Mathematics 3000 Series
3011 SET THEORY AND MATHEMATICAL LOGIC
This course provides a mathematical introduction to the basic ideas of set theory and logic. Topics covered may include: axiom of choice, cardinal and ordinal numbers, Boolean algebras and their applications, completeness, decidability, philosophies of mathematics.
Prereq: Mathematics 2211; or permission of the Department.
3031 HISTORY OF MATHEMATICS
A survey of the history of Mathematics. Topics include: the achievements of early civilizations, the developments in Europe leading to the calculus and its consequences, the growth of rigor in the 18th and 19th centuries, the axiomatic method in the 20th century.
Prereq: Mathematics 1121 (or 1131) and 6 credits from Mathematics 2111, 2121, 2211 and 2221.
3111 REAL ANALYSIS I
A systematic and rigorous study of the basic concepts of functions of real variables and to develop
some further technique of Calculus. Topics emphasized are limits, continuity
Prereq: Mathematics 2111, 2121, 2211; or permission of the Department.
Note: Not available for credit for students who have completed mathematics 3110.
3121 REAL ANALYSIS II
A continuation of Mahtematics 3111 including the study of concepts from calculus, differentiation and integration.
Prereq: Mathematics 3111; permission of the Department.
Note: Not available for credit for students who have compoleted Mathematics 3110.
3131 MATHEMATICAL METHODS FOR DIFFERENTIAL EQUATIONS
This course is designed primarily for students in mathematics, physics, or engineering. It covers systems of 1st and 2nd order ordinary differential equations, Laplace and Fourier transforms, power series solutions for equations with singular points, and Fourier series.
Prereq: Mathematics 2121 and 2221; or permission of the Department.
3151 AN INTRODUCTION TO MATHEMATICAL MODELLING
This course provides an introduction to the nature of theoretical
mathematical modelling illustrated by examples drawn from the
physical and engineering sciences, pursuit and conflict problems,
population dynamics (mathematical ecology), traffic flow, sociological
problems (voting, kinship, cultural stability) and other areas
depending on the interests of the class.
Prereq: Mathematics 2121 and 2221; or permission of the Department.
3211 MODERN ALGEBRA I
An introduction to the theory of groups and rings.
Prereq: Mathematics 2211 and Mathematics 2221; or permission of the Department.
3221 ADVANCED LINEAR ALGEBRA
An advanced course in linear algebra, covering selected topics from: change of basis and
similarity matrices; multilinear forms and determinants; canonocal forms,
Primary Decomposition Theorem, Jordan form; semisimple and normal
operators; spectral theory; quadratic forms; applications to geography,
electrical networks, linear programming, differential equations, or
the geometry of conoc sections.
Prereq: Mathematics 2221; (Mathematics 2211 is recommended); or
permission of the Department.
3231 NUMBER THEORY
An introductory half-course in the theory of numbers covering such topics as: Euclidean algorithm, Fundamental Theorem of Arithmetic, congruences, diophantine equations, Fermat and Wilson Theorems, quadratic residues, continued fractions, Prime number theorem.
Prereq: Mathematics 2211; or permission of the Department.
3251 INTRODUCTION TO COMBINATORICS AND GRAPH THEORY
Topics covered include enumeration (permutations and combinations,
inclusion-exclusion and pigeonhole principles, recurrence relations
and generating functions), algorithmic graph theory (minimum-weight
spanning trees and minimum-weight paths) and combinatorial design
theory (latin squares and finite geometries, balanced incomplete
block designs, triple systems).
Prereq: Mathematics 2211, 2221; or permission of the Department.
3311 PROBABILITY AND STATISTICS I
An introduction to the mathematical theory of probability and statistics. The following topics are covered: special distributions, distributions of functions of random variables, interval estimation, order statistics, Central Limit Theorem, statistical tests.
Prereq: Mathematics 2111; or permission of the Department.
Note: Not available for credit for students who have completed Mathematics 3310.
3321 PROBABILITY AND STATISTICS II
An introduction to the mathematical theory of probability and statistics. The following topics are covered: special distributions, distributions of functions of random variables, interval estimation, order statistics, Central Limit Theorem, statistical tests.
Prereq: Mathematics 3311; or permission of the Department.
3411 NUMERICAL ANALYSIS
This course is an introduction to numerical methods for solving a variety of problems in mathematics, the natural sciences, and engineering. Topics to be studied include numerical solution of linear and nonlinear systems of equations, Gauss elimination, pivoting strategies, numerical stability, PLU factorization, tridiagonal matrices, polynomial and cubic spline approximation and interpolation.
Prereq: Mathematics 1121, 2221, and Computer Science 1711 or 1751; or
permission of the Department.
Note: This course is cross listed as Computer Science 3411 and may therefore count as three credits in either discipline.
3431 ORDINARY DIFFERENTIAL EQUATIONS
This course utilizes both numerical and theoretical techniques to study ordinary differential equations. Topics include numerical, integration, Runge-Kutta and multistep methods, stability, introduction to qualitative methods, phase-plane analysis, stability of non-linear systems, Lyapunov's method, chaos theory.
Prereq: Mathematics 2121 and Mathematics/Computer Science 3411;
or permission of the Department.
M/CS 3511 LINEAR PROGRAMMING
Among the topics covered are linear and integer programming, the simplex and revised simplex methods, duality theory and sensitivity analysis, and various applications.
Prereq: Mathematics 2221, Computer Science 1711 or 1751; or permission of the Department.
3531 SIMULATION AND MODELLING
An introduction to the simulation technique for studying mathematical models. Specific topics to be considered include: systems theory and system models, continuous system simulation, discrete system simulation, Monte Carlo methods, random number generators, and simulation languages. Emphasis will be placed upon computer implementation of the methods studied.
Prereq: Mathematics 1111; one of Mathematics 2311,
Mathematics 3311, Psychology 2001 and 2101;
one of Computer Science 1711 or 1851; or permission of the Department.
Note: This course is cross listed as Computer Science 3531 and may therefore count as three credits in
either discipline.
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