| source University of Toronto, Mississauga (X) |
level |
department Mathematics (X) |
Understanding, using and developing precise expressions of mathematical ideas, including definitions and theorems. Set theory, logical statements and proofs, induction, topics chosen from combinatorics, elementary number theory, Euclidean geometry. [
Score: 7.976118 Details | Listing | Web page
Mathematics of finance, matrices and linear equations. Review of differential calculus; applications. Integration and fundamental theorem; applications. Introduction to partial differentiation; applications. NOTE: This course cannot be used as the calculus prerequisite for any 200-level MAT or STA course, except in combination with
Score: 7.976118 Details | Listing | Web page
Trigonometric functions. Limits, continuity. Techniques of differentiation and integration with applications to the life sciences. Extreme values and optimization. Graphing. The fundamental theorem of calculus. Introduction to sequences and series, power series. Introduction to discrete and continuous time modeling. [
Score: 7.976118 Details | Listing | Web page
Trigonometric functions. Limits, continuity. Review of differential calculus; applications. Graphing, extreme values and optimization. Integration and fundamental theorem; applications. Sequences and series. Power Series. Introduction to differential equations. [
Score: 7.976118 Details | Listing | Web page
A conceptual approach for students with a serious interest in mathematics. Geometric and physical intuition are emphasized but some attention is also given to the theoretical foundations of calculus. Material covers first a review of trigonometric functions followed by discussion of trigonometric identities. The basic concepts of calculus: limits and continuity, the mean value and inverse function theorem, the integral, the fundamental theorem, elementary transcendental functions, Taylor's theorem, sequences and series, power series. [
Score: 7.976118 Details | Listing | Web page
Mathematics derives its great power from its ability to formulate abstract concepts and techniques. In this course, students will be introduced to abstraction and its power through a study of topics from discrete mathematics. The topics covered will include: Sets, relations and functions; Basic counting techniques: subsets, permutations, finite sequences, inclusion-exclusion; Discrete probability: random variables paradoxes and surprises; Basic number theory: properties of the integers and the primes. The course will emphasize active participation of the students in discussion and written assignments. [
Score: 7.976118 Details | Listing | Web page
Modeling with differential equations, applied to examples from Life Sciences and Medicine. Exponential and logistic growth of population, stability in first-order equations, higher order linear equations, forced oscillations, systems of first order equations, phase plane analysis, predator-prey models, modeling chemical reactions, modeling heart beat. [
Score: 7.976118 Details | Listing | Web page
Systems of linear equations, matrix algebra, determinants. Vector geometry in R
Score: 7.976118 Details | Listing | Web page
Abstract vector spaces: subspaces, dimension theory. Linear mappings: kernel, image, dimension theorem, isomorphisms, matrix of a linear transformation. Change of basis, invariant subspaces, direct sums, cyclic subspaces, Cayley-Hamilton theorem. Inner product spaces, orthogonal transformations, orthogonal diagonalization, quadratic forms, positive definite matrices. Complex operators: Hermitian, unitary and normal. Spectral Theorem. Isometries of R
Score: 7.976118 Details | Listing | Web page
Differential and integral calculus of several variables: partial differentiation, chain rule, extremal problems, Lagrange multipliers, classification of critical points. Multiple integrals, Green's theorem and related topics. [
Score: 7.976118 Details | Listing | Web page
"Bridging Course"; accepted as prerequisite for upper level courses in replacement of
Score: 7.976118 Details | Listing | Web page
Solution of first order differential equations. Applications. Linear equations, especially of second order. Systems of linear equations. Nonlinear phenomena, linearization of nonlinear systems. (
Score: 7.976118 Details | Listing | Web page
Power series solutions, boundary value problems, Fourier series solutions. Laplace transform, numerical methods. [
Score: 7.976118 Details | Listing | Web page
This courses provides a richly rewarding opportunity for students in their second year to work in the research project of a professor in return for 299Y course credit. Students enrolled have an opportunity to become involved in original research, learn research methods and share in the excitement and discovery of acquiring new knowledge. Participating faculty members post their project descriptions for the following summer and fall/winter sessions in early February and students are invited to apply in early March. See
Score: 7.976118 Details | Listing | Web page
Permutations and permutation groups. Linear groups. Abstract groups, homomorphisms, subgroups. Symmetry groups of regular polygons and platonic solids, wallpaper groups. Group actions, class formula. Cosets, Lagrange's theorem. Normal subgroups, quotient groups. Classification of finitely generated Abelian Groups. Emphasis on examples and calculations. [
Score: 7.976118 Details | Listing | Web page
This course will consist of an introduction to the theory of finite fields. We will also discuss some of the many practical applications of finite fields, including algebraic coding theory for the error-free transmission of information and cryptology for the secure transmission of information. [
Score: 7.976118 Details | Listing | Web page
The nature of axioms, proofs and consistency. Introduction to the theory of recursive functions. Gödel's incompleteness theorems and related results. This course emphasizes rigour. [
Score: 7.976118 Details | Listing | Web page
Partial differential equations of applied mathematics, mathematical models of physical phenomena, basic methodology. [
Score: 7.976118 Details | Listing | Web page
Elementary topics in number theory such as: prime numbers; arithmetic with residues; Gaussian integers, quadratic reciprocity law, representation of numbers as sums of squares. (This course emphasizes rigour). [
Score: 7.976118 Details | Listing | Web page
Stability in nonlinear systems of differential equations, bifurcation theory, chaos, strange attractors, iteration of nonlinear mappings and fractals. This course will be geared towards students with interest in sciences. [
Score: 7.976118 Details | Listing | Web page
Theory of functions of one complex variable: analytic and meromorphic functions; Cauchy's theorem, residue calculus. Topics from: conformal mappings, analytic continuation, harmonic functions. [
Score: 7.976118 Details | Listing | Web page
Basic counting principles, generating functions, permutations with restrictions. Fundamentals of graph theory with algorithms; applications (including network flows). [
Score: 7.976118 Details | Listing | Web page
The implicit function theorem, vector fields. Transformations. Parametrized integrals. Line, surface and volume integrals. Theorems of Gauss and Stokes with applications. [
Score: 7.976118 Details | Listing | Web page
Metric spaces; compactness and connectedness. Sequences and series of functions, power series; modes of convergence. Interchange of limiting processes; differentiation of integrals. Function spaces; Weierstrass approximation; Fourier series. Contraction mappings; existence and uniqueness of solutions of ordinary differential equations. Countability; Cantor set; Hausdorff dimension. [
Score: 7.976118 Details | Listing | Web page
The course discusses the Mathematics curriculum (K-12) from the following aspects: the strands of the curriculum and their place in the world of Mathematics, the nature of the proofs, applications of Mathematics, and the connection of Mathematics to other subjects.
Score: 7.976118 Details | Listing | Web page