Mathematics

Mathematics is a discipline which has been said to be the Queen of the Sciences, and is the foundation of most modern quantitative and qualitative studies. The permanence and universality of mathematics throughout the ages is a consequence of its very nature. Mathematics is cumulative, developing from the earliest use of numbers by prehistoric civilizations to the highly deductive nature of geometry as developed by the Greeks, from the practical applications of calculus developed in the seventeenth century to the modern use of number theory in computer cryptography. Mathematics has many faces, from practical uses of its statistical tools to theoretical studies of abstract relationships. Our goal is to introduce students to all facets of the discipline, and to give them an appreciation of the historical, theoretical and applied nature of the discipline, as well as a full understanding of the beauty of the subject.

The Department offers a broad variety of courses and programs in Mathematics. Beginning courses may introduce students to the applications to which Calculus may be applied or the practical uses of statistics; more advanced courses deal with topics ranging from geometry to game theory. All courses in the Mathematics curriculum offer a blend of theory and practical applications. Many of the courses offered include a substantial computational component, and students are encouraged to use the mathematical software tools available. Courses are designed to address the needs of a wide variety of users, from the casual to the professional. Some students may enrol in a course to familiarize themselves with university level mathematics, while others will take a series of courses related directly to their chosen study area. Those choosing to pursue a minor or major in mathematics will be exposed to more advanced courses which blend Mathematical theory and practice.

Mount Allison has been very successful in placing many of its students in graduate programmes in Mathematics, while many others have found employment after graduation in one of many fields for which mathematical understanding is an asset. Teaching, actuarial work, law and medicine are all areas requiring the ability to think and reason logically and for which a mathematical background can prove beneficial.

Disciplinary B.A. and B.Sc. Programmes

B.A. OR B.Sc. MINOR in Mathematics is 24 credits earned as follows:

6	from Mathematics 1111, 1121
12	from Mathematics 2111, 2121, 2211, 2221, 2311, 2321.
6	from Mathematics at the 3/4000 level.

B.A. MAJOR AREA OF STUDY in Mathematics is 60 credits earned as follows:

15	from Mathematics 1111, 1121, 2111, 2211, 2221
3	from Mathematics 2121, 2311
6	from Mathematics 3311, 3321
18	from Mathematics at the 3/4000 level
6	from Computer Science 1711, 1721
12	credits from complementary disciplines chosen in consultation with the Programme Advisor

B.A. HONOURS in Mathematics is 72 credits earned as follows:

18	from Mathematics 1111, 1121, 2111, 2121, 2211, 2221
6	from Computer Science 1711, 1721
24	from Mathematics 3011, 3111, 3121, 3211, 3311, 3321, 4131, 4221
3	from Mathematics 3411
15	from Mathematics at the 3/4000 levels
6	from Mathematics or Computer Science at the 3/4000 levels

B.A. OR B.Sc. HONOURS in Computer Science and Mathematics is 75 or 87 credits earned as follows:

18	from Computer Science 1711, 1721, 2211*, 2611, 2711, 2931
15*	from Mathematics 1111, 1121, 2111, 2121, 2221
9	from Mathematics 3111, 3211, 3311
3	from Mathematics 3011, 3221, 3231, 3251, 4221
3	from Mathematics at the 3/4000 levels
15	from Computer Science 3361, 3411, 3611, 3911, 4721
12	from Computer Science or Mathematics at the 3/4000 level
12	from Chemistry 1001, 1021; Physics 1051, 1551 (only for B.Sc.)

* Computer Science 2211 was formerly listed as Mathematics 2211

Note: The listing of a course in the calendar is not a guarantee that the course is offered every year.

Note: Students must obtain a grade of at least C- in all courses used to fulfill prerequisite requirements. Otherwise, written permission of the appropriate Department or Programme Coordinator must be obtained.

