Mathematics and Statistics Department

This course surveys topics from diverse areas of mathematics, including problem solving, set theory, logic, historical numeration systems, and number theory. Students will solve problems using processes such as abstraction, pattern recognition, deduction and generalization. Credit will be granted for only one of MATH 101 or MATH 100. Acceptable for credit in all BA, BASc, BBA, HKIN, HNU, MUSI and NURS degrees. Prerequisite: Grade 12 math or equivalent. Three credits.

This course will give an introduction to descriptive and inferential statistics. Topics include descriptive statistics; graphical display of data, random variables and probability distributions, parameter estimations, hypothesis testing and simple linear regression. Students will learn to use statistical software tools; to identify bias in data collection; to organize and summarize data; to make inferences from data and to be able to test the significance of the results. Acceptable for credit in the Faculties of Arts and Business, and the Departments of Human Kinetics, Human Nutrition and B.Sc. Nursing. STAT 101.H will focus on applications to health sciences and STAT 101.B will focus on applications to business and economics. Credit will be granted for only one of STAT 101, STAT 224, STAT 231, or PSYC 292(290). Three credits.

The course surveys interesting and useful topics from diverse areas of mathematics, including problem solving, algebra, graphs and functions, geometry, counting methods, and probability. Students will solve problems using processes such as abstraction, pattern recognition, deduction and generalization. Credit will be granted for only one of MATH 102 or MATH 100. Acceptable for credit in all BA, BASc, BBA, HKIN, HNU, MUSI and NURS degrees. Prerequisite: Grade 12 math or equivalent. Three credits.

This course will give an introduction to some of the quantitative methods used in the fields of business. A presentation of mathematics applicable to business, including functions, modelling, finance, regression, forecasting, simulation, and linear programming. Use of spreadsheets will be a fundamental part of this course. Acceptable for credit in all programs. May only be used as an open or an approved elective in mathematics or computer science programs. Credit will be granted for only one of MATH 105 or MATH 205. Three credits and one-hour lab.

An introduction to differential calculus of a single variable, with applications to physical, life, and social sciences. Topics include limits, differentiation of polynomial, exponential, logarithmic, and trigonometric functions, inverse functions and their derivatives, implicit differentiation, curve sketching, and applied max-min problems. The format of MATH 106 has been structured to provide students with additional learning resources to support and foster a conducive learning environment. Credit will be granted for only one of MATH 106, 121, 126 or ENGR 121. Prerequisite: Grade 12 pre-calculus or equivalent. Six credits of calculus is required in the B.Sc. major, advanced major or honours program. Three credits and one-hour problem-session and one-hour lab.

An introduction to integral calculus for functions of one variable. Topics include definite and indefinite integrals; the fundamental theorem of calculus; methods of integration; numerical approximation of definite integrals; applications to area and volume; probability density functions and distributions; differential equations; and Taylor polynomials. The format of MATH 107 has been structured to provide students with additional learning resources to support and foster a conducive learning environment. Credit will be granted for only one of MATH 107, 122, 127 or ENGR 122. Prerequisite: MATH 106 or 126. Six credits of calculus is required in the B.Sc. major, advanced major or honours program. Three credits and one-hour problem-session and one-hour lab.

This course examines the main idea of calculus of a single variable. It covers functions, limits, continuity; differentiation and integration of polynomial, exponential, logarithmic, and trigonometric functions; product, quotient, and chain rules; applications of differentiation to graphing; maximum-minimum problems, and related rate problems; definite and indefinite integrals, and the fundamental theorem of calculus. Credit will be granted for only one of MATH 121 or MATH 106 or MATH 126. Cross-listed as ENGR 121. Prerequisite: grade 12 pre-calculus or equivalent. Three credits and one-hour lab and one-hour problem session.

A continuation of ENGR 121, this course covers the applications of integration, including areas, volumes, moments, pressure, and work; techniques of integration; numerical integration; length of curves; surfaces of revolution; parametric equations; polar co-ordinates; sequences and series; and Taylor series. Credit will be granted for only one of MATH 122 or MATH 107 or MATH 127. Cross-listed as ENGR 122. Prerequisite: MATH 121. Three credits and one-hour lab and one-hour problem session.

