## Mathematics MATH

Instruction offered by members of the Department of Mathematics and Statistics in the Faculty of Science.

Department Head - T. Bisztriczky

Note: For listings of related courses, see Actuarial Science, Applied Mathematics, Pure Mathematics, and Statistics.

### Mathematics 113 E(8 hours)

(formerly Mathematics 013)

#### Eigenvalues and Eigenvectors

A review of these particular topics for students who have completed Mathematics 211 or equivalent.

**
Note:
** Open to students with credit in Mathematics 211 or 221 or equivalent.

**
NOT INCLUDED IN GPA
**

### Mathematics 114 E(16 hours)

(formerly Mathematics 014)

#### Multivariate Topics from Applied Mathematics 219

Multiple Integration and applications.

**
Prerequisites:
** Mathematics 253 or 263 or 283 or consent of the Department.

**
Note:
** Designed to rectify a deficiency for those students whose Calculus I and II courses did not cover the multivariate topics from Applied Mathematics 219.

**
NOT INCLUDED IN GPA
**

### Mathematics 117 E(8 hours)

(formerly Mathematics 017)

#### Topics from Applied Mathematics 217

Inverse functions and inverse trigonometric functions. Hyperbolic and inverse hyperbolic functions. Indeterminate forms. Applications of integration.

**
Prerequisites:
** Mathematics 249 or 251 or 281 or consent of the Department.

**
Note:
** Designed to rectify a deficiency for those students whose first Calculus course did not cover some of the topics from Applied Mathematics 217.

**
NOT INCLUDED IN GPA
**

## Junior Courses

Note: Students who have not studied mathematics for some time are strongly advised to review high school material thoroughly prior to registering in any junior level mathematics course.

### Mathematics 205 H(3-1)

#### Mathematical Explorations

A mathematics appreciation course. Topics selected by the instructor to provide a contemporary mathematical perspective and experiences in mathematical thinking. May include historical material on the development of classical mathematical ideas as well as the evolution of recent mathematics.

**
Prerequisites:
** Pure Mathematics 30 or Mathematics II (offered by Continuing Education).

**
Note:
** For students whose major interests lie outside the sciences. Highly recommended for students pursuing an Elementary School Education degree.

**Note:** It is not a prerequisite for any other course offered by the Department of Mathematics and Statistics, and cannot be used for credit towards any Major or Minor program in the Faculty of Science except for a major in General Mathematics.

### Mathematics 211 H(3-1T-1)

#### Linear Methods I

Systems of equations and matrices, vectors, matrix representations, and determinants. Complex numbers, polar form. Eigenvalues, eigenvectors. Applications.

**
Prerequisites:
** A grade of 70 per cent or higher in Pure Mathematics 30. (Alternatives are presented in the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)

**
Note:
** Credit for both Mathematics 211 and 221 will not be allowed.

### Mathematics 249 H(4-1T-1)

#### Introductory Calculus

Algebraic operations. Functions and graphs. Limits, derivatives, and integrals of exponential, logarithmic and trigonometric functions. Fundamental theorem of calculus. Applications.

**
Prerequisites:
** A grade of 70 per cent or higher in Pure Mathematics 30. (Alternatives are presented in the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)

**
Note:
** Not open to students with 60% or higher in Mathematics 31, except with special departmental permission.

**Note:** Credit for more than one of Mathematics 249, 251, 281, or Applied Mathematics 217 will not be allowed.

### Mathematics 251 H(3-1T-1)

#### Calculus I

Functions and graphs, transcendental functions. Limits, derivatives, and integrals of exponential, logarithmic and trigonometric functions. Fundamental theorem of calculus. Applications.

**
Prerequisites:
** A grade of 70 per cent or higher in Pure Mathematics 30 and a grade of 50 per cent or higher in Mathematics 31. (Alternatives to Pure Mathematics 30 are presented in the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)

**
Note:
** Credit for more than one of Mathematics 249, 251, 281, or Applied Mathematics 217 will not be allowed.

**
Note:
** This course provides the basic techniques of differential calculus as motivated by various applications. Students performing sufficiently well in a placement test may be advised to transfer directly to Mathematics 253.

### Mathematics 253 H(3-1T-1)

#### Calculus II

Inverses of trigonometric functions. Methods of integration, improper integrals. Separable differential equations, first and second order linear differential equations, applications.

**
Prerequisites:
** Mathematics 249 or 251 or 281 or Applied Mathematics 217.

**
Note:
** Credit for more than one of Mathematics 253, 263, 283, or Applied Mathematics 219 will not be allowed.

**
Note:
** Mathematics 253 or 283 is a prerequisite for many 300-level courses in Pure Mathematics, Applied Mathematics, Statistics and Actuarial Science. Students in programs offered by the Department of Mathematics and Statistics are strongly recommended to take Mathematics 283.

### Mathematics 271 H(3-1T-1)

#### Discrete Mathematics

Proof techniques. Sets and relations. Induction. Counting and probability. Graphs and trees.

**
Prerequisites:
** Mathematics 211 or 221.

**
Note:
** Credit for both Mathematics 271 and 273 will not be allowed.

**
Note:
** Philosophy 279 or 377 is highly recommended to complement this course.

### Mathematics 273 H(3-1T-1)

#### Numbers and Proofs

Introduction to proofs. Functions, sets and relations. The integers: Euclidean division algorithm and prime factorization; induction and recursion; integers mod n. Real numbers: sequences of real numbers; completeness of the real numbers; open and closed sets. Complex numbers.

