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While the SMP community still exists and is active, the summer program no longer runs due to lack of funding. The goals of the program include: introducing students to new areas of mathematics; honing students' mathematical reasoning, proof writing, problem solving, and presentation skills; building self-confidence, encouraging enthusiasm for mathematics, and increasing awareness of opportunities for continued study in the mathematical sciences; connecting students into a supportive network of other female college math majors, graduates and professionals to support them through their graduate studies in mathematics.
To date, 56 SMP alumnae have earned PhDs, and 71 are currently enrolled in graduate programs in the mathematical sciences. The program consists of four weeks of intense coursework, seminars, and group discussions all aimed at challenging the participants and providing them with a network of peers and mentors.
The program has expanded to include many activities for its extensive network of alumnae. Use of implicit and inverse function theorems. Real number axioms, limits, continuous functions, differentiability, infinite series, uniform convergence, the Riemann integral.
Polar, cylindrical and spherical coordinates. Partial derivatives, gradients, extrema and Lagrange multipliers. Exact differentials. Multiple integrals over rectangular and general regions. Integrals over surfaces. Line integrals. Vector differential operators. Polar coordinates, parametric equations. Indeterminate forms, sequences and series, Taylor's formula and series.
Lectures three hours a week and one hour tutorial. Improper integrals. The fundamental theorem of calculus. An introduction to differential equations. Sequences and series of functions. Power series. Uniform convergence. Introduction to ring theory: ring of polynomials, integral domains, ideals, homomorphism theorems.
Hermitian forms, spectral theorem for normal operators, bilinear and quadratic forms, classical groups. Linear transformations and matrices. Inner product spaces over R and C ; Orthonormal bases. Eigenvalues and diagonalization. Bilinear and quadratic forms; principal axis theorem. Eigenvalues and eigenspaces. Diagonalization and other canonical forms. Inner products.
This course is intended for a general audience, and is available to B. Prerequisite s : Grade 12 Mathematics and second-year standing. First-order equations, linear second- and higher-order equations, linear systems, stability of second-order systems.
Basic number theory and counting methods