Covers first order linear and non-linear ordinary differential equations; ordinary differential equations of higher order with constant coefficients; applications to engineering problems; power series solutions; Laplace transforms; periodic functions; applications of Laplace transforms to linear systems; Fourier series. Credit will be granted for only one of MATH 221 or MATH 367. Cross-listed as ENGR 221. Prerequisite: MATH 122. Three credits and two-hour problem session.

Extends the ideas introduced in MATH 121 to the calculus of several variables, and covers space curves, arclength, curvature; partial derivatives; implicit functions; constrained and unconstrained extrema; multiple integrals; line, surface, and volume integrals; change of variables in multiple integrals; scalar and vectors fields; gradient, divergence, and curl; Stokes theorem. Credit will be granted for only one of MATH 222 or MATH 267. Cross-listed as ENGR 222. Prerequisite: MATH 122. Three credits and two-hour problem session.

Covers geometric vectors in three dimensions; dot product; cross product; lines and planes; complex numbers; systems of linear equations; matrix algebra; matrix inverse; determinants; Cramer’s rule; introduction to vector spaces; linear independence and bases; rank; linear transformations; orthogonality and applications; Gram-Schmidt algorithm; eigenvalues and eigenvectors. Credit will be granted for only one of MATH 223, MATH 253 or ENGR 123. Cross-listed as ENGR 223. Prerequisites: MATH 122. Three credits and two-hour problem session.

This course covers probability laws and the interpretation of numerical data, probability distributions and probability densities, functions of random variables, joint distributions, characteristic functions, inferences concerning mean and variance, tests of hypotheses, linear regression, and time series analysis. Engineering applications are emphasized and statistical computer packages are used extensively. Credit will be granted for only one of STAT 224, STAT 101, STAT 231, or PSYC 292(290). Cross-listed as ENGR 224. Prerequisite: ENGR 122 or MATH 122. Three credits and two-hour problem session.

Topics include descriptive statistics; data collection, tabulation, and presentation; measures of central tendency and variability; elementary probability; binomial, normal and chi-square distributions; parameter estimation and tests of hypotheses; linear regression and correlation. Students will learn about statistical significance and the communication of statistical evidence, and be introduced to a statistics computer package. Credit will be granted for only one of STAT 231, STAT 101, STAT 224, or PSYC 292 (290). Prerequisite: One of MATH 107, 122, 127. Three credits and a one-hour lab.

An introduction to solution of linear systems, algebra of matrices, determinants, two- and three-dimensional vector spaces, and the matrix eigenvalue problem. Credit will be granted for only one of MATH 253 or MATH 223. Prerequisite: One of MATH 101/102 ,106, 121, 126, CSCI 162. Three credits.

An introduction to abstract vector spaces, including discussion of bases, dimension and homomorphisms of vector spaces; linear transformations, including invariant subspaces; matrix representations and diagonalization procedures. Prerequisites: one of MATH 253, 223 or ENGR 123 and one of MATH 107, 122, 127. Three credits.

Topics include: vectors in two and three dimensions; equations of lines, planes and surfaces; calculus of vector functions, multivariate functions, partial derivatives, multiple integration and applications. Credit will be granted for only one of MATH 267 or MATH 222. Prerequisite: One of MATH 107, 122, 127. Three credits.

An introduction to sets, binary relations and operations; induction and recursion; partially ordered sets; simple combinations; truth tables; Boolean algebras and elementary group theory, with applications to logic networks, trees and languages; binary coding theory and finite-state machines. Cross-listed as CSCI 277. Prerequisite: One of MATH 101/102 ,106, 121, 126, CSCI 162. Three credits.

An investigation of statistics and experimental design in the context of biological and health science issues. Topics include analysis of variance, categorical data; distribution-free tests; linear and multiple regression. Students will learn to analyze data and interpret conclusions using a statistical software package. Recommended strongly for all major, advanced major, and honours students. Credit will be granted for only one of STAT 331, PSYC 394, or PSYC 390. Cross-listed as BIOL 331. Prerequisite: One of STAT 101, 224, 231. Three credits and a one-hour lab.

Material will include combinational analysis; axioms of probability; the law of total probability and Bayes’ Theorem; discrete and continuous random variables; mathematical expectation and variance; joint distributions; introduction to moment-generating functions and their applications; limit theorems. Prerequisites: One of MATH 222, 267 and one of STAT 101, 224, 231 or permission by the department chair. Three credits.

