stat. Inst.)
H. Shank, M.Sc.(Chicago), Ph.D.(Cornell)
D.H. Younger, Ph.D.(Columbia)
M. Best, M.Math.(Waterloo), Ph.D(U.C. Berkeley)
Assistant Professors
R.N. Burns, B.Sce.(Toronto), Ph.D (Waterloo)
Faculty listed in 1975–76
A.R. Conn, B.Sc.(Imperial College), M.Sc.(Manitoba), Ph.D.(Waterloo)
G.B. Faulkner, B.A.Sce.(Toronto), Ph.D.(Waterloo)
D.M. Jackson, Ph.D.(Cantab.)
P. Schellenberg, Ph.D.(Waterloo)
Faculty listed in 1975–76
Lecturer, Assistant Chairman Administration E. Anderson, B.A.(McMaster)
Lecturers.
R.G. Dunkley, B.A.(Western)
Faculty listed in 1975–76
R.G. Scoins, B.A.(Western), M.Math.(Waterloo) P. Zima, M.Sc.(Prague)
Postdoctoral Fellows
Faculty listed in 1975–76
F.R. Bernhart, M.S.(Michigan), Ph.D.(Kansas State) C. Charalambous, B.Sc.(Surrey), Ph.D.(McMaster) C. Huang, B.A.Dublin), Ph.D.(McMaster)
Adjunct Professors
E.L. Johnson, B.S.(Georgia Tech.), Ph.D(U.C. Berkeley).
C.St. J.A. Nash-Williams, Ph.D.(Cantab.), F.R.S.E.
Faculty listed in 1975–76
R.G. Stanton, B.A.(Western), Ph.D.(Toronto)
RE. Woolsey, Ph.D.(Texas)
” 3358
Department of Computer Science
Faculty listed in 1975–76
Professor, Chairman of the Department J.D. Lawson, B.A.Sc.(Toronto), Ph.D.(Waterloo), F.LM.A.
Professor, Associate Chairman of the Department W.M. Gentleman,® B.Sc.(McGill), Ph.D.(Princeton)
Professors J.A. Brzozowski, M.A.Sc.(Toronto), Ph.D.(Princeton)
P.C. Fischer, M.B.A.(Michigan), Ph.D.(M.1.T.), F.S.A.
(On leave, 1975-76)
B. Forte,’ Ph.D.(Pisa), Habil.D.Sc.(Rome)
C. Froese Fischer,? 4.4 (U.B.C.), Ph.D.(Cantab.) (On leave, 1975-76)
J.W. Graham, M.A.(Toronto)
Faculty listed in 1975–76
T. Pietrzykowski, M.A (Warsaw), Ph.D(Polish Acad. Sci.)
Associate Professors
Faculty listed in 1975–76
E.A. Ashcroft, B.A.(Cantab.), Ph.D.(Imperial College)
D.D. Cowan, B.A.Sc.(Toronto), Ph.D.(Waterloo)
K. Culik, M.Sc., R.N.Dr.(Prague), Ph.D.
(Czechoslovak Acad. Sci.)
Faculty listed in 1975–76
J.A. George, M.Sc.(Alberta), Ph.D (Stanford)
J.G. Linders, M.A.Sc.(Toronto), Ph.D (imperial College)
E.G. Manning, M.Sc.(Waterloo), Ph.D.(llinois)
R.B. Simpson, M.A .Sc.(Toronto), Ph.D (Maryland)
Assistant Professors R. Benesch, M.Sc.(Alberta), Ph.D.(Queen’s) P.C. Brillinger, B.A.(McMaster), M.A .(Waterloo} K.O. Geddes, B.A.(Saskatchewan), M.Sc., Ph.D. (Toronto) J.F. Gentleman,t M.S.(Chicago), Ph.D.{(Waterloo) J. Majithia,=>B.Sc.(London), M.Eng., Ph.D.(McMaster) M. Malcolm, B.Sc., M.S.Eng.(Denver) M.S., Ph.D.(Stanford) D.E. Morgan, B.Sc.(Rose Polytechnic Inst.), M.S. (Michigan), Ph.D.(Waterloo) . J.I. Munro, B.A..New Brunswick), M.Sc{U.B.C.), Ph.D (Toronto) C.T. Ng. B.Sc.(Chinese Univ.}), Ph.D.(Waterloo) R.W. Peebles, B.Sc.(McGill), Ph.D.(Pennsylvania) L.D. Rogers, B.Se.(McGill), Ph.D.(Waterloo) G. Sager, Ph.D.(Washington) F.W. Tompa, Sc.M.(Brown), Ph.D.(Toronto) J.H. Vellinga, B.A.(Western), M.A.(Waterloo) (part-time) /
Course Descriptions og Mathematics
Research Assistant Professors
E.J.H. Chang, B.Sc.(Manitoba), M.D.(U.B.C.), M.Math(Waterloo)
Faculty listed in 1975–76
C.M. Hoffman, Vordiplom(Hamburg), M.A.{Indiana), Ph.D.(Wisconsin)
TS.E. Maibaum, B.Sc.(Toronto), Ph.D.(London)
R.T. Moenck, B.Sc.(Sussex), M.Sc., Ph.D.(Toronto)
J.W. Welch, B.Sc.(McGill), Ph.D.(Waterloo)
Lecturers
R.J. Beach, M.Math.(Waterloo)
V.A. Dyck, M.Math.(Waterloo)
MI. Irland, M.Se.(flinois), M.Phil.(Waterloo) J.A. Smith, M.Sc.(Waterloo)
Faculty listed in 1975–76
Postdoctoral Fellow P.H. Morris, M.Sc.(Nat. Univ.ireland), Ph.D. (U.C. Irvine)
Adjunct Professors
P.H. Dirksen,® M.A .(Waterloo)
Faculty listed in 1975–76
E.L. Robertson, B.Sc.(California Inst. Tech.), Ph.D. (Wisconsin)
Faculty Members holding cross-appointments as
shown
1 Applied Mathematics and Statistics and Computer Science
* Applied Mathematics and Computer Science
3? Computer Science and Statistics
* Statistics and Computer Science
5 Electrical Engineering and Computer Science
° Director, Computing Centre
Department of Pure Mathematics
Faculty listed in 1975–76
Associate Professor, Chairman of the Department A. Kerr-Lawson, B.A.(Toronto), M.A.(Chicago) Ph.D (McMaster)
Distinguished Professor J. Aczel, Ph.D.(Budapest), Habil.D.Sc.(Hungarian Acad. Sci.), F.R.S.C.
Professors .
HLH. Crapo, A.B.E.(Michigan), Ph.D(M.1L.T.)
Faculty listed in 1975–76
G.E. Cross, M.A.(Dathousie), Ph.D.(U.B.C.)
D.Z. Djokovic, Ph.D.(Belgrad)
H. Haruki, Ph.D.(Osaka)
Faculty listed in 1975–76
P.N. Hoffman, B.A.(Toronto), Ph.D (Manchester) M.A. McKiernan,' M.A.(Loyola), Ph.D.(1.1.T.)
R.A. Staal, Ph.D.(Toronto)
Faculty listed in 1975–76
D.B. Sumner, [email protected].(Cantab.), D.Phil (Witwatersrand) J.W. Tucker,’? B.Sc.(London), Ph.D.(London)
Associate Professors
Faculty listed in 1975–76
J.G. Anderson, M.Sc.(Durham), Ph.D.(Newcastle)
J.A. Baker, M.A.(Saskatchewan), Ph.D.(Waterloo)
S.N. Burris, Ph.D(Oklahoma)
Y. Chen, M.Ph.(Frankfurt), Ph.D.(Bochum)
G. Dankert, Dip.Math.(T.U. Hanover), Ph.D. (Cologne)
Faculty listed in 1975–76
W.J. Gilbert, M.A.(Cantab.), D.Phil.(Oxon.)
D.A. Higgs, B.Sc.Hons. (Witwatersrand), M.A. (Cantab.), Ph.D.(McMaster)
P.L. Kannappan, B.Sc.(Annamalia), Ph.D. (Washington)
D. Mowat,® Ph.D.(Waterloo)
F.C.Y. Tang, B.Se.(Hong Kong), M.S.(South Carolina), Ph.D.(Ilinois)
Faculty listed in 1975–76
Associate Professor of Foundations of Mathematics P. de Witte, M.Sc.Theor.Phys.(Ghent), M.Sc.Math., ‘Ph.D.(Brussels)
Assistant Professors
L.J. Cummings, Ph.D.(U.B.C.)
Faculty listed in 1975–76
LJ. Dickey, M.A.(Arizona), Ph.D.(Wisconsin)
J. Malzan, Ph.D.(Toronto)
Faculty listed in 1975–76
E.M. Moskal, B.A (Toronto), Ph.D (Ilinois)
K.A. Rowe, B.S.(Toronto), M.S{Wisconsin), Ph.D (Iinois)
Faculty Members holding cross appointments as shown
1 Pure Mathematics and Applied Mathematics
® Pure Mathematics and Philosophy
* St. Jerome’s and Pure Mathematics
Course Descriptions 359 Mathematics
Department of Statistics
Faculty listed in 1975–76
Professor, Chairman of the Department J.G. Kalbfleisch, Ph.D.(Waterloo)
Professors
G.A., Barnard, M.A., D.Sc.(Cambridge)
W.F. Forbes, Ph.D., D.Sc(London), D.LC.
