# Courses

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### Prerequisites for MATH 1102 and 1113 and the Mathematics Placement Test

The Mathematics Placement Test is designed to ensure that students begin their university mathematics study at a level appropriate to their background. Students who plan to take MATH 1102 or MATH 1113 must write the placement test unless they have a university credit prerequisite—high school Precalculus Mathematics alone is not sufficient. Brochures on the topics covered by the placement test are available from the Mathematics Department. Depending on their performance on the test, students may be placed into MATH 1113, 1102 or 0020. Students are advised to write the placement test before they register for their mathematics courses, but not necessarily in the same semester. Placement test assessments are valid for up to three years, but the test may be written only once per semester. Placements may be appealed to the department Chair, whose decision is final. Further information, including sample questions and test schedules, is available from the department.

### Prerequisites for MATH 2208

The prerequisites for this course is grade XI or grade XII Mathematics, or MATH 0017 with a grade of C or higher or MATH 0020 with a grade of C or better, or any 1000 level Mathematics course. Since mathematical skills deteriorate over time, students who have been away from mathematics for a while often need to review basic mathematics beforehand in order to succeed in MATH 2208. An online self-test is available on the Mount’s website under Departments, Mathematics. Brochures on the topics from high school mathematics required for these courses are available from the Mathematics Department, a booklet reviewing these topics is on sale in the bookstore, and the course MATH 0020 provides an intensive review for those who need it. Students unsure of their mathematical preparation should consult the Mathematics Department for advice.

Courses*Note: Students who do not meet the formal prerequisites for the courses listed below, but think they may qualify due to special circumstances, should consult the department.*

## MATH 0017*

Statistics Preparation**0.25 non-credit unit**An introduction to the mathematics needed for students who plan to take MATH 2208 and MATH 2209 (Introduction to Statistics I and II).

**MATH 0017 may not count toward the major or minor requirements.*

## MATH 0020*

College Algebra**0.5 non-credit unit**A study of the fundamentals of algebra: the real numbers, polynomials and factoring, rational and radical expressions, equations and inequalities, rectangular coordinates, systems of linear equations.

*MATH 0020 may not count toward the major or minor requirements.

*MATH 0020 may not count toward the major or minor requirements.

## MATH 1102

Precalculus I: Algebraic Functions**0.5 unit**

*Prerequisite: grade XI and grade XII academic mathematics and mathematics placement test or MATH 0020 passed in the last three years with a grade of C or higher or equivalent*

A first course to prepare students for calculus. Linear, quadratic, polynomial, rational, radical, and piecewise functions will be studied numerically, graphically, and algebraically. Conic sections and limits will also be introduced. There will be an emphasis on problem solving and applications.

## MATH 1103

Precalculus II: Transcendental Functions**0.5 unit**

*Prerequisite: MATH 1102*

A second course to prepare students for calculus. Trigonometric, exponential and logarithmic functions will be studied numerically, graphically, and algebraically. Finite sequences and series and mathematical induction will also be introduced. There will be an emphasis on problem solving and applications.

## MATH 1113

Introductory Calculus I**0.5 unit**

*Prerequisites: high school precalculus mathematics and mathematics placement test, or MATH 1103*

An introduction to differential and integral calculus for algebraic and transcendental functions. Topics include: limits, continuity, differentiation, curve sketching, implicit differentiation and applications.

## MATH 1114

Introductory Calculus II**0.5 unit**

*Prerequisite: MATH 1113*

An introduction to integral calculus. Topics include: the Fundamental Theorem, techniques of integration, improper integrals, polar co-ordinates, parametric equations, and applications.

## MATH 2206

Introduction to Probability**0.5 unit**

*Prerequisite: MATH 1114*

A calculus-based introduction to probability theory. Topics include sample spaces, random variables, discrete and continuous distributions, expectation, functions of a random variable, sums of random variables and the Central Limit Theorem. May include an introduction of the theory to statistical applications.