The course covers the principle of inclusion and exclusion; generating functions; recurrence relations; rings and modular arithmetic; finite state machines; group and coding theory; Pólya’s method of enumeration; finite field and combinatorial design; graph theory. Prerequisite: MATH 277. Three credits. Offered 2024-2025 and in alternate years.

This course introduces algebraic structures such as groups, rings and fields along with fundamental algebraic concepts such as symmetries, permutations, isomorphisms and homomorphisms. Applications from diverse areas may include coding theory, crystallography, circuits, logic, geometry and graph theory. Prerequisites: MATH 254, 277. Three credits.

Topics include vectors; vector differentiation including gradient, divergence, and curl; vector integration including the Gauss and Stokes theorems. Prerequisites: One of MATH 222 or 267 and one of MATH 223 or 253. Three credits. Offered 2024-2025 and in alternate years.

This course considers rigorous development of the real number system; numerical sequences and series; properties of continuous functions; metric spaces; sequences and series of functions. Prerequisites: MATH 254, 267, 277. Three credits.

Topics include first- and second-order linear differential equations; systems of linear differential equations; methods of solution including Laplace transforms and series solution; introduction to non-linear differential equations and numerical methods. Credit will be granted for only one of MATH 367 or MATH 221. Prerequisite: one of MATH 107, 122, 127. Three credits.

A survey of Euclidean and non-Euclidean geometries. Topics include geometric axioms, the parallel postulate, constructions, models of hyperbolic geometry, topology, and fractals. Prerequisite: One of MATH 253, 277. Three credits. Offered 2024-2025 and in alternate years.

Modern sports science and professional teams increasingly require the use of applied statistical and analytical techniques. This course introduces the use of statistical analysis in a variety of contexts applicable to sport, including models, prediction, inference, simulation, and performance metrics. A research project involving the analysis of real-world data is an integral part of the course. Credit will only be granted for one MATH 382 or MATH 471(2019-2020) or MATH 399(2020-2021). Prerequisite: One of STAT 101, 224, 231. Three credits.

This course teaches the use of mathematical models to solve real-world problems. The modelling cycle will be practiced using problems found in the real world. Prerequisites: One of MATH 222, 267, and one of MATH 223, 253. Three credits. Offered 2024-2025 and in alternate years.

Topics include stochastic models of financial markets; forward and futures contracts; European options and equivalent Martingale measures; hedging strategies and management of risk; term structure models and interest rate derivatives; and optimal stopping and American options. Ito’s lemma and Girsanov’s theorem to develop methods for pricing financial derivatives are examined. Pricing problems are considered in discrete (Binormal option price model) and continuous-time (Black-Scholes Merton price model). Credit will be granted for only one of MATH 389 or MATH 471 offered in 2012-2013. Prerequisites: One of MATH 106, 126 and one of STAT 101, 231. Three credits. Offered 2024-2025 and in alternate years.

The topics are: polynomial rings, unique factorization, irreducible polynomials; Sylow theorems, solvability of polynomial equations; Galois theory; and the Jordan canonical form. Prerequisite: MATH 354. Three credits. Offered 2024-2025 and in alternate years.

Topics include complex numbers, elementary functions, series and integration, Laurent series, and residue theory. Prerequisites: One of MATH 221, 367 and one of MATH 222, 267. Three credits. Offered 2024-2025 and in alternate years.

Students will prepare and present a thesis based on original research conducted under the supervision of a faculty member. Required for honours students. Six credits.

Students will prepare and present a thesis based on original research conducted under the supervision of a faculty member. Required for honours students. Six credits.

Cross-listed as STAT 491. The purpose of this non-credit course is to assist students in carrying out research, composition, and oral presentation. Students will present a project topic in the fall term and their project in the spring. Attendance at departmental seminars is mandatory. No credit.

Cross-listed as MATH 491. The purpose of this non-credit course is to assist students in carrying out research, composition, and oral presentation. Students will present a project in the fall term and their completed project in the spring. Attendance at Departmental seminars is mandatory. No credit.

Students will prepare and present a thesis based on original research conducted under the supervision of a faculty member. Required for honours students; permitted for advanced major students. Three credits.

Students will prepare and present a thesis based on original research conducted under the supervision of a faculty member. Required for honours students; permitted for advanced major students. Three credits.