B.Sc. MAJOR AREA OF STUDY in Mathematics is 60 credits earned as follows:

18	from Mathematics 1111, 1121, 2111, 2121, 2211, 2221
6	from Mathematics 3311, 3321
18	from Mathematics at the 3/4000 level
6	from Computer Science 1711, 1721
6	from Chemistry 1001, 1021
6	Physics 1051, 1551

B.Sc. HONOURS in Mathematics is 84 credits earned as follows:

18	from Mathematics 1111, 1121, 2111, 2121, 2211, 2221
6	from Computer Science 1711, 1721
27	from Mathematics 3011, 3111, 3121, 3211, 3311, 3321, 3411, 4131, 4221
15	from Mathematics at the 3/4000 level
6	from Mathematics or Computer Science at the 3/4000 level
6	from Chemistry 1001, 1021
6	from Physics 1051, 1551

Interdisciplinary B.Sc. Programme

B.Sc. HONOURS in Mathematics and Physics is 90 credits earned as follows:

18	from Mathematics 1111, 1121, 2111, 2121, 2211, 2221
3	from Computer Science 1711
6	from Chemistry 1001, 1021
12	from Physics 1051, 1551, 2251, 2801
9	from Mathematics 3111, 3211, 3311
9	from Mathematics 3131, 3141, 4131
6	from Mathematics 3121, 3151, 3231, 3321, 3411, 3431, 3531, 4111, 4151, 4211
18	from Physics 3101, 3201, 3401, 3701, 3811, 3821
3	from Physics at the 4000 level
6	from Physics 4990

Note: The listing of a course in the calendar is not a guarantee that the course is offered every year.

PLACEMENT IN MATHEMATICS

Students wishing to take the introductory calculus course (Mathematics 1111) are required to write a Mathematics Placement Test to determine their level of mathematical preparation. Based on their test scores and the University regulations, students will be placed in Mathematics 1011 or Mathematics 1111. The Mathematics Placement Test will be administered prior to the beginning of classes. Students will be allowed to re-write the test during the first week of classes.

MATHEMATICS COURSES

MATH 1011 (3CR)
SETS, FUNCTIONS AND RELATIONS

This course will focus on the real number system, inequalities, plane analytic geometry (lines and conics), functions, inverse functions, polynomials, rational functions, trigonometric functions, exponential and logarithmic functions. Fundamental methods of graphing functions, using non-calculus based techniques, will be emphasized. This course is primarily intended for non-science students or as a prerequisite for MATH 1111 for those students who have not passed the Mathematics Placement Test. Science students who have passed the Mathematics Placement Test require the permission of the Department of Mathematics and Computer Science to enrol in this course. This course cannot be used to satisfy the Bachelor of Science degree requirement of a course in MATH/COMP (7.3.3). Credit will not be given for this course if credit has already been granted for MATH 1111.

MATH 1111 (3CR)
INTRODUCTION TO CALCULUS I

Derivatives of the algebraic and exponential functions are developed. Applications include curve sketching, related rates, and optimization problems.

Prereq: A passing score on the Mathematics Placement Test, or MATH 1011; or permission of the Department. Students enrolling in Mathematics 1111 should normally have completed a university preparatory course in Mathematics designed to prepare them for University calculus

MATH 1121 (3CR)
INTRODUCTION TO CALCULUS II

The derivatives of trigonometric functions are introduced, various techniques of integration studied and some applications presented. Among these applications are: area between curves, volume work and elementary differential equations.

Prereq: MATH 1111; or permission of the Department

MATH 1131 (3CR)
MATHEMATICS FOR LIFE AND ENVIRONMENTAL SCIENCE

An application-oriented continuation of the study of calculus and an introduction to other topics of interest to students in the life and environmental sciences.

Prereq: MATH 1111; or permission of the Department

MATH 1251 (3CR)
FINITE MATHEMATICS

This course introduces students at all levels to the most applicable branches of finite mathematics and is particularly suitable for students in the social and behavioural sciences and commerce. Topics discussed include Markov chains, linear programming and game theory.

MATH 2111 (3CR)
MULTIVARIABLE CALCULUS

Topics include: Sequences and series, power series, Taylor and MacLaurin series; conic sections, quadric surfaces, cylindrical and spherical coordinates in three space; functions of several variables: continuity, partial derivatives, tangent planes, chain rule, maximum and minimum values, Lagrange multipliers, double and triple integrals.