**
Prerequisites:
** A grade of 70 per cent or higher in Pure Mathematics 30. (Alternatives are presented in the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)

**
Note:
** Credit for both Mathematics 271 and 273 will not be allowed.

### Mathematics 281 H(3-1T-1)

#### Honours Calculus I

Limits and continuity; Differentiation of functions of one real variable; the Mean Value Theorem and its consequences; Riemann integration; fundamental theorem of calculus; applications.

**
Prerequisites:
** A grade of 80 per cent or higher in Pure Mathematics 30 and a grade of 50 per cent or higher in Mathematics 31. (Alternatives to Pure Mathematics 30 are presented in the paragraph titled Mathematics Diagnostic Test in the Program section of this Calendar.)

**
Note:
** Credit for more than one of Mathematics 249 or 251 or 281 or Applied Mathematics 217 will not be allowed.

### Mathematics 283 H(3-1T-1)

#### Honours Calculus II

Methods of integration, improper integrals. Sequence and series, Taylor series, functions defined by series. Ordinary differential equations. Partial derivatives.

**
Prerequisites:
** Mathematics 281 or a grade of B+ or better in Mathematics 249 or 251 or Applied Mathematics 217 or equivalent.

**
Note:
** Credit for more than one of Mathematics 253 or 263 or 283 or Applied Mathematics 219 will not be allowed.

## Senior Courses

### Mathematics 311 H(3-1T)

#### Linear Methods II

Vector spaces and subspaces. Linear independence. Matrix representation of linear transformations. Eigenvalues and eigenvectors. Quadratic forms. Inner products. Gram-Schmidt orthogonalization. Students will complete a project using a computer algebra system.

**
Prerequisites:
** Mathematics 211 or 221.

### Mathematics 321 H(3-1T)

#### Mathematical Probability

Sample spaces. Discrete probability. Discrete and continuous random variables. Standard distributions. Mathematical expectation and variance. Moments and moment generating functions. Central limit theorem. Functions of random variables. Introduction to statistical inference.

**
Prerequisites:
** Mathematics 253 or 263 or 283 or Applied Mathematics 219.

### Mathematics 323 H(3-1T)

#### Introduction to Mathematical Statistics

Bivariate distributions. Sampling distributions. Chi-squared, F and t distributions. Estimation. Hypothesis tests (proportions, means, variance, chi-square). Method of moments. Maximum likelihood estimators. Neyman-Pearson lemma. Likelihood ratio tests. Elementary regression and correlation.

**
Prerequisites:
** Mathematics 321.

### Mathematics 331 H(3-1T)

#### Multivariate Calculus

Systems of ordinary differential equations. Calculus of functions of several variables. Introduction to vector analysis, theorems of Green, Gauss and Stokes.

**
Prerequisites:
** Mathematics 253 or 263 or 283 or Applied Mathematics 219 and either Mathematics 221 or 211.

**
Note:
** Credit for both Mathematics 331 and either 353 or 381 or Applied Mathematics 309 will not be allowed.

**
Note:
** This course is not a member of the list of courses constituting the fields of Actuarial Science, Applied Mathematics, Pure Mathematics, or Statistics and cannot normally be substituted for Mathematics 353 or 381 in degree programs in any of those fields.

### Mathematics 349 H(3-1T)

#### Calculus III

Infinite sequences and series. Polar coordinates, parametric equations, arc length. Vector geometry, differentiation of vector-valued functions. Partial differentiation. Students will complete a project using a computer algebra system.

**
Prerequisites:
** Mathematics 253 or 263 or 283 or Applied Mathematics 219; and Mathematics 211 or 221.

**
Note:
** Credit for both Mathematics 349 and 381 will not be allowed.

### Mathematics 353 H(3-1T)

#### Calculus IV

Applications of partial differentiation, multiple integrals, vector calculus including Stokes' and the Divergence Theorems.

**
Prerequisites:
** Mathematics 349.

**
Note:
** Credit for more than one of Mathematics 353, Mathematics 381, 331 or Applied Mathematics 309 will not be allowed.

### Mathematics 381 H(3-1T)

#### Honours Calculus III

Functions of several variables; differentiability, extrema. Implicit and inverse function theorems. Integration of functions of several variables; line integrals; surface integrals. Students will complete a project using a computer algebra system.

**
Prerequisites:
** Mathematics 283; or a grade of B+ or better in Mathematics 253 or Applied Mathematics 219.

**
Corequisites:
** Mathematics 211 or 221.

**
Note:
** Credit for more than one of Mathematics 331, 353, 381, and Applied Mathematics [AMAT309] will not be allowed.

**Note:** Credit for both Mathematics 349 and 381 will not be allowed.

### Mathematics 401 H(3-0)

#### Special Topics

Higher level topics which can be repeated for credit.

**
Prerequisites:
** Consent of the Department.

**
Note:
** This course is designed to add flexibility to completion of an undergraduate pure mathematics or general mathematics program.

**
MAY BE REPEATED FOR CREDIT
**

### Mathematics 403 H(3-0)

#### Topics in Mathematics for Economics

Techniques of integration. Multiple integrals. Analysis of functions. Continuity. Compact sets. Convex sets. Separating hyperplanes. Lower and upper hemi-continuous correspondences. Fixed point theorems, Optimal control.

**
Prerequisites:
** Mathematics 211 or 221 and 253 or 263 or 283 or Applied Mathematics 219; or both Economics 387 and 389.

### Mathematics 411 H(3-1T)

(formerly Applied Mathematics 441)

#### Linear Spaces with Applications

Linear operators and matrices. Jordan forms. Eigenvalue problems. Quadratic forms. Applications.

**
Prerequisites:
** Mathematics 311 and one of 331, 353, 381 or Applied Mathematics 309.

**
Note:
** May not be offered every year. Consult the Department for listings.