# Mathematics and Statistics Department

## Introductory Statistics

STAT
101
In-Person, Online-Scheduled Delivery
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, PSYC 292(290). Three credits.

## Sets, Logic & Number Theory

MATH
101
In-Person
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.

## Graphs, Functions, Geometry

MATH
102
In-Person
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.

MATH
105
In-Person
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 and MATH 205. Three credits and one-hour lab.

## Calculus l

MATH
106
In-Person
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, ENGR 121 or MATH 126. 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.

## Calculus ll

MATH
107
In-Person
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, ENGR 122 or MATH 127. 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.

## Calculus I for Engineers

MATH
121
In-Person
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.

## Calculus II for Engineers

MATH
122
In-Person
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.

## Calculus l

MATH
126
In-Person
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. Credit will be granted for only one of MATH 106, ENGR 121 or MATH 126. 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 a one-hour lab every other week.

## Calculus ll

MATH
127
In-Person
An introduction to integral calculus for functions of one variable. Topics include definite and indefinite integrals; 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. Credit will be granted for only one of MATH 107, MATH 127 or ENGR 122. Prerequisite: MATH 106 or MATH 111 or MATH 126. Six credits of calculus is required in the B.Sc. major, advanced major or honours program. Three credits and a one-hour lab every other week.

## Differential Equation for Engr

MATH
221
In-Person
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.

## Calculus III for Engineers

MATH
222
In-Person
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.

## Linear Algebra for Engineers

MATH
223
In-Person
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 or MATH 253. Cross-listed as ENGR 123. Prerequisites: MATH 122. Three credits and two-hour problem session.

## Prob & Stats for Engineers

STAT
224
In-Person
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.

## Stats for Students in Sciences

STAT
231
In-Person
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.

MATH
236
In-Person
Evidence-based decision-making in business required the use of the mathematical models to analyze data and to help identify and assess possible answers to what-if questions. This course introduces the student to what should be considered when using mathematical models for business. Topics include model construction, analyzing and modeling data sets, optimization, risk analysis and model testing. Prerequisite: One of MATH 105, 106 or 126. Three credits. Offered 2023-2024 and in alternate years.

## Matrix Algebra

MATH
253
In-Person
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.

## Linear Algebra

MATH
254
In-Person
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.

## Calculus III

MATH
267
In-Person
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.

## Discrete Structures

MATH
277
In-Person
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.

## Natural Resource Modeling

MATH
287
In-Person
The course covers formulating real-world problems from renewable natural resources; using software to solve mathematical models; formulating and testing policies for managing dynamic systems; and developing communication skills through report writing. Prerequisite: One of MATH 107, 122, 127. Three credits. Offered 2023-2024 and in alternate years.

## Statistical Methods

STAT
331
In-Person
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.

## Intro Probability Theory

STAT
333
In-Person
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.

## Mathematical Statistics

STAT
334
In-Person
Topics include distribution theory; order statistics; point and interval estimation; MVUEs and the Rao-Blackwell theorem; consistency and sufficiency; the method of maximum likelihood; the method of moments; uniformly most powerful tests and the Neymann-Pearson fundamental lemma; likelihood ratio tests; least squares theory; statistical models and estimation in ANOVA. Prerequisite: STAT 333. Three credits.

## Management Science

MATH
335
In-Person
This course prepares students for careers as analysts and consultants in industries with a focus on enhancing business value through operations, logistics and supply chain management. A variety of successful implementations of management science/operations research tools in different application areas will be studied. Tools such as linear programming, project scheduling with uncertain activity times, various inventory models and simulation will be introduced and coupled with application in the fields of managing operations in manufacturing, long term financial planning and management of healthcare systems. Cross-listed as CSCI 335. Prerequisites: One of MATH 106, 121, 126 or CSCI 161. Three credits. Offered 2023-2024 and in alternate years.

## Modern Algebra I

MATH
354
In-Person
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.

## Regression Analysis

STAT
357
In-Person
An investigation of the statistical techniques for modelling the relationship between a dependent variable and one or more independent or predictor variables. Topics include ordinary least squares method and linear regression, matrix algebra and multiple regression, variable selection, residual analysis, multicolinearity, and generalized linear models. Credit will be granted for only one of STAT 357 or STAT 435. Prerequisites: One of MATH 223, 253 and one of STAT 101, 224, 231 or permission of the chair. Three credits and a one-hour lab. Offered 2023-2024 and in alternate years.

## Real Analysis I

MATH
366
In-Person
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.

## Differential Equations

MATH
367
In-Person
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.

## Theory of Numbers

MATH
372
In-Person
Topics include divisibility of integers; congruences; the Chinese remainder theorem; quadratic residues and non-residues; Gaussian reciprocity law; number theoretic functions; and the Moebius inversion formula. Prerequisite: MATH 277. Three credits. Offered 2023-2024 and in alternate years.

## Sports Analytics

MATH
382
In-Person
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.

## Real Analysis II

MATH
466
In-Person
Material includes topology of Euclidean nspace; differentiation; Riemann Stieltjes integration; limits and continuity in n-dimensions; differentiation of nonlinear transformations; and the implicit function theorem. Prerequisite: MATH 366. Three credits. Offered 2023-2024 and in alternate years.

## Partial Differential Equations

MATH
481
In-Person
The study of special functions and partial differential equations, including the wave, heat, and Laplace equations in various coordinate systems. Prerequisites: MATH 254 and one of MATH 221, 367 and one of MATH 267, 222. Three credits. Offered 2023-2024 and in alternate years.

## Honours Thesis

STAT
490
In-Person
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.

## Honours Thesis

MATH
490
In-Person
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.

## Senior Seminar

STAT
491
In-Person
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.

## Senior Seminar

MATH
491
In-Person
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.

## Senior Thesis

MATH
493
In-Person
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.

## Senior Thesis

STAT
493
In-Person
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.