B. Forte,’ Ph.D.(Pisa), Habil.D.Sc.(Rome)
Faculty listed in 1975–76
V.P. Godambe, M.Sc.(Bombay), Ph.D(London)
P.M. Reilly,? B.A.Sc.(Toronto), D.LC., Ph.D. (London), F.S.S.
D.A. Sprott? Ph.D.(Toronto)
Faculty listed in 1975–76
M.D. Vogel-Sprott,' B.A.McMaster), Ph.D.(Toronto)
Associate Professors
G.W. Bennett, Ph.D.( Adelaide)
Faculty listed in 1975–76
M.A. Bennett, B.A.(Nottingham), F.S.A., F.C.LA.
W.H. Cherry, Ph.D.(Melbourne)
Faculty listed in 1975–76
W.M. Gentleman,° B.Sc.(McGill), Ph.D (Princeton)
LD. Kaibfleisch, Ph.D.(Waterloo)
J.F. Lawless, Ph.D.(Waterloo)
WSS. Rickert, Ph.D. Waterloo)
Faculty listed in 1975–76
K.R. Shah, M.A.(Bombay), Ph.D (Indian Stat. Inst.)
M.E. Thompson, B.Sc.(Toronto), Ph.D.{Illinois)
R.V. Thysell,! B.Sc.(Montana), Ph.D (lowa)
J.C. Young, B.A.Sc.(Toronto), M.Sc.(Waterloo), Ph.D. (Edinburgh)
Assistant Professors
K.S. Brown, Ph.D.(Waterloo)
Faculty listed in 1975–76
B.L. Eyford, B.Sc.(U.B.C.), Ph.D (Southampton) J.F. Gentleman,® M.S.(Chicago), Ph.D.(Waterloo) J.C. Robinson, M.A.Sc., P.Eng., Ph.D (Waterloo) J.B. Whitney, M.A.(Western), Ph.D.(Toronto)
Research Assistant Professor P.A. McBride-Warren, B.A.(Datlas), Ph.D.(Kansas State)
Lecturers
R.L.Brown, B.Math.(Waterloo), A.S.A.
Faculty listed in 1975–76
F. Reynolds, M.Sc.(Manitoba), F.S.A., F.C.1.A. C. Springer, M.Sc.(McGill)
Instructors S. Esterby, M.Math.(Waterloo) I. McLeod, M.Math.(Waterloo)
300! chs
Postdoctoral Fellows
J.A. Chapman, Ph.D.(Waterloo)
J.A. Jackson, M.A.(Cambridge), M.B., B.Chir. (Cambridge)
Faculty listed in 1975–76
R.R. Knispel, M.Sc.(Toledo), Ph.D (Montana State)
C.Y. Lee, M.Se., Ph.D.(Simon Fraser)
I. Rabinovitch, B.Se(McGill), Ph.D.(Dartmouth)
Adjunct Professors
LP. Fellegi, Ph.D.(Carleton)
A. Finch, Ph.D., D.Sc.(London), DIC.
R.C. Frecker, B.Sc.(Memorial), M.D(Dalhousie)
Faculty listed in 1975–76
M. Zelen, B.Sc.(City College, New York), M.A. (North Carolina), Ph.D.(American)
Faculty Members holding cross-appointments
as shown
1 Applied Mathematics and Statistics and Computer Science
* Chemical Engineering and Statistics
® Statistics and Psychology
‘ Psychology and Statistics
5 Computer Science and Statistics
® Statistics and Computer Science
Strategy Board Members
University of Waterloo Faculty of Mathematics RS. Aberg
General Manager
Corporate Planning
Shell Canada Limited
W.R. Clark
General Manager
Personnel and Community Relations Simpsons, Limited
R.G. Clifford
Vice President
Central Region
IBM Canada Limited
P.D. Drouillard
Assistant Director General Planning and Evaluation
Public Service Canada
W.A.R. MacFadden
Partner
Coopers and Lybrand
J.V. Masterman
Vice President (Operations)
Mutual Life Assurance Co. of Canada E. L. Pursey
Comptroller
Canadian Imperial Bank of Commerce Dr. C.D. Sadleir
Manager.
Information Systems
Reed Paper Ltd.
GF. Sekely
Director
Information Systems
Canadian Pacific Limited
H.J.M. Watson
Assistant Comptroller Management Information Services The Steel Company of Canada Ltd. R.P. Wismer
Manager
Systems Development
Noranda Mines Limited
D.T. Wright
Deputy Provincial Secretary Secretariat for Social Development Province of Ontario
The University of Waterloo Strategy Board was established to provide liaison between the Faculty of Mathematics and knowledgeable representatives from key sectors of the economy. Board meetings are normally held twice a year.
Electives for Mathematics Students
The following courses may be counted as nonmathematics electives by mathematics students.
Mthel 206 may be taken only by students in the Co-operative Mathematics Teaching Option.
MATH 101A Applications of Mathematics
Math 101, 201, 301 and 401 is a sequence of courses designed to illustrate the representation of a real situation by a mathematical model. The mathematical techniques necessary to formulate the model and to discuss its behaviour are developed as required. Exarnples will be taken from diverse fields since one of the aims of the course is to formulate models to describe unfamiliar situation.
a) First term: Models using difference equations will be formulated for examples drawn from biology, ecology, economics and psychology.
3 hours lectures, 1 hour tutorial. Fall term
MATH 101B Applications of Mathematics
See preamble to Mathematics 101a.
b) Sets of difference equations, probability and matrix theory will be used to describe models from biology, ecology, economics, psychology and physiology.
3 hours lectures, 1 hour tutorial. Winter term
MATH 201A Applications of Mathematics
See Mthel 101a.
Ordinary differential equations will be applied to models drawn from biology, economics, physiology and physics.
2 hours lectures, 1 hour tutorial
Prerequisite: M101, 120, 230 or consent of instructor
MATH 201B Applications of Mathematics
See Mthel 201a.
Other examples from biology, ecology, economics, physiology and physics will be discussed using sets of differential equations.
2 hours lectures, I hour tutorial
Prerequisite: M20la
Course Descriptions 361 Mathematics
MATH 206A Introduction to Mathematics Education
Current trends in education, professional practices and administration, the role of the department head, lesson planning, techniques of teaching, evaluation of students, special students, extra-curricular activities, the relationship between elementary and secondary school mathematics, audio-visual materials, current text books.
Note Mthel 206a is offered only to students in the Co-op Teaching Option
Mthel 3012 Applications of Mathematics
See Mthel 101a.
Partial differential equations are applied to diffusion processes, blood flow and wave phenomena.
2 hours lectures, 1 hour tutorial
Prerequisite: M217 or equivalent, or consent of instructor
MATH 301B Applications of Mathematics
See Mthel 301a.
Laplace transforms are applied to problems in ecology, physiology and other fields.
2 hours lectures, 1 hour tutorial
Prerequisite: M217 or equivalent, or consent of instructor
MATH 302 Applications of Mathematics to the Biological Sciences
The course material has been selected with particular reference to some of the fundamentals of Medical Science including Macromolecular processes, Environmental Health, Genetics and aging processes and quantitative models which describe events in these areas.
2 hours lectures, 1 hour tutorial
Note: 302 may not be counted as Mathematics credit but may be counted as an elective credit.
MATH 304A Foundations of Mathematics
An introduction to the problems of the foundations of mathematics. This course will normally be taken in third or fourth year. It will be an elective credit for mathematics students.
3 hours lectures .
Prerequisite: Consent of instructor
MATH 304B Foundations of Probability Theory
An introduction to the problems of the foundations of probability theory. This course will normally be taken in third or fourth year. It will be an elective credit for mathematics students.
3 hours lectures
Prerequisite: Consent of instructor
MATH 401A Applications of Mathematics
See Mthel 101a.
Integral equations and integral transforms will be applied to systems with memory.
2 hours lectures. Fall term
Prerequisite: Consent of instructor
MATH 401B Applications of Mathematics
See Mathematics 401a.
Students will construct a model and interpret it as a project.
2 hours lectures. Winter term
Prerequisite: Consent of instructor
MATH 402 Topics in Mathematical Aspects of Chemistry, Biology, and the Medical Sciences
Subjects will be selected from areas such as epidemiology and mathematical models of disease processes including heart disease, cancer and aging. Consideration will be given to the quantitative evaluation of the role of environmental factors important in human disease processes.
2 hours lectures
Prerequisite: M302 or consent of the instructor
Course Descriptions
Mathematics
Undergraduate Course Descriptions
Note
The number of hours or lectures shown after the course description is an attempt to indicate the “normal”; each instructor determines how often his particular class will meet.
12 Calculus 1
Differential and integral calculus of functions of one real variable. Transcendental functions. Integration techniques. Applications to rate, max./min., area, volume, moment, fluid pressure and work problems. Parametric and polar equations. Series of constants; power series; Taylor and Maclaurin series.
3 hours lectures, 3 hour tutorials, 2 hours labs
21 Algebra and Vector Geometry
Complex numbers. Matrix algebra. Systems of linear equations. Vectors in Euclidean space, lines, planes, hyperplanes, spheres. Determinants. Subspaces of Cartesian space and matrices. Linear transformations, eigenvalue problems. Linear programming.
3 hours lectures, I hour problems
22 Calculus 2 (For Chemical Engineers)
Partial differentiation, the gradient, multiple integrals with applications, line and surface integrals, divergence and curl, theorems of Green and Stokes. Applications to physical problems.