Prereq: MATH 1121; or permission of the Department

MATH 2121 (3CR)
ELEMENTARY DIFFERENTIAL EQUATIONS

This is an introduction to the techniques and applications of first and second order differential equations. Included will be: applications of first order equations to areas such as growth and decay, cooling and diffusion, mixture problems, chemical reactions, the logistic equation, orthogonal trajectories, higher order differential equations and applications, and power series solutions of differential equations.

Prereq: MATH 2111; or permission of the Department

MATH/COMP 2211 (3CR)
DISCRETE STRUCTURES

An introduction to the terminology and concepts of discrete mathematics, covering such topics as: sets, functions, induction, enumeration, graphs and trees, boolean algebras, semigroups and groups, and the design of algorithms.

Prereq: MATH 1111; or permission of the Department

MATH 2221 (3CR)
LINEAR ALGEBRA

An introductory course in linear algebra covering such topics as linear equations, matrices, determinants, vector spaces, linear transformations, inner products, eigenvalues, and eigenvectors. Whenever possible, concepts are given a geometric interpretation in two and three-dimensional space.

Prereq: MATH 1111; or permission of the Department

MATH 2311 (3CR)
STATISTICS I

This course is designed to introduce students to some of the concepts and techniques of probability and statistics. Attention is focused on some special probability distributions including binomial, normal, Student's t, chi-square, and F. Some basic statistical ideas are developed and the testing of statistical hypotheses is introduced. Examples are drawn from a wide variety of sources. A statistical software package is introduced.

Prereq: University preparatory level Mathematics or MATH 1011 and either MATH 1111, or registration in second year or higher; or permission of the Department

MATH 2321 (3CR)
STATISTICS II

Further applications of hypothesis testing. Topics selected from analysis of variance, linear and nonlinear regression, correlation estimation and prediction, independence, Wilcoxon and goodness-of-fit tests.

Prereq: MATH 2311 or 3311; or permission of the Department

MATH 3011 (3CR)
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: MATH 2211; or permission of the Department

MATH 3031 (3CR)
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: MATH 1121 (or 1131) and 6 credits from MATH 2111, 2121, 2211 and 2221

MATH 3111 (3CR)
REAL ANALYSIS I

A systematic and rigorous study of the real numbers and functions of a real variable, emphasizing limits and continuity.

Prereq: MATH 2111, 2121, 2211; or permission of the Department

MATH 3121 (3CR)
REAL ANALYSIS II

A continuation of Mathematics 3111 including the study of concepts from the Calculus, including differentiation and integration.

Prereq: MATH 3111; or permission of the Department

MATH 3131 (3CR)
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: MATH 2121 and 2221; or permission of the Department

MATH 3141 (3CR)
VECTOR CALCULUS

Topics covered include vectors in the plane and in three space, vector functions, curves, tangent and normal vectors, velocity and acceleration; curvature and arc length, directional derivatives and the gradient, vector fields, line integrals, the Fundamental Theorem of line integrals, divergence and curl, Green's Theorem, parametrized surfaces, surface area and surface integrals, flux, Stokes' Theorem, and the Divergence Theorem.

Prereq: MATH 2111; or permission of the Department

MATH 3151 (3CR)
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: MATH 2121 and 2221; or permission of the Department

MATH 3211 (3CR)
MODERN ALGEBRA I

An introduction to the theory of groups and rings.

Prereq: MATH 2211 and MATH 2221; or permission of the Department

MATH 3221 (3CR)
ADVANCED LINEAR ALGEBRA

An advanced course in linear algebra, covering selected topics from: change of basis and similarity of matrices; multilinear forms and determinants; canonical 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 conic sections.

Prereq: MATH 2221; (MATH 2211 is recommended); or permission of the Department

MATH 3231 (3CR)
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: MATH 2211; or permission of the Department

MATH 3251 (3CR)
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: MATH 2211, 2221; or permission of the Department

MATH 3311 (3CR)
PROBABILITY AND STATISTICS I

An introduction to the mathematical theory of probability. Topics covered include: sample space, events, axioms, conditional probability, Bayes Theorem, random variables, combinatorial probability, moment generating functions, transformations of random variables, univariate and jint distributions with reference to the binomial, hypergeometric, normal, Gamma, Poisson, and others; convergence of sequences of variables, central Limit Theorem.

