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**Math 100 Mathematical Concepts: **This course surveys interesting and useful topics from diverse areas, including geometry, number theory, mathematical systems, algebra, logic, and set theory. Students will solve problems using processes such as abstraction, pattern recognition, deduction, and generalization. Acceptable for credit in the Faculties of Arts and Business, and the Departments of Human Kinetics and Human Nutrition. Prerequisite: grade 12 MATH or equivalent. Six credits.

** COURSE WEBSITES:**

Learn about the new Calculus courses for the 2016/17 term here!

**Math 106/126 Calculus I:** An introduction to differential calculus of a single variable, with applications to the 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. Prerequisite: grade 12 pre-calculus or equivalent. Three credits and a one-hour lab.

**Math 107/127 Calculus II:** 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. Prerequisite: MATH 111. Three credits and a one-hour lab.

**Math 121 Calculus I for Engineers:** 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. Prerequisite: grade 12 pre-calculus or equivalent. Cross-listed as ENGR 121. Three credits and one-hour lab and one-hour problem session.

**Math 122 Calculus II for Engineers****: **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. Prerequisite: MATH 121. Cross-listed as ENGR 122. Three credits and one-hour lab and one-hour problem session.

**Math 205 Business Mathematics: **A presentation of mathematics applicable to business, including functions, modelling, linear programming, matrix algebra, interest, and annuities. Use of spreadsheets will be a fundamental part of this course. Acceptable for credit in the Faculties of Arts and Business. Three credits.

**Math 221 Differential Equations for Engineers: **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. Cross-listed as ENGR 221. Prerequisites: ENGR 121, 122 or MATH 121, 122. Credit will be granted for only one of MATH 221 and MATH 367. Three credits and two-hour problem session.

**Math 222 Calculus III for Engineers:** 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. Cross-listed as ENGR 222. Prerequisite: ENGR 121, 122 or MATH 121 or 122. Credit will be granted for only one of MATH 222 and MATH 267. Three credits and two-hour problem session.

**Math 223 Linear Algebra for Engineers: **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. Cross-listed as ENGR 223. Prerequisites: ENGR 121, 122 or MATH 121, 122. Credit will be granted for only one of MATH 223 and MATH 253. Three credits and two-hour problem session.

**Math 253 Matrix Algebra: **An introduction to solution of linear systems, algebra of matrices, determinants, two- and three-dimensional vector spaces, and the matrix eigenvalue problem. Prerequisite: MATH 112 or 122. Credit will be granted for only one of MATH 253 and MATH 223. Three credits.

**Math 254 Linear Algebra:** 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. Prerequisite: MATH 253. Three credits.

**Math 267 Calculus III: **Topics include the Taylor polynomial theorem; indeterminate forms and l’Hôpital’s rule; improper integrals; infinite and power series and tests of convergence; parametric equations; partial differentialation; and selected concepts from multivariate differential calculus, and multiple integration. Prerequisite: MATH 112 or 122. Credit will be granted for only one of MATH 267 and MATH 222. Three credits.

**Math 277 Discrete Structures:** 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. Prerequisite: MATH 112 or 122. Three credits.

**Math 287 Natural Resource Modelling:** 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: MATH 112 or 122. Three credits.

**Math 347 Combinatorics: **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. Not offered 2013-2014.

**Math 354 Modern Algebra I:** This course introduces algebraic systems and the fundamental algebraic concepts. Applications to diverse areas such as coding theory, crystallography, circuits, logic, geometry, and graph theory will be considered. Prerequisites: MATH 254, 277. Three credits.

**Math 361 Advanced Vector Calculus: **Topics include vectors; vector differentiation including gradient, divergence, and curl; vector integration including the Gauss and Stokes theorems. Prerequisites: MATH 222 or 267 and 223 or 253. Three credits.

**Math 366 Real Analysis I:** 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 and 277. Three credits.

**Math 367 Differential Equations:** 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. Prerequisite: MATH 222 or 267 and MATH 223, 253. Three credits.

**Math 371 Modern Geometries:** A brief survey of geometries including projective, affine, similarity, equiareal, Euclidean, and non-Euclidean. Emphasis is on the invariants of transformational geometry. Prerequisite: MATH 277. Three credits. Not offered 2013/14.

**Math 372 Theory of Numbers: **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.

**Math 384 Numerical Methods: **This course covers methods used to solve mathematical problems on computer systems, including mathematical background and error analysis of solutions to non-linear equations; polynomial interpolations; integration and differentiation; quadrature methods; systems of equations and differential equations. Prerequisites: MATH 223 or 253; CSCI 161 or 125. Three credits.

**Math 387 Mathematical Modelling: **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: MATH 222 or 267, and MATH 223 or 253. Three credits. Not offered 2013/14.

**Math 391 Mathematical Logic:** Symbolic logic is introduced and the concepts of tautology and proof are studied. Using formal languages, propositional and predicate logic are presented, including the completeness theorem for predicate logic. Sequent-style deductive systems and tableau methods of proof are introduced. Prerequisite: MATH 277 or permission of the instructor. Three credits. Not offered 2013/14.

**Math 454 Modern Algebra II: **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. Not offered 2013/14.

**Math 462 Complex Variables: **Topics include complex numbers, elementary functions, series and integration, Laurent series, and residue theory. Prerequisites: MATH 221 or 367 and 222 or 361. Three credits. Not offered 2013/14.

**Math 466 Real Analysis II:** 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.

**Math 471 Topics in Mathematics: Topic from 2012/2013** The is a course focus on derivative - a financial instrument whose value depends derives from the values of underlying variables. In the last 30 years, it becomes much bigger than stock market. It is used by large intuitions such as Ontario teacher pension and government treasury and individual person buying any US financial product, which is **hedged** by Canadian dollar. We shall cover the basic concept such as future contracts, hedges, and arbitrageurs and basic mechanics of future markets. The reason this is called financial mathematics because the concepts of differentiation, probability, and differential equations are used extensively. We will concentrate in two areas where mathematics used the most, pricing and risk management. Prerequisite: MATH 254, 267, 277. Three credits. Not offered 2013/14

**Math 481 Partial Differential Equations: **The study of special functions and partial differential equations, including the wave, heat, and Laplace equations in various coordinate systems. Prerequisites: MATH 254 and 221 or 367. Three credits. .

**Math 491 Senior Seminar:** Cross-listed as CSCI 491 and 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.

**Math 493 Senior Thesis: **Students will prepare and present a thesis based on original research conducted under the supervision of a faculty member. Three credits.