3 hours lectures, one term
25 Calculus 2 (For Electrical Engineers)
Differential calculus of functions of several variables. Differential equation. Multiple integrals. Prerequisite: M12 or equivalent
31 Differential Equations
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.
3 hours lectures
32 Numerical Analysis
A survey of numerical procedures with emphasis upon computer implementation using the FORTRAN 1V programming language. Topics include: interpolation, curve fitting, solution of non-linear equations, numerical integration, numerical solution of ordinary and partial differential equations, matrix algebra and solution of systems of linear equations.
2 hours lectures, 2 hours problems, one term
Offered in the Fall and Spring terms
Prerequisite: An introductory programming course
35 Advanced Calculus (for Electrical Engineers) Fourier series. Partial differential equations: sepa- . ration of variables, wave equations, heat equation and Laplace’s equation. Fourier integral. Properties of complex analytic functions. Complex integration. 2 lectures, 1 hour problems, one term
44 Complex Variable
Cauchy-Reimann equations, the Cauchy integral theorems, conformal mapping, the Taylor and Laurent series, contour integration.
2 lectures, ] hour problems, one term
§1 Probability and Statistics
Frequency distributions; probability; Binomial, Normal, Poisson laws. Sampling theory. Distribution of Chi-squared, F, and t. Hypothesis testing, quality control, regression theory. Curve fitting. Analysis of variance, introduction to experimental design.
3 lectures, 2 hours problems, one term
§2 Applied Probability and Statistics
(for Mechanical Engineers)
Axiomatic development of probability. Conditional probability, Bayes’ Theorem and independence. Permutations and combinations as related to probability. Discrete and continuous random variables. Special cases of uniform, binomial, Poisson, normal, etc. distributions. Mathematical expectation and moment generating functions, Derived distributions. Sampling from a normal population. Elements of decision theory. Various methods of estimating parameters and testing hypotheses. °
3 hours lectures, I hour tutorial, one term
Note This course is cross listed in Management Sciences as MS2!.
73a Introduction to Solving Business Problems - by Computer
An introduction to algorithms with emphasis on the solution of mathematical problems arising in the business world. Concept and properties of an algorithm, language and notation for describing algorithms. Analysis of problems, development of models and algorithms for their solution; implementation in procedure oriented languages (FORTRAN IV and BASIC) and the execution of these programs using several computing facilities.
2 hours lectures, 2 hours tutorial, one term
Offered in the Fall and Winter terms
Note Math 73a is a prerequisite for Math 73b, 73c and 73d
, Course Descriptions . 363
Mathematics
Note Only one of Math 73a, 112a and 122a can be taken for credit.
Note Math 73a cannot be counted for credit towards a B.Math degree.
73b Modelling & Simulation for Business Applications
This course is intended to introduce students to the techniques of modelling, simulation asd analysis of business systems. Simulation is developed as an effective tool for studying various types of business system environments. Students will be required to develop and run simulation models using both GPSS and dynamo programming languages.
3 hours lectures, Winter term
Prerequisite: Math 73a or the equivalent. An introductory statistics course
Note Math 73b cannot be counted for credit toward a B.Math degree.
73c The Computing Process
This course is designed for the student who will encounter computing facilities in his or her career and must have an understanding of the terminology, hardware (computing machinery), software (computer programs), and financial and management aspects of the computing process. Topics include: historical development of computing machinery and programming languages; methods of job processing; development/ maintenance of application programs; organization and management of a computer installation; uses of specialized applications packages.
2 hours lectures, Winter term
Prerequisite: Math 73a or the equivalent
Note Math 73c was formerly called Math 72b.
Note Only one of Math 73c, 112b can be taken for credit.
Note Math 73c cannot be counted for credit towards a B.Math degree.
364 ..
73d Introduction to File Processing
File processing is an integral part of most commercial applications, This course will give a thorough introduction to the most common file processing techniques such as file maintenance, sorting and report generation. Language and notation for describing such algorithms. Analysis of problems dealing with files, and develo-ment of ‘algorithms for their solution. Introduction to procedure-oriented: languages (usually COBOL) for solving such problems.
2 hours lectures, 2 hours tutorial (laboratory).
Fall term
Prerequisite: Math 73a or the equivalent
Note Math 73d was formerly called Math 72a.
Note Credit wiil only be granted for one of Math 73d or
MATH 132A Note
Math 73d cannot be counted for credit towards a B.Math degree.
81 Introduction to Functions, Analytic Geometry, and Calculus
Polynomial functions. Inverse of a function. Rational functions. Exponential functions and identities. The straight line. Conic sections. Problems solved by analytic means. Simple transformation. The limit concept and an introduction to calculus including the derivative and its application to graph sketching.
2 hours lectures —
82 Introduction to Algebra
Properties of real numbers including inequalities and absolute value. Systems of equations in two and three variables including linear, quadratic, and cubic
-equations. Complex numbers and polar representation.
Exponents. Permutations and combinations. The Binominal Theorem. Sequences and series. 2 hours lectures
83 Introductory Mathematics for Sociology Students Set Theory, Permutations and Combinations, Vectors and Matrices, Probability Theory, Solution of Linear Equations, Game Theory, Linear Programming.
2 hours lectures, 2 hours problems lab (alternate weeks)
2 term.
Course Descriptions Mathematics
84 Algebra
A special course designed for students i in Psychology and related subjects.
Polynomial, rational, exponential and trigonometric functions. Elementary analytic geometry. Polar coordinates. Fundamental concepts in the Calculus. Linear and quadratic systems of equations. Vectors, complex numbers. Mathematical Induction. Permutations and combinations, the Binomial theorem.
2 hours lectures, 2 hours problems lab (alternate weeks)
85 Mathematics for Environmental Studies Quantitative analysis in environmental research. Elementary concepts in Algebra, notation, terminology, operations. Introductory matrix algebra. Probability Theory. Permutations and Combinations, approaches to probability, dependent and independent events, conditional probability, Markov processes, distribution functions, including the Binomial, Poisson and Normal distributions, with applications to problems in Environmental Studies.
3 hours lectures, one term
MATH 100 Fundamental Concepts of Modern Mathematics
A course for non-mathematicians to provide some insight into the many aspects of modern mathematics. The “human interest” point of view will be stressed in order to reveal mathematics as an endeavour holding a strong place in man’s culture. Emphasis will be on twentieth century ideas. To integrate the traditional with the modern, material will be organized in a conceptual rather than a chronological manner.
MATH 112A Introduction to Computers
The purpose of Mathematics 112 is to provide students in programs of study which do not emphasize Mathematics with an appreciation of the capabilities and limitations of machine computing, together with a reasonable capability for programming in one or more programming languages. Topics will include: concept of an algorithm, representation of information, programming in a higher level language, concept of a compiler.
. 2 hours lectures, I hour tutorial, Fall term
Note
Credit will only be granted for one of Math 73a, Math 112a or Math 122a. Math 112a cannot be counted as a credit towards a B.Math General or Honours degree.
.
MATH 112B Applications and Implications of Computers
A continuation of the concepts introduced in Mathematics 112a — the applications of computers to several fields and the impact (past, present and future) of computing on society.
2 hours lectures, 1 hour tutorial, Winter term — Prerequisite: Math Il2a
Note
Credit will only be granted for one of
Math 112b or Math 132b. Math 112b cannot be counted as a credit towards a B.Math General or Honours degree.
MATH 119A Algebra and Geometry
Elementary number theory, mathematical! induction, binomial theorem, monotone sequences, inequalities, complex numbers, elementary functions of a complex variable, polynomials and polynomial equations. 3 hours lectures, I hour tutorial
MATH 119B Algebra and Geometry
Determinants and matrices, vectors in two and three space, quadric surfaces, systems of equations, elementary linear transformations.
3 hours lectures, 1 hour tutorial
Note Maths 119a and 119b are not courses for Honours Mathematics students.
MATH 120A Calculus
Functions and limits, differentiation of algebraic and trigonometric functions, applications of the derivative, the differential, Riemann sums, the first and second fundamental theorems of the integral calculus. 3 hours lectures, I hour tutorial
MATH 120B Calculus
. Differentiation and integration of exponential and logarithmic functions, techniques of integration, applications of integration, indeterminate forms, sequences, convergence of series, power series.
3 hours lectures, 1 hour tutorial
Note Maths 120a and 120b are not courses for Honours
Mathematics students.
Course Descriptions 365 Mathematics.
MATH 122A Introduction to Mathematical Problem
Solving by Computer
An introduction to the analysis of scientific problems, development of mathematical models and algorithms for their solution; implementation in a procedure oriented language (normally FORTRAN IV). Topics discussed are: solution of equations, computation of integrals, graph plotting, and simulation.
2 hours lectures, 2 hours tutorial, one term
Offered in the Fall, Winter and Spring terms Prerequisite: Grade 13 mathematics is recommended
Note Only one of Math 73a, 112a and 122a can be taken for credit.
Note Both Math 122a and 132a may be taken for credit.
MATH 129 Algebra and Geometry
Functions and permutations. Elementary number theory. Real and complex number systems. Polynomial functions. Linear geometry and algebra in 2 and 3 space. Algebraic systems.
3 hours lectures, I hour tutorial
MATH 130 Calculus
Functions and limits, the derivative, differentiation of algebraic and other functions, applications of the derivative.
The integral, theorems on the integral, applications of the integral.