Prereq: MATH 2111; or permission of the Department

MATH 3321 (3CR)
PROBABILITY AND STATISTICS II

An introduction to mathematical statistics. Topics covered include: Estimation, unbiasedness, efficiency, Cramer-Rao lower bound, consistency, sufficiency, maximum likelihood estimators, hypothesis testing, power of tests, likelihood ration, regression analysis and analysis of variance.

Prereq: MATH 3311; or permission of the Department

MATH/COMP 3411 (3CR)
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: MATH 1121, 2221, and COMP 1711 or 1751; or permission of the Department

MATH 3431 (3CR)
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: MATH 2121 and MATH/COMP 3411; or permission of the Department

MATH/COMP 3511 (3CR)
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: MATH 2221, 3 credits in Computer Science; or permission of the Department

MATH/COMP 3531 (3CR)
SIMULATION AND MODELLING

An introduction to the simulation technique for studying mathematical models. Specific titles 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: MATH 1111; one of MATH 2311, 3311, PSYC 2001 and 2011; three credits in Computer Science; or permission of the Department

MATH 4111 (3CR)
TOPOLOGY

An introduction to the study of metric and topological spaces, convergence, and continuous functions.

Prereq: MATH 3111; or permission of the Department

MATH 4121 (3CR)
TOPICS IN ANALYSIS

This course covers selected topics in Analysis, depending on the background and interests of the students involved.

Prereq: MATH 3111; or permission of the Department

MATH 4131 (3CR)
COMPLEX VARIABLES WITH APPLICATIONS

This course is designed primarily for students in mathematics, physics, or engineering. It covers analytic functions, Cauchy-Riemann equations, conformal mapping, complex integrals, Cauchy's integral theorem, Taylor and Laurent Series, residues, evaluation of real integrals, and inverse transforms.

Prereq: MATH 2111, 2121; or permission of the Department

MATH 4141 (3CR)
MEASURE AND INTEGRATION

Topology of Rn, Lebesque Measure, Measurable Functions, the Lebesque integral, the convergence theorems and products measures. As time permits, other topics such as abstract measure theory, Lp-spaces and absolute continuity will be covered.

Prereq: MATH 3110 or 3121; or permission of the Department

MATH 4151 (3CR)
BOUNDARY AND EIGENVALUE PROBLEMS

This course is designed primarily for students in mathematics, physics, or engineering. It extends the material studied in Mathematics 3131. Topics include separation of variables (product method), generalized Fourier series, Sturm-Liouville theory, Legendre polynomials, Bessel Functions, Green's functions, and calculus of variations.

Prereq: MATH 3131; or permission of the Department

MATH 4161 (3CR)
TOPICS IN CLASSICAL APPLIED MATHEMATICS

This course covers selected topics in Classical Applied Mathematics, depending on the back-ground and interests of the students involved.

Prereq: MATH 4131 and 4151; or permission of the Department

MATH 4211 (3CR)
TOPICS IN ALGEBRA

This course covers selected topics in Algebra, depending on the background and interests of the students involved.

Prereq: MATH 3221; or permission of the Department

MATH 4221 (3CR)
MODERN ALGEBRA II

The classical theory of fields and rings and their applications.

Prereq: MATH 3211; or permission of the Department

MATH 4311 (3CR)
TOPICS IN PROBABILITY AND STATISTICS

This course covers selected topics in Probability and Statistics, depending on the background and interests of the students involved.

Prereq: MATH 3311 and 3321; or permission of the Department

MATH/COMP 4631 (3CR)
THEORY OF COMPUTATION

This course is an introduction to theoretical aspects of Computer Science such as formal language and automata theory and complexity theory.

Prereq: MATH 2211 and COMP 1721; or permission of the Department

MATH 4951 (3CR)
SPECIAL TOPICS IN MATHEMATICS

This course enables students to pursue their interests in areas not covered by other classes offered at the 4000 level. It usually involves independent study in a programme planned by the student and approved by the Department.