## MATH 2208

Introduction to Statistics I**0.5 unit**

*Prerequisite: grade XI or grade XII academic mathematics or equivalent, or MATH 0017 with a grade of C or higher or MATH 0020 with a grade of C or higher, or any 1000 level mathematics course*

An introduction to statistical methods. Topics include graphical presentations of data, summary statistics, the normal curve, least-squares regression, correlation, two-way tables, survey and experimental design, probability, random variables, distribution of sample proportions, confidence intervals and hypothesis testing for one and two population proportions. Laboratory sessions demonstrate applications from various disciplines. Laboratory required (75 minutes/week)

## MATH 2209

Introduction to Statistics II**0.5 unit**

*Prerequisite: MATH 2208*

A continuation of MATH 2208. Topics include: distribution of the sample mean, one-sample, two-sample and paired t procedures, the chi-square test, inference for simple and multiple regression, one-factor and two-factor Analysis of Variance. Laboratory sessions demonstrate applications from various disciplines.

*Note: Students who have received credit for MATH 2207 may not take this course for credit.*Laboratory required (75 minutes/week)

## MATH 2211

Intermediate Calculus I**0.5 unit**

*Prerequisite: MATH 1114*

A third course in calculus. Topics include ordinary differential equations, sequences, series, functions of several variables, partial derivatives and an introduction to double intergrals.

*Note: Students who have received credit for MATH 2210 may not take this course for credit.*

## MATH 2212

Intermediate Calculus II**0.5 unit**

*Prerequisite: MATH 2211*

Vector functions, directional derivatives, double integrals with polar co-ordinates, line integrals, Green’s theorem and applications.

*Note: Students who have received credit for MATH 2210 may not take this course for credit.*

## MATH 2221

Linear Algebra I

**0.5 unit***Prerequisite: at least 1.0 unit of university mathematics completed. If this unit does not include MATH 1113, then MATH 1113 must be taken concurrently.*

An introduction to linear algebra, with applications. Topics include systems of linear equations, matrices, determinants, Euclidean n-space, spanning, linear independence, basis and dimension, dot products, orthogonality, and orthogonal projections.

## MATH 2222

Linear Algebra II

**0.5 unit***Prerequisite: MATH 1114, 2221 and 2225 (MATH 1114 may be taken concurrently)*

A continuation of MATH 2221 with an emphasis on theory. Topics include real and complex vector spaces and subspaces, linear transformations, kernel and range, inner product spaces, eigenvalues and eigenvectors, diagonalization, and orthogonal diagonalization.

## MATH 2225

Mathematical Proof**0.5 unit**

*Prerequisite: MATH 1103 or MATH 1113*

An introduction to writing and analyzing formal proofs in mathematics. Topics include: logic, direct proof and proof by contradiction, mathematical induction, set theory, relations and functions, partitions and equivalence relations.

## MATH 2245

History of Mathematics I**0.5 unit**

*Prerequisite: permission of the instructor*

History of mathematics before the seventeenth century.

## MATH 2462/EDUC 2462

Fundamental Concepts of Mathematics 1**0.5 unit**

*Prerequisite: any 5.0 units successfully completed at the university level*

A study of the fundamental concepts of mathematics, focusing on elementary and middle school mathematics. Topics include counting, whole number operations, fractions, decimals, rates and proportions, measurement, and geometry. This course focuses on problem solving, mathematical reasoning, and multiple approaches as applied to these topics

This course and MATH 2463/EDUC 2463 are recommended primarily for pre-education students and will not be acceptable for the mathematics major or minor. Students who have received credit for MATH 2243/EDUC 2461 may not take this course for credit.

## MATH 2263/EDUC 2463

Fundamental Concepts of Mathematics 2**0.5 unit**

*A study of the fundamental concepts of mathematics, focusing on elementary and middle school mathematics. Topics include the integers, real and rational numbers, number theory, introductory algebra, functions, graphing, probability, statistics, and sampling. This course focuses on problem solving, mathematical reasoning, and multiple approaches as applied to these topics.*

*Prerequisite: MATH 2462/EDUC 2462 (or MATH 2243/EDUC 2461)*## MATH 2277

Topics in Mathematics

**0.5 unit**

*Prerequisite: permission of the instructor*

An opportunity for students to examine a topic or topics in mathematics.