Sequences, convergence of series, power series. Some elementary differential equations. 3 hours lectures, I hour tutorial
MATH 131A Algebra and Solid Geometry ,
The real and complex number system, Mathematical Induction, the Binomial Theorem, Monotone sequences and the Cauchy criterion, polynomial functions, Theory of equations.
3 hours lectures
Note For Science students only.
MATH 131B Algebra and Solid Geometry
Determinants Vector and Matrix notation, Elementary Solid Geometry, Linear transformations, Eigenvalues and Eigenvectors.
3 hours lectures
Note ; For Science students only.
MATH 132A Introduction to Computer Science
~ Programming and File Processing
A thorough introduction to the use of computers. Concept and properties of an algorithm, language and notation for describing algorithms. Analysis of problems dealing with files, and development of algorithms for their solution. Introduction to a procedureoriented language (usually COBOL). The preparation, implementation and debugging of programs in such a language. Topics will normally include: file processing, file maintenance, sorting, report generation and file design.
2 hours lectures, 2 hours tutorial (laboratory), one term.
Normally offered in the Fall and Winter terms Prerequisite: Grade 13 mathematics
Note Credit will only be granted for one of Math 73d or Math 132a..
Note Both Math 122a and 132a may be taken for credit.
MATH 132B Introduction to Computer Science
~ Characteristics of Computers
A general introduction to machine and assemblylanguage programming and basic machine architecture. The representation of data in a computer. Address modification, indexing and indirection. Character manipulation, floating point operations and subroutine linkage. Characteristics of peripheral devices. A brief survey of software which assists user programs: compilers, loaders, input-output routines, operating systems.
2 hours lectures, 2 hours tutorial (laboratory), one term
Normally offered in the Fall and Winter terms Prerequisite: Math 112a or 122a or 132a
Note Credit will only be granted for one of Math 1226 or Math 1326.
MATH 217 Advanced Calculus
Differential calculus of functions of several variables, multiple integrals and applications. Line integrals, Green’s theorem, infinite series, uniform convergence, first and second order ordinary differential equations. 3 hours lectures, 1 hour tutorial
Note M217 is not a course for Honours Mathematics students.
Course Descriptions Mathematics
MATH 219 Linear Algebra
Vector spaces, linear maps, matrix theory. Inner products. Bilinear and quadratic forms. Applications. 3 hours lectures
Note M219 is not a course for Honours Mathematics students.
MATH 223A Introduction to Statistical Methods — 1
Descriptive statistics, graphical methods, model fitting; correlation, regression and the method of least squares. Probability theory; discrete and continuous random variables.
3 hours lectures, 2 hours tutorial, one term Prerequisites: M120 or M130; one of Mi l2a, M122a, M132a
MATH 223B Introduction to Statistical Methods — 2
Tests of significance, maximum likelihood estimation and large sample theory; estimation and testing in the normal distribution.
3 hours lectures, 2 hours tutorial, one term Prerequisite: M223a
Note
M223 is not a course for Honours Mathematics students. Credit will be given for only one of M223, M233 and M243.
MATH 228 Introduction to Pure Mathematics
Examples and results in modern geometry, number theory, and algebra and analysis; the historical sources of modern mathematics.
2 hours lectures
MATH 229 Linear Algebra
Real and complex vector spaces. Linear transformations. Matrices. Determinants. Diagonalization of Matrices. Inner products spaces. Orthogonal and unitary matrices. The spectral theorem for hermitian and real symmetric matrices. Applications.
3 hours lectures
MATH 233 Probability and Statistics
An introduction to probability theory and statistics, and their applications. The laws of probability, discrete and continuous random variables, expectation, central limit theorem; estimation, tests of significance, contingency tables, normal distribution theory, simple linear regression.
3 hours lectures, 2 hours tutorial, two terms Prerequisite: M120 or M130
Note Credit will be given for only one of M223, 233, 243.
MATH 234 Introduction to Applied Mathematics
MATH 234A Mathematical Modelling
Mathematical models for problems in the physical and biological sciences. Typical problems chosen from ecolcgy, special relativity, spread of epidemics, rumours and tumors. Solutions to problems will be obtained primarily by differential equations. Prerequisite: Math 130
MATH 234B Mathematical Modelling
Further mathematical models from various disciplines. An introduction to Newtonian mechanics will also be included in the course. . Prerequisite: M234a or consent of instructor
MATH 235A Actuarial Mathematics
Mathematics of Investment
The theory of rates of interest and discount, annuities and sinking funds; application to financial problems, including the determination of mortgage payments and the price and yield of bonds.
2 hours lectures, 1 hour problems, one term
MATH 235B Basic Life Insurance Mathematics
. Applications of probability to problems of life and death. The determination of single and annual premiums for assurances and annuities. Reserves. Company expenses and their incorporation into premium and cash value calculations. 2 hours lectures, 1 hour problems, one term
MATH 236 Elementary Differential Equations
An introduction to first order djfferential equations. Applications to growth, decay, reactions. Linear equations with constant coefficients. Systems of equations; vector and matric methods. Solutions in series. Introduction to partial differential equations.
2 hours lectures
Note M236 is not a course for Honours Mathematics Students.
MATH 237 Advanced Calculus
Sequences and series of functions: uniform convergence, power series, Introduction to ordinary differential equations: first and second order linear equations, power series solution method, applications. Differential calculus of functions of several variables: continuity, partial derivatives, differentials, chain rule, Taylor expansion, extreme values, mappings and Jacobians. Integral calculus of functions of several variables: multiple integrals, change of variable, line integrals, Green’s theorem and independence of path. 3 hours lectures, 2 hour tutorial
Prerequisite: First year algebra (M119 129)
Course Descriptions 367
. Mathematics
MATH 239 Introduction to Combinatorics and Optimization
MATH 239A An Introduction to Combinatorics
Existence and non-existence. Enumeration. Combinations and Permutations. Inclusion-exclusion principle. Linear equations with unit coefficients. Recursion. Generating functions. Chromatic polynomials. Applications to geometry designs.
Recommended for students wishing an introduction to discrete mathematics, and for students intending to pursue a course of study in combinatorics and optimization.
2 hours lectures, 2 hours tutorial Prerequisite: First year algebra (M119{ 129).
MATH 239B An Introduction to Optimization
Convex sets. Linear programming, Directed graphs. Applications of Boolean Algebra to Combinatorial Circuits. Probability; Markov chains; random walks. Theory of Games.
Recommended for students wishing an introduction to optimization, and for students intending to pursue a course of study in combinatorics or optimization.
2 hours lectures, 2 hours tutorial, one term Prerequisites: First year algebra (M129); Note that 239a is not a prerequisite but is highly recommended
MATH 240A Numerical Applications in Computer Science
An introduction to Numerical Procedures with emphasis upon computer implementation using the FORTRAN IV programming language. In particular, the following topics are introduced: concept of numerical errors, interpolation, curve fitting, solution of non-linear equations, numerical integration, matrix operations and solution of systems of linear equations, numerical solution of ordinary differential equations. Offered in the Fall, Winter and Spring terms Prerequisites: M122a or equivalent, and M120 or M130 and M119 or M129
There is a special section for non-mathematics students
MATH 240B Principles of Programming Languages and Data Structures
This course is intended to cover a number of basic principles of programming languages and data structures. The emphasis will be on basic principles with motivation for programming languages arising from practical examples. ALGOL and SNOBOL will normally be the languages used.
2 hours lectures, 2 hours tutorial
Offered in the Fall, Winter and Spring terms Prerequisite: Math 122a or Math 132a or the equivalent. Math 132b is recommended
MATH 243 Statistics for the Sciences
The topics of Mathematics 233 with particular emphasis on the analysis and interpretation of experimental data and the design of experiments in the Sciences. The more difficult mathematical techniques associated with these problems will be omitted and many examples from Physics, Chemistry, Biology and other natural Sciences will be considered.
2 hours lectures, 1 hour laboratory
Note Credit will be given for only one of M223, 233, 243
MATH 300A Mathematical Discovery and Invention
A study of.about 100 challenging problems taken from many areas of elementary mathematics — number theory, combinatorics, geometry, probability, logic.
2 hours lectures, one term
MATH 300B Mathematical Discovery and Invention
A study of about 100 challenging problems taken from many areas of elementary mathematics — number theory, combinatorics, geometry, probability, logic.
2 hours lectures, one term
Prerequisite: No formal prerequisites are demanded
Note 300a is not a prerequisite to 300b
MATH 307 Combinatorial Geometry
A study of combinatorial properties of plane figures, covering problems, addition of figures, maxima and minima problems, curves of constant breadth and delta-curves.
This course is designed for the student who particularly likes geometry and for the serious student of combinatorics. Occasionally brief contact is made with the subject of analysis. Thus a concurrent course in real variables would be helpful, but not essential. 2 hours lectures Prerequisite: First year calculus (M120/130)
MATH 312A Elements of Real Variable Theory
Elementary properties of the real numbers: completeness and its relation to limits, continuity, differentiability; mean value theorems; Riemann integration, integrability of continuous and monotone functions; uniform convergence and uniform continuity.
3 hours lectures
Note Emphasis will be on applications rather than theory.
Note M312a is not a course for Honours Mathematics students.
