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 1130 and 2208
The prerequisites for both courses are the same: grade XI or grade XII Mathematics, 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 1130 or 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.
CoursesNote: 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.
College Algebra0.5 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 be taken for credit toward any degree.
Precalculus I: Algebraic Functions0.5 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.
Precalculus II: Transcendental Functions0.5 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.
Introductory Calculus I0.5 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.
Introductory Calculus II0.5 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 11300.5 unit
Applications of Matrices
Prerequisite: grade XI or grade XII academic mathematics or equivalent or MATH 0020 with a grade C or higher, or any 1000 level mathematics course
An applied course on matrix models for business, economics and the social sciences. Topics include: matrices, systems of linear equations, linear programming for optimization. Markov processes for population and market share distributions, and game theory. Emphasis is on applications rather than theory. This course is primarily intended for non-math majors.
Introduction to Probability0.5 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.
Introduction to Statistics I0.5 unit
Prerequisite: grade XI or grade XII academic mathematics or equivalent, 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)
Introduction to Statistics II0.5 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)
Intermediate Calculus I0.5 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.
Intermediate Calculus II0.5 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 2221Linear Algebra I
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. If this unit does not include MATH 2225, then MATH 2225 must be taken concurrently
An introduction to linear algebra. Topics include systems of linear equations, matrices, determinants, Cramer’s Rule, Euclidean n-space, dot products, linear transformations, eigenvalues and eigenvectors, vector spaces and subspaces, spanning, linear independence, basis and dimension. Note: Students who have received credit for MATH 2220 may not take this course for credit.
MATH 2222Linear Algebra II
Prerequisite: MATH 1114, 2221 and 2225 (MATH 1114 may be taken concurrently)
A continuation of MATH 2221. Topics include row space, column space, nullspace, rank, nullity, inner products, orthogonality, the Gram-Schmidt process, diagonalization, general linear transformations, kernel and range. Note: Students who have received credit for MATH 2220 may not take this course for credit.
MATH 2225Mathematical Proof
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 2243/EDUC 2461Fundamental Concepts in Mathematics
Prerequisite: any 5.0 units successfully completed at the university level
A study of fundamental mathematics concepts in the areas of numeration systems, rational and irrational numbers, number theory, geometry, probability, statistics and measurement. This course is intended primarily for pre-education students and for teachers and will not be acceptable for the mathematics major or minor.
MATH 2245History of Mathematics I
Prerequisite: permission of the instructor
History of mathematics before the seventeenth century.
Topics in Mathematics
Prerequisite: permission of the instructor
An opportunity for students to examine a topic or topics in mathematics.
MATH 22840.5 unitPrerequisite: 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 2289Applied Numerical Analysis
Prerequisites: CMPS/INTE 1153 or CMPS 1155, and MATH 1114, and either MATH 1130 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 33030.5 unitPrerequisites: MATH 2209
Intermediate Applied Statistics I: Linear Models
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 33040.5 unit
Intermediate Applied Statistics II: ANOVA and Experimental Design
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.
Intermediate Mathematical Statistics0.5 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
Analysis I0.5 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.
Analysis II0.5 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.
Introduction to Differential Equations0.5 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.
Abstract Algebra I0.5 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.
Abstract Algebra II 0.5 unit
Prerequisite: MATH 3325
One or two advanced topics in algebra will be treated in depth.
Introduction to Graph Theory0.5 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.
Theory of Probability I0.5 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.
Theory of Probability II0.5 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
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.
Graph Theory0.5 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.
Concepts in Mathematical Statistics0.5 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.
Complex Analysis I0.5 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.
Complex Analysis II0.5 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.
Special Topics in Mathematics0.5 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.
Directed Study0.5 unit
Directed Study0.5 unit
Directed Study1.0 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
Honours Project0.5 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.