## MATH 2283

Introduction to Nonparametric Statistics

**0.5 unit***Prerequisite: MATH 2209*

An introduction to nonparametric statistical methods. Topics include rank-based tests; the sign test; randomization and permutation tests; and developing confidence intervals and hypothesis tests for means, proportions and in regression with the bootstrap.

## MATH 2284

Survey Design

**0.5 unit**

*Prerequisite: MATH 2209*

A practical course in designing surveys and analysis of survey data. Topics include questionnaire design, conducting a survey, ethical considerations, types of sampling, selecting samples, inference for random sampling, stratified random sampling and cluster sampling, and power calculations. The emphasis is on practical applications, using appropriate software.

*Note: Students who have received credit for CMPS 2284 may not take this course for credit.*

## MATH 2289

Applied Numerical Analysis**0.5 unit***Prerequisites: CMPS/INTE 1153 or CMPS 1155, and MATH 1114, and either MATH 2283 or 2222*

An introductory course in simple numerical analysis techniques (root finding, matrix inversion, integration, etc.). Additional topics which may be included are floating point arithmetic, error analysis, approximation theory and algorithm design for numerical methods. Implementation will be in a procedure-oriented language such as FORTRAN. *Note: Students who have received credit for MATH 2239 may not take this course for credit.*

## MATH 3303

Intermediate Applied Statistics I: Linear Models

**0.5 unit**

*Prerequisites: MATH 2209*

A continuation of MATH 2209 with a focus on linear models: simple, polynomial and multiple regression, with continuous and categorical explanatory variables; indicator variables and contrasts; transformations, diagnostics, and variable selection; bootstrap methods for inference; odds ratios and an introduction to logistic regression. The emphasis is on practical applications, using appropriate software.

## MATH 3304

Intermediate Applied Statistics II: ANOVA and Experimental Design

**0.5 unit**

*Prerequisite: MATH 2209*

A continuation of MATH 2209. Topics include one-way and two-way ANOVA; factorial and nested designs; residual analysis; transformations; and analysis of covariance. This course emphasizes practical applications, rather than theory, using appropriate software.

## MATH 3307

Intermediate Mathematical Statistics**0.5 unit**

*Prerequisites: MATH 2206, 2208, 2209, and 2211*

Intermediate theory of statistical inference based on the likelihood function. Topics will include the likelihood function for single and multiple parameter families, likelihood intervals and their relationship to confidence intervals, and likelihood ratio tests. Further topics may include sufficiency, Fisher information, comparison of frequentist, likelihood and Bayesian approaches to inference.

*Note: Students may not take both MATH 3307 and MATH 4407 for credit*

## MATH 3311

Analysis I**0.5 unit**

*Prerequisites: MATH 2211, 2222, and 2225 (MATH 2211 may be taken concurrently)*

An introduction to analysis. Topics may include sets, functions, the real numbers, limits, sequences and series, continuity, derivatives and mean value theorems. This course stresses mathematical proofs.

## MATH 3312

Analysis II**0.5 unit**

*Prerequisite: MATH 3311*

A continuation of MATH 3311. Topics may include uniform continuity, fixed point theorems, sequences of functions, approximation theorems, the Riemann integral, and an introduction to metric spaces and topology.

## MATH 3314

Introduction to Differential Equations**0.5 unit**

*Prerequisites: MATH 2212 and 2222*

A study of differential equations arising in many areas of science. Topics may include first and second order linear equations, classical partial differential equations, series solutions, systems of linear equations, Sturm-Liouville theory, Fourier series and the Poincare-Bedixson Theorem.

## MATH 3325

Abstract Algebra I**0.5 unit***Prerequisites: MATH 2222 and 2225*

An introduction to the theory of groups, rings, and fields. Topics include: groups, subgroups, Lagrange’s theorem, isomorphism, Cayley’s theorem, rings, ideals, ring homomorphism theorems, finite fields, irreducible polynomials over a field, and the division algorithm theorem.

## MATH 3326

Abstract Algebra II **0.5 unit**

*Prerequisite: MATH 3325*

One or two advanced topics in algebra will be treated in depth.