Course Descriptions Mathematics
MATH 312B An Introduction to Complex Variable Theory
Complex numbers; continuity, differentiability, analyticity of functions; the Cauchy-Riemann equations; solutions of Laplace’s equation; conformal mapping by elementary functions, and applications, the Cauchy and allied theorems; Taylor and Laurent expansions; uniform convergence and power series; the residue calculus, and applications.
3 hours lectures
Note . Emphasis will be on applications rather than theory. M3126 is not a course for Honours Mathematics students.
MATH 314A Introduction to Scientific Computation: Numerical Algebra
Pitfalls in computation; solution of linear algebraic equations; Finding zeros of a single nonlinear equation and systems of nonlinear equations; the algebraic eigenvalue problem. The emphasis is on exposure to modern computer techniques for solving mathematical problems. Heavy use of mathematical subroutine libraries is anticipated.
2 hours lectures, 2 hours tutorial, one term Prerequisites: Knowledge of a high level language, 217 or 237, or equivalent
preferably FORTRAN, Math 219 or 229 and Math
Note - Math 314a and 334a cannot both be taken for credit.
MATH 314B Introduction to Scientific Computation: Numerical Approximation
Polynomial interpolation; least squares and minimax approximation; numerical integration and differentiation; numerical solution of initial value problems and boundary vatue problems. As in Math 31l4a, the intent is to expose students to modern computational techniques for solving mathematical problems.
2 hours lectures, 2 hours tutorial, one term Prerequisites: Knowledge of a high level language, preferably FORTRAN; Math 219 or 229 and Math 217 or 237, or equivalent
Note Math 314b, Math 334b cannot both be taken for credit.
MATH 319 Abstract Algebra
Introduction to rings, fields, groups. Applications.
Note
Emphasis will be on examples rather than on proofs of theorems. ‘
M319 is not a course for Honours Mathematics students.
MATH 320A Computer Applications in Business
A discussion of the algorithms for the storage and retrieval of information using storage media such as disks and tapes. The techniques developed are applied to a number of general business application areas such as billing, inventory control and general ledger accounting. Good system design and programming practices will be stressed throughout the course.
2 hours lectures, 2 hours tutorial, one term Prerequisite: Math 132a
Note Math 320a and 340a cannot both be taken for credit.
MATH 320B Computer Applications in Business
A continuation of the topics presented in Mathematics 320a.
2 hours lectures, 2 hours tutorial, one term Prerequisite: Math 320a
Note Math 320b and 340b cannot both be taken for credit.
MATH 329 Abstract Algebra
Introduction to rings, integral domains, fields, groups. Further topics and applications.
MATH 330A Projective Geometry
Projective spaces over fields, collineations and correlations, quadric curves and surfaces, References to non-euclidean geometries.
3 hours lectures, one term
Prerequisite: M229
MATH 330B Geometry of the Complex Numbers
The plane of complex numbers. The group of circle preserving mappings and its subgroups. Connections with non-euclidean geometries. Other number systems and their geometries (Laguerre, Minkowski).
3 hours lectures, one term
Prerequisite: M229
MATH 330C Euclidean Geometry
Concurrent lines, collinear points, the Euler line, the Simson line, the nine point circle. Cross ratio, projection, Harmonic range, the quadrilateral and the quadrangle. Properties of circles.
3 hours lectures, one term
MATH 332A Real Variables
Real numbers. Continuous functions. Functions of bounded variation. Riemann integral. Cesaro summability of series. Inequalities. Inner product and normed linear spaces. Orthonormal systems. Fourier series.
3 hours lectures
Prerequisite: M237
Course Descriptions 369 Mathematics
MATH 332B An Introduction to Complex Variable Theory
Complex numbers; continuity, differentiability, analyt-. icity of functions; the Cauchy Riemann equations; solution of Laplace’s equation; conformal mapping by elementary functions, and applications; the Cauchy and allied theorems; Taylor and Laurent expansions; uniform convergence and power series; the residue calculus, and applications.
3 hours lectures
Prerequisite: M327
MATH 334A Numerical Algebra
Zero finding: real functions of a single real variable, polynomials, systems of non-linear equations, Linear Algebra: linear systems of equations, linear least squares, eigenvalue problems.
3 hours lectures, 2 hours tutorial, one term
Offered in the Spring and Fall terms
Prerequisite: Math 122a, Math 219 or 229 and Math 217 or 237
MATH 334B Numerical Approximation
Interpolatory, least squares, and minimax approxi- | mation of functions by polynomials, trigonometric series, rational functions, splines and exponentials. Inverting Laplace transforms. Acceleration techniques. Numerical approximation of derivatives. Quadrature.
3 hours lectures, 2 hours tutorial, Winter term Prerequisite: Math 122a, Math 219 or 229 and Math 217 or 237
MATH 335A Finite Differences
A course in the calculus of finite difference, to include: summation, numerical integration and differentiation, relation between integration and summation; and error theory.
2 hours lectures, 1 hour problems, one term
MATH 335B Graduation of Tables
Applications of finite differences to actuarial problems in graduation of statistical tables.
2 hours lectures, 1 hour problems, one term Prerequisites: M235a] b
MATH 336A Life Contingencies
An advanced course on problems with single lives, including population theory.
3 hours lectures, one term
Prerequisite: M235b
MATH 336B Life Contingencies
An advanced course on problems with multiple lives; multiple decrement theory; accidental death and disability benefits.
3 hours lectures, one term
Prerequisite: M235b
MATH 338A Mathematical Statistics
Continuous random variables; moments and moment generating function; distribution of t, chi-squared, and F, and their applications. Large sample theory. 3 hours lectures, one term
Prerequisites: M233, 237
MATH 338B Mathematical Statistics
The multivariate norma! distribution, its properties and uses; quadratic forms and Cochran’s theorem; multiple regression; introduction to the analysis of variance.
3 hours lectures, one term
Prerequisites: M229, 338a
Note M338b and 349a cannot both be taken for credit.
MATH 339A Probability and Stochastic Processes — 1
Discrete probability models. Random walk models. Recurrent events. Theory and applications of Markov chain models.
3 hours lectures, one term
Prerequisite: One of M223, 233 or 243
MATH 339B Probability and Stochastic Processes — 2
Continuous probability distributions. Applications of Poisson and other continuous time stochastic processes. Renewal processes. Stationary processes.
3 hours lectures, one term
Prerequisite: M339a or consent of instructor
340a: Machine, Data and Program Structures Representation of numbers and strings. Addressing schemes. Compound data structures. Program structure.
3 hours lectures, one term
Offered in the Fail, Winter and Spring terms Prerequisite: Math 240b
340b: Implementation Schemes for Programming Structures
Searching and sorting. Run time representation of a high level language. Dynamic storage management. Text manipulation.
3 hours lectures, one term
Offered in the Fall and Winter terms
Prerequisite: Math 340a
Course Descriptions Mathematics
MATH 341 Algebra }
Theory of groups, rings, fields and other algebraic structures.
3 hours lectures
Corequisite: M229
MATH 342 Real Analysis 1
Theory of functions of real variables. The notions of compactness, connectedness, and uniformity are used’ in a study of continuity, differentiation, and integration.
2 hours lectures
Prerequisite: M237
MATH 343 Complex Analysis 1
Analysis of complex numbers; fundamental theorems of holomorphic functions; meromorphic functions.
2 hours lectures
Prerequisite: M237
MATH 344A Topology
Intuitive set theory, metric spaces, point set topology.
3 hours lectures, one term
Prerequisite: Consent of instructor
MATH 349A Applied Statistical Analysis
Review of Normal, t, Chi-squared and F distributions and their applications. Introduction to the design of experiments and surveys. Analysis of variance, multiple regression.
3 hours lectures, one term
Prerequisite: One of M223, 233 or M243
Note M349a and 338b cannot both be taken for credit
MATH 349B Statistical Decision Theory
The decision problem; utilities and subjective probabilities; decision rules; decision trees, normal and extensive analyses; conjugate prior distributions and associated distribution theory; applications to business decisions. Loss functions, risk functions; admissability, minimax rules, tests of hypothesis. An introduction to statistical quality control and control charts.
3 hours lectures, one term
Prerequisites: M223, 233 or 243; M217 or 237
Note M349a/b may be taken in either order
MATH 351A Introduction to Graph Theory and Combinatorics
A study of the basic concepts and problems of graph theory: connection, minimum path problems; bipartite graphs, the marriage problem; 1-factors of arbitrary graphs; planar graphs.
2 hours lectures, one term
Prerequisites: No formal prerequisites. M239 recommended.
MATH 351B Introduction to Graph Theory and Combinatorics
Hamiltonian circuits in a graph, four colour problem, other colouring problems; directed graphs, balanced orientations; an introduction to the theory of enumeration, with applications to counting graphs and other combinatorial objects.
2 hours lectures, one term
Prerequisites: No formal prerequisites. M239 and M35la recommended
MATH 352A Fundamentals of Optimization
Introductory study of optimization techniques common to a wide variety of operations research and engineering problems, and of fundamental theoretical interest. Linear programming, simplex method, duality; integer programming, branch and bound, transportation problems, games.
2 hours lectures, one term
Prerequisites: M219, 229 and 217, 237
MATH 352B Fundamentals of Optimization
Introductory study of optimization techniques complementary to those studied in 352a. Extrema of functions of n-variables, Lagrange multipliers, network programming. Applications to PERT, CPM, replacement policies, knapsack problems, inventory theory, capital budgeting.
2 hours lectures, one term
Prerequisites: Same as M352a
MATH 353A Modelling and Optimization
An applications oriented course that illustrates how various mathematical models and methods of optimization can be used to solve problems arising in business, industry and science.
2 hours lectures, one term
MATH 360A Tensor Analysis
Elementary introduction to classical differential geometry and tensor analysis. Curves and surfaces in Euclidean spaces, coordinate transformation, invariance of length, introduction of tensors and metric, Riemannian spaces, covariant differentiation, geodesics, curvature and Einstein tensors.
2 hours lectures + 1 hour tutorial. Fall term Prerequisites: M237, consent of instructor
371
MATH 360B Differential Geometry
Intermediate level course on Riemannian spaces (continuation of 360a). Conformal spaces, spaces with corresponding geodesics, theory of subspaces.
2 hours lectures + 1 hour tutorial. Winter term Prerequisites: M237, 360a or consent of instructor
MATH 361A Calculus of Variations
Euler-Lagrange equations for constrained and unconstrained single and double integral variationa] problems. Parameter-invariant single integrals. General variational formula. The canonical formalism. Hilbert’s independent integral. Hamilton-Jacobi equation and the Caratheodory complete figure. Fields and the Legendre and Weierstrass sufficient conditions.
2 hours lectures + 1 hour tutorial. Fall term Prerequisite: M237 or consent of instructor
MATH 361B Mechanics .
Three-dimensional rigid body. motion. Lagrange’s equations of motion for holonomic and nonholonomic systems. Ignorable coordinates. Hamilton’s principle for holonomic systems and its counterparts for non-holonomic systems. Noether’s theorem and conservation laws. Canonical equations of motion. Canonical transformations. Lagrange and Poisson bracket relations. Integral invariants.
2 hours lectures + I hour tutorial. Winter term Prerequisites: M237, 361la or consent of instructor
MATH 362A Introduction to Continuum Mechanics
Vector Integral Calculus, motion of a system of particles, methods of continuum mechanics. Stress and strain tensors; analysis of stress and strain. Lagrangian and Eulerian methods for describing flow. Equations of continuity, motion and energy. Navier- Stokes equation. Basic equations of elasticity.
2 hours lectures, 1 hour tutorial. Winter term Prerequisites: M234, 237 or consent of instructor
MATH 362B Partial Differential Equations of Applied Mathematics
Derivation of the equations of heat flow, the vibrating membrane and the electro-magnetic field equations by various elementary techniques and illustrations of the use of calculus of variations in the derivation of equations; solutions of the above equations by separation of variables; Fourier analysis and Fourier integral.
2 hours lectures, 1 hour tutorial. Fall term Prerequisites: M234, 237 or consent of instructor
MATH 363 Differential Equations |
Existence of solutions. Second-order linear equations. Sturm-Liouville boundary-value problems. Fourier series, Partial differential equations.
2 hours lectures + 1 hour tutorial
Prerequisites: M234, 237 or equivalent, 332 (Real Variables) may be taken concurrently
MATH 371A Digital Networks
Combinational networks. Integrated-circuit modules: comparators, multiplexers, decoders, priority encoders, arithmetic/logic units. Boolean algebras. Boolean functions and expressions. Simplification of Boolean expressions. Asynchronous sequential networks. Latches and flip-flops. Synchronous operation. Analysis and synthesis of synchronous sequential networks. Sequential integrated-circuit modules: shift registers, counters, memories.
3 hours lectures, one term
Offered in the Fall, Winter and Spring terms Prerequisite: M132b
MATH 372B Introduction to the Theory of Computing
Models of computers including finite automata and Turing machines, Basics of formal languages. Relations between machine models and formal languages with applications to syntax of programming languages. Unsolvable problems and their relevance to the semantics of programming. Concepts of computational complexity including algorithm optimality. 3 hours lectures, one. term Offered in the Fall, Winter and Spring terms Prerequisite: Math 240b
MATH 380A Introduction to Information Theory with Applications
Finite probabilistic schemes. Measures of uncertainty.
Shannon’s Entropy as a measure of uncertainty and expected information. Maximizing expected information. Applications to problem solving in coding, logics and linguistics.
2 hours lectures, I hour tutorial
MATH 380B Introduction to Information Theory with Applications
Measures of expected conditional information. Maximizing expected conditional information. Applications to communication theory and programming. Basics irf questionnaire theory.
2 hours lectures, I hour tutorial
Prerequisite: M380a
MATH 398 Undergraduate Seminar
_2 hours lectures
399 Reading in Mathematics
Course Descriptions Mathematics
MATH 406 Linear Algebra 2
Continuation of linear algebra. Main topics; representations of endomorphisms, structures of bilinear forms, multilinear products.
2 hours lectures
Prerequisite: M329 or M341
MATH 407 Algebraic Geometry
An introduction to the theory of algebraic varieties. Special topics such as the Theorem of Riemann-Roch. 2 hours lectures
Prerequisite: M329 or M341
MATH 408 Mathematical Logic
First order languages and theories. A treatment of at least one of the following: set theory, model theory, undecidability. This course is more specialized and at a more advanced level than Mathematics 436.
2 hours lectures
MATH 409 Foundations of Geometry
An axiomatic treatment of geometry. Geometrical structures, such as projective planes and inversive planes.
2 hours lectures
MATH 410 Ring Theory
Continuation of the theory of rings and modules. 2 hours lectures
Prerequisite: M329 or M341
MATH 411 Group Theory
Continuation of group theory 2 hours lectures
Corequisite: M329 or M341
MATH 412 Field Theory
Field extensions and Galois theory. 2 hours lectures
Prerequisite: M329 or M341
MATH 413 Non-Linear Differential Equations
Non-linear mechanics, stability, quasi-linear and strongly non-linear systems, linear periodic systems, non-linear integral equations.
2 hours lectures
Prerequisite: M363 or consent of instructor
MATH 417A Optimizational Combinatorics
Algorithms and theory relating to both combina-
torics and optimization. Brief review of linear pro-
gramming duality theory. Optimum paths and flows
in networks. Efficiency of algorithms. Convex poly-
hedra. Combinatorial max-min relations. Totally
unimodular matrices. Integer programming. Optimum
matchings and constrained subgraphs. Recommended for students interested in theor-
etically advanced study in Combinatorics and
Optimization or Computer Science.
2 hours lectures, one term
Prerequisite: M352a or consent of instructor
MATH 417B Optimizational Combinatorics
Branchings in networks. Elementary matroid theory
illustrated by forests, transversals, algebraic depen-
dence, and geometry. Matroid partitions and inter-
sections. Submodular functions and polymatroids. Recommended for students interested in theor-
etically advanced study in Combinatorics and Opti-
mization or Computer Science.
2 hours lectures, one term
Prerequisite: M417a or consent of instructor
MATH 418A Combinatorial Applications of Computers
General topics: methods of data storage for combinatorial problems, representation of sets, etc. Algorithms for permutations, combinations, partitions, etc. The use of generating functions, and methods of handling them on a,computer. Enumeration problems: Polya’s theorem and variations. Applications.
Useful for students wishing to specialize in the more computationally-oriented aspects of graph theory or operations research.
2 hours lectures, one term
Prerequisites: Practical knowledge of at least one computer programming language. Algebra (M319 ] 329)
- 418b Combinatorial Applications of Computers Methods for searching and sorting. Tree-like data structures: branch and bound methods. Back-track methods. Boolean programming. Construction problems: construction of graphs, digraphs, trees. The cell-growth problem and its variations.
Useful for students wishing to specialize in the more computationally-oriented aspects of graph theory or operations research.
2 hours lectures, one term
Prerequisites: Practical knowledge of at least one computer programming language. Algebra (M329). M418a is a prerequisite for M418b
Course Descriptions 373 Mathematics
MATH 425 Theory of Numbers
Multiplicative-algebraic theory of numbers. Foundations of natural number theory. Elements of additive-combinatorial number theory.
2 hours lectures
Corequisite: M329 or 341
MATH 426 Topology
Continuation of general topology; selected topics from other branches of topology.
2 hours lectures
Prerequisite: M344
MATH 428 Lattice Theory
Ordered sets, lattices, and Galois connections. Applications in algebra, geometry and logic.
2 hours lectures
Consent of instructor
MATH 429 Combinatorial Topology
Homology theory of complexes. Theorems of invariance, covering, and duality.
2 hours lectures
MATH 430 Finite Geometries
Finite incidence structures. Designs. Finite projective and affine planes.
2 hours lectures
Corequisite: M330a Projective Geometry
MATH 432 Complex Analysis 2
Further properties of holomorphic and meromorphic functions. Riemann surfaces.
2 hours lectures
Prerequisite: M332a or M343
MATH 433 Real Analysis 2
An introduction to integration and measure theory with emphasis on the real line.
2 hours lectures
Prerequisite: M332a or 342
MATH 434 Differential Equations
Green’s functions. Cauchy problems. Classification of partial differentia! equations. Orthogonal functions. Bessel functions. Legendre polynomials. Fourier Integral and Laplace transform. Variational properties of eigenvalues and eigenfunctions.
374. - ‘ ‘
MATH 435 Laboratory
a) Numerical problems arising in actuarial science and statistics.
3 hours laboratory, one term ©
Prerequisite ~ Corequisite: M335b, 461a or consent of instructor
b) Numerical problems arising in actuarial science and statistics
3 hours laboratory, one term
Prerequisite: M336a/b or consent of instructor
Note Only advanced actuarial students are advised to take _ this course.