## MATH 3333

Introduction to Graph Theory**0.5 unit**

*Prerequisites: MATH 2222, 2225, and either CMPS 1153 or 1155, or permission of instructor*

An introduction to graph theory. Topics will include graphs, digraphs and trees, connectivity, graph colouring, spanning tree and shortest path algorithms, and related additional topics.

*Note: Students who have received credit for MATH 4333 may not take this course for credit.*

## MATH 3407

Theory of Probability I**0.5 unit**

*Prerequisites: MATH 2211 and either MATH 2206 or permission of the instructor*

A rigorous study of probability theory, developed from the axioms of probability using calculus, set theory and combinatorics. Topics include univariate and multivariate distributions, joint distributions of discrete and continuous random variables, conditional and marginal distributions, Jacobians, and distributions of functions of random variables.

## MATH 3408

Theory of Probability II**0.5 unit**

*Prerequisite: MATH 3407*

A continuation of MATH 3407. Topics include: Jacobians, transformations of several random variables, indicator variables with applications, limit theorems with applications, Poisson processes and Markov chains.

## MATH 3500/PHYS 3500

Topics in Mathematics and Physics

0.5 unit*Prerequisites: permission of the Mathematics and Computer Science Department*

A study of one particular area of theoretical physics that applies the principles of calculus and other areas of mathematics. Examples of areas that could be studied are relativity, dynamics and fluid mechanics.

## MATH 4333

Graph Theory**0.5 unit**

*Prerequisites: MATH 3311 or 3325, and either CMPS/INTE 1153 or 1155, or permission of instructor*

An introduction to graph theory. Topics will include graphs, digraphs, and trees, connectivity, graph colouring, spanning tree and shortest path algorithms, and related additional topics. Students will also be expected to complete independent work involving the graph theory literature. This course is intended for honours students or potential honours students; other students may prefer MATH 3333.

*Note: Students who have received credit for MATH 3333 may not take this course for credit.*

## MATH 4407

Concepts in Mathematical Statistics**0.5 unit**

*Prerequisites: MATH 2208, 2209, 2212, and 2222*

The theory of statistical inference based on the likelihood function. Topics will include likelihood function for single and multiple parameter families, likelihood intervals and their relationship to confidence intervals, likelihood ratio tests, sufficiency, Fisher information, and a comparison of frequentist, likelihood and Bayesian approaches to inference. Students will be introduced to the concept of uniformly most powerful tests and the Neyman-Pearson Lemma.

*Note: Students may not take both MATH 3307 and MATH 4407 for credit*.

## MATH 4411

Complex Analysis I**0.5 unit**

*Prerequisites: MATH 2225, and either MATH 2212 or 3311 and permission of the department*

An introduction to complex analysis. Topics may include: complex numbers and functions, differentiation and integration in the complex plane, Taylor and Laurent series, residues, Cauchy’s theorem, maximum modulus principle, harmonic functions, entire and meromorphic functions.

## MATH 4412

Complex Analysis II**0.5 unit**

*Prerequisite: MATH 4411*

A continuation of MATH 4411. Topics may include further study of analytic functions, conformal mapping theory, Moebius maps, the Schwarz-Christoffel transformation, canonical products, and the prime number theorem.

## MATH 4414

Special Topics in Mathematics**0.5 unit**

*Prerequisites: will vary depending on the topic, but will include at least one 3000 level MATH course and permission of the instructor*

An opportunity for advanced students to examine a selected topic or topics in mathematics.

## MATH 4447

Directed Study**0.5 unit**

## MATH 4448

Directed Study**0.5 unit**

## MATH 4449

Directed Study**1.0 unit**

*Prerequisites: advanced standing and permission of the department*

Directed study of an advanced topic in mathematics. Emphasis will be placed on the learning of new material through reading and discussion. Hours to be arranged

## MATH 4499

Honours Project**0.5 unit**

*Prerequisite: permission of the department. Normally students must have received a grade of at least B- in MATH 3311 and 3325 before starting an honours project*

A required course for mathematics honours students, to be taken in their final year. Each student will complete an honours project under the supervision of a faculty member, will submit a formal written report, and will give an oral presentation on the project.

Academic Note: This web-based calendar information is applicable for the 2019-2020 academic year which runs from September 01, 2019 to August 31, 2020.

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