MATH 436 Introduction to Logic
An introduction to the logic of sentences and predicates with some emphasis on familiar algebraic structures. At first informal, then leading to a formal axiomatic treatment with proofs of consistency and completeness.
2 hours lectures
Prerequisite: Consent of instructor
MATH 437A Measurement of Mortality
Methods of analysis of data to produce raw rates for mortality and other tables.
3 hours lectures, one term
Prerequisite: M235 or consent of instructor
MATH 437B Risk Theory
Individual and collective risk theory. Ruin theory. Stop loss reinsurance premiums, Monte Carlo methods.
3 hours lectures, one term
Prerequisites: M223, 233 or 243 or consent of instructor
MATH 438A Topics in Estimation and Hypothesis Testing
Discussion of general inference problems under the headings of point and interval estimation, hypothesis testing, and decision theory, Large sample normal likelihoods, maximum likelihood estimation, theory of UMV estimation, least squares, Neyman-Pearson theory of hypothesis testing.
2 hours lectures, one term
Prerequisite: M338a
MATH 438B Statistical Inference with Small Samples
Logic of tests of significance; exact tests and confidence intervals; normal approximations accurate for small samples and relationship to the normality of the likelihood function. Introduction to problems involving more than one parameter.
2 hours lectures, one term
Prerequisite: M438a or permission of instructor
(Course Descriptions
Mathematics
MATH 439A Theory of Experimental Design - A
Logical requirements of designed experiments. Design ° and analysis of basic complete designs with fixed effects, random effects, or both. Analysis of covariance. Latin squares. Applications.
3 hours lectures, one term
Prerequisite: M338a or consent of instructor
MATH 439B Theory of Experimental Design - B
Construction and analysis of incomplete designs: latin square, confounded, fractional factorial, incomplete block. Applications..
3 hours lectures, one term
Prerequisite: M338b or consent of instructor
MATH 441 Quantum Mechanics
Schrodinger equation. Solution of one dimensional problems, commutation relations, uncertainty principle, W.K.B. approximation. Hydrogen atom, angular momentum. Scattering theory. Matrix mechanics, symmetry groups. Introduction to relativistic wave equations.
2 hours lectures
MATH 442 Theory of Relativity
Flat space-time and special relativity, curved spacetime and the Einstein gravitational field equations. The Schwarzschild solutions and the experimental tests of relativity. Maxwell’s equations in space time and the Reissner-Nordstrom solution. Selected topics from cosmology, Petrov classification, spinors, gravitational waves, special solutions, mathematical aspects of the Einstein field equations.
2 hours lectures. Winter term
Prerequisite: M360a, Consent of instructor
MATH 443 Electromagnetism
Applications of the Maxwell equations. Reflection and refraction. Introduction to wave guides and antennae. 2 hours lectures. Fall term
Prerequisite: Consent of instructor
MATH 444 Elasticity
Basic equations of elasticity for homogeneous isotropic bodies; bending of beams; plane elastic waves; Rayleigh surface waves, Love waves. Solution of problems by potentials, variational methods and Saint Venants’ principle.
2 hours lectures + I hour tutorial. Winter term Prerequisite: M445a
MATH 445A Fluid Mechanics
Fundamental! equations of inviscid fluids, compressibility, vorticity; two and three dimensional irrotational, incompressible flow, Blasius’ theorem, Joukowski hypothesis.
2 hours lectures, 1 hour tutorial, Fall term Prerequisite: M363b
MATH 445B Fluid Dynamics
Shock wave theory, supersonic flow around a corner, Prandtl-Meyer flow. Dynamics of real fluids, Navier- Stokes equations, exact solutions, Stokes and Oseen flow; introduction to boundary layer theory.
2 hours lectures, L hour tutorial. Winter term Prerequisite: M445a
MATH 446A History of Mathematics — A
A study of selected topics from Greek geometry. Some related work of post-renaissance scholars is included. Topics include: famous construction problems, pythagorean arithmetic, regular solids, four discoveries of Archimedes, the problem of Apollonius; selected works of Archimedes, Euclid, Apollonius, Euler, Steiner.
2 hours lectures, one term
Prerequisites: No formal prerequisites are demanded
MATH 446B History of Mathematics — B
A study of selected topics from post-renaissance mathematics. Topics include material on prime numbers, Fermat's Last Theorem, the Gaussian Integers, the Fibonacci Sequence, other topics for elementary number theory, a collection of outstanding problems in geometry (Fagnano, Steiner-Lehmus, Morley).
2 hours lectures, one term
Prerequisites: No formal prerequisites are demanded
MATH 447 Statistical Mechanics
Applications of probability theory to theoretical Physics.
2 hours lectures. Fall term
MATH 448 Differential Geometry
Differentiable manifolds, tensors and forms, Connexions, Riemannian manifolds.
2 hours lectures
Prerequisites: M229 and 237
MATH 449A Experimental Design — A
The requirements for a good experimental design prior to the accumulation of data. The concepts of randomization, replication and experimental error as applied to basic designs; the completely randomized block and Jatin square designs. Analysis of variance. 2 hours lectures, one term
Prerequisite: M338b or 349a, or consent of instructor
MATH 449B Experimental Design - B
Factorial experiments, confounding, fractional replication. Applications of designs. Incomplete block designs. Analysis of covariance.
2 hours lectures, one term
Prerequisite: M449a
Course Descriptions 375 Mathematics
MATH 450 Applied Analysis
Applied Mathematics for Science majors. Ordinary and partial differential equations. Laplace and Fourier transforms. Special functions.
Fourier Series. Vector and matric methods, Calculus of variations. Other topics in advanced calculus. 2 hours lectures
Note This course is not for Honours Mathematics students
MATH 451A Nonlinear Optimization - A
Recent algorithms for constrained and unconstrained
differentiable optimization problems will be presented.
Topics will include first and second order Newton
methods, quasi-Newton methods, conjugate gradient
directions, feasible direction methods, and penalty
algorithms. Applications and implementations will
be given. : ‘ Recommended for students interested in operations
research, industrial engineering, computer science
and for those wishing to pursue graduate courses in
mathematical programming.
2 hours lectures, one term
MATH 451B Nonlinear Optimization ~ B
Nonlinear Programming; convergence conditions and convergence rates for some unconstrained optimization methods, introduction to the Kuhn-Tucker conditions and duality theory for nonlinear programmes, optimality conditions for a quadratic programme.
Quadratic Programming; Lemke’s complementary pivot scheme to solve a quadratic programme. 2 hours lectures, one term Prerequisite: M455a or consent of the instructor
MATH 452A Linear and Integer Programming
(Theory, Applications and Related Topics) Formulation of problems as linear programming problems. Convex sets, convex functions, geometric motivation for the Simplex Algorithm. Simplex Algorithm. Revised Simplex Algorithm, product form of inverse. Degeneracy. Post-optimal analysis (parametric programming, sensitivity analysis, etc.). Applications, Computerized methods of solution.
2 hours lectures, one term
Prerequisites: Linear Algebra and Elementary FORTRAN or consent of instructor.
376 \
MATH 452B Linear and Integer Programming
(Theory, Applications and Related Topics)
Duality theory, Dual Simplex Algorithms, Primal Dual Algorithms. Assignment Problem, Transportation Problem. Network problems. Bounded variable problems, Decomposition of large systems. Formulaiton of integer, mixed integer, and discrete programming problems. Methods of solution (Cutting plane methods, implicit enumeration, branch-andbound, etc.). Partitioning methods. Applications, computerized methods of solution.
2 hours lectures, one term
Prerequisite: M452a or 352a or consent of instructor
MATH 453A Queueing Theory - A
Simple queues with Poisson arrival and Exponential service distributions, multi-server queueing models including: homogeneous and heterogeneous parallel servers; servers in series; and phase type service. Advanced models including: baulking, reneging, jockeying between queues, pre-emptive and nonpreemptive priority queues, batch arrivals and service processes. Methods of analysis introduced include differential-difference equations, probability generating functions and simulation.
2 hours lectures, one term
Prerequisite: Introductory Probability
MATH 454A Game Theory A
A mathematically-oriented course on the basics of game theory, with applications to economics, bargaining, and strategy.
Classification of games; solution of matrix games and their relationship to linear programming; infinite zero-sum games; utility theory; bimatrix games and the bargaining problem.
2 hours lectures, one term Prerequisites: Linear algebra (M229) and basic probability theory
MATH 454B Game Theory B
N-person games; Shapley value; metagames. Prerequisites: M454a
MATH 455A Mathematical Programming — A
Dynamic Programming; deterministic decision pro-
cess problems, monotonic path problems, equipment
replacement, resource allocation, reduction of dimen-
sion by use of Lagrange multipliers, shortest path
problems, cargo loading problem, the travelling sales-
man problem; introduction to optimal control. Convex functions; first and second order character-
ization of convex functions.
2 hours lectures, one term
Prerequisite: M352a or consent of the instructor
Course Descriptions Mathematics
MATH 456A Scheduling
Single machine job shops, parallel machines, flowshop scheduling, the general m/n job shop. Capital budgeting, distribution problems occurring in scheduling trucks, trains, and in warehouse movements.
2 hours lectures, one term
Prerequisite: M352 is recommended but not required
MATH 457A This course will be concerned with the combinatorial
problems of retrieving data from a store and discusses the principal algorithms for doing this. Methods for constructing appropriate relational structures and their stability are considered, as well as devices for improving substantial gains in efficiency. _
MATH 457B This course considers the application of combinatorial
structures, such as block designs, to information retrieval. The construction of such structures will be considered together with methods for optimising a general model for the retrieval problem.
MATH 458A Graph Theory - A
Topics in graph theory. These may include symmetry
in graphs, planarity, bipartite graphs, minimax
theorems, directed graphs, enumeration, algorithms.
colouring problems, matrices and graphs. Recommended for students who have taken a
course in graph theory and wish to study additional
topics not normally covered in an introductory
course.
2 hours lecture, one term
Prerequisite: M35la or consent of instructor
MATH 458B Graph Theory — B
Continuation of topics covered in 458a. 2 hours lectures, one term Prerequisite: M458a
459a Algebraic Graph Theory —- A 459b Algebraic Graph Theory - B
460a Combinatori,s-A Enumerative Mathematics Combinatorial identities, generating functions, counting of labelled and unlabelled objects, theorems of Polya, Redfield-Fead, and de Bruijn.
Recommended as a useful preliminary for M785 “Planar graphs”. 2 hours lectures, one term Prerequisite: A knowledge of elementary group theory (M329)
MATH 460B Combinatorics-B
The existence and construction of error correcting codes, projective geometries, orthogonal Latin squares balanced incomplete block designs and other combinatorial configurations.
Recommended for M780, Combinatorial Analysis
2 hours lectures, one term
Prerequisite: Theory of finite groups, rings and
fields (M329)
MATH 461A Demography
Mathematical applications in demography.
3 hours lectures, one term
Prerequisite or Corequisite: M336 or consent of instructor
MATH 461B Topics in Actuarial Mathematics
A selection of topics for the advanced actuarial student.
3 hours lectures, one term
MATH 462A Measure and Integration
The theory of measure and the Lebesgue integral. 2 hours lectures. Fall term
MATH 462B Linear Operators .
Linear operators in Hilbert spaces. Compact operators. Introduction to functional analysis.
2 hours lectures. Winter term
MATH 463 Control Theory
Dynamical systems, controllability and observability. Minimization of functions and functionals. Optimal control. Pontryagin’s Maximum Principle.
2 hours lectures. Fall term
Prerequisite: Consent of instructor
MATH 464A Topics in Applied Mathematics
A selection of topics given by members of the Applied Mathematics Department. Typical topics are: elasticity, fluid mechanics, electromagnetic theory, statistical mechanics, perturbation theory, calculus of variation, partial differential equations, distribution theory.
2 hours lectures, Fall term
Prerequisite: Consent of instructor
MATH 464B Topics in Applied Mathematics
Same description as in 464a.
2 hours lectures, Winter term Prerequisite: Consent of instructor
Course Descriptions : 377 Mathematics
MATH 466A Statistical Data Analysis
Summary statistics. Transformation of data. Plotting techniques. Comparisons of specific distributions via probability plots. Analysis of residuals. Random number generation techniques. Outliers in regression and analysis of variance data. W-statistics and tests for normality. Computational techniques in multiple unweighted and weighted regression.
2 hours lectures, one term
Prerequisites: 1) A course in FORTRAN Programming or equivalent
2) M338b or 349a
MATH 466B Topics in Statistics
An introduction to several areas of Statistics, such as multivariate analysis, time series, data analysis, non-parametric theory, decision theory, etc.
2 hours lectures, one term
Prerequisite: M338b or consent of instructor
MATH 467A Sampling Theory and Practice
Introduction to sample theory and practice. Elementary sampling designs and estimation procedures. Statistical inference in survey sampling. Interrelationships between survey sampling and the design of experiments.
3 hours lectures, one term
Prerequisite: One of 223, 233 or 243
MATH 467B Sample Survey Design
Procedures for construction of sampling designs commonly used in agricultural, economic and scientific surveys, and corresponding estimation techniques. Validation of survey results.
2 hours elctures, one term
Prerequisites: M467a; 338b or 349a
MATH 468A Introduction to Convexity and Extrema, and Economic Applications
Not offered in 1975–76.
MATH 468B Introduction to Convexity and Extrema, and Economic Applications
Not offered in 1975–76.
MATH 469A Statistical Methods with Socio-Economic Applications
Survey and analysis of typical statistical models in the Social Sciences. Review of regression analysis. Extensions of the linear model. Specification errors. Time series and forecasting.
2 hours lectures and one hour seminar, one term
_Prerequisite: 338(b) or 349(a)
MATH 469B Statistical Methods with Socio-Economic Applications
Structural models, identification, estimation and forecasting. Nonlinear estimation. Discussion of data base.
2 hours lectures and one hour seminar, one term Prerequisite: M469a
MATH 470A Numerical Solution of Differential and Integral Equations
Initial value problems: existence and uniqueness of solutions, one step methods, multistep methods, stability, error analysis. Boundary value problems: shooting and discretization methods, implementation problems especially for non-linear equations. Integral equations: correspondence to ordinary differential equations, initial value and boundary value problems, solution techniques.
3 hours lectures, Fall term
Prerequisite: Consent of the instructor
MATH 470B Partial Differential Equations
Discretization methods for partial differential equations, convergence and stability, grid and characteristic methods for hyperbolic equations; iterative methods of solution for parabolic and‘elliptic equations, rate of convergence estimates.
3 hours lectures, Winter term
Prerequisite: Consent of the instructor
MATH 471A Computer Architecture
This course is intended to prepare the student to choose a suitable computer for a given application. Review of combinatorial and sequential logic circuits. Discussion of modules or “building blocks” — central processing units, stores, input/output systems, and bus structures. Case studies of machines.
3 hour lectures, one term
Offered in the Fall, Winter and Spring terms Prerequisite: Math 371la
MATH 472A Program Correctness and Complexity
Methods of program verification. Implications for structured programming. Inductive reasoning about recursive programs and recursively defined data structures, Analysis of program running time. Models of computation for showing algorithm optimality. Lower bounds on problems related to searching and sorting. “Fast” matrix multiplication and lower bounds on the number of arithmetic operations required to compute certain functions.
3 hours lectures, Winter term
Prerequisite:Math 372b
Course Descriptions ’ Mathematics
MATH 472B Abstract Models of Computation
Models of the computational process as reflected by computers, linguistic systems, functional specifications, transformational systems, formal logic, etc. Equivalence of these models. Computational complexity for specific models and abstractions fitting all models. Formal] reducibilities between computational problems, and the complexity of these reducibilities.
3 hours lectures, Winter term
Prerequisite: Math 3726
472¢ Theory of Context Free Languages and Parsing Languages and their representations. Grammars ~ Chomsky hierarchy. Regular sets and sequential machines, Context-free grammars — normal forms, basic properties, Pushdown automata and transducers. Operations on languages. Undecidable problems in language theory. Applications to the design of programming languages and compiler construction.
3 hours lectures, one term
Offered in the Spring and Fall terms
Prerequisite: Math 372b
MATH 474A Scientific Applications Software
Practical computing problems encountered in scientific applications: An overview of batch operating systems; the importance of loaders and overlays; Check points, post mortems and operating system services; FORTRAN as a programming language; Current programming techniques: Design and use of program libraries and human engineering of input and output; Magnetic tapes and bulk storage.
3 hours lectures, one term
Prerequisite: Two of Math 314a, Math 314b, Math 334a, Math 334b, Math 340a and Math 3406
MATH 474B Principles of Operating Systems
Basic concepts of computer hardware: Program trans- Jation; program loading and linking; cooperating sequential processes - computational and data structures, critical section problem, process synchronization primitives (semaphores, etc.), parallel programming; Introduction to multiprogramming; Operating system nucleus; File systems; Reliability; Protection; System performance, meastirement and evaluation.
3 hours lectures, one term
Prerequisite: Math 340a and 340b. Also recommended as a prerequisite or corequisite is Math 47 1a
MATH 474C Business Systems Analysis
Survey of organization and management theory. Systems theory and the systems approach. Systems design: Data base concepts; Implementation of computer based information systems.
3 hours lectures, one term
Prerequisite: Math 320a and 320b or 340a and fourth year standing
MATH 474D Simulation
Simulation techniques are used to study systems which do not lend themselves to analysis. This course is intended to introduce the basic notions of simu- ~ lation as well as introduce the student to programming languages for simulation, The course contents will be: An introduction to simulation; random number generators; stochastic processes; modelling; simulation programming languages; the GPSS language.
3 hours lectures, one term
Prerequisite: Math 320a and 320b or 340a and fourth year standing
MATH 479 Advanced Topics in Computer. Science
MATH 480 Functional Equations
Cauchy’s, Pexider’s and similar equations. Equations for polynomials and for trigonometric functions. Reduction to differential equations. General methods and theorems. Iteration. Applications, Further topics, such as equations for functions of several variables, or equations for analytic functions, or equations on algebraic structures.
MATH 499 Readings in Mathematics
2 hours lectures, one term
MATH 515 Principles of Survey Design
The design of surveys of human or natural populations for research and planning. How to take a representative sample; efficient estimation of population quantities and sample size determination; ways of reducing response bias.
2 hours lectures, 1 hour tutorial per week, one term Prerequisite: An introductory half course in Statistics
Note M515 is intended for senior undergraduate and
graduate students in faculties other-than Mathematics.
It cannot be taken for credit towards a Mathematics degree
Course Descriptions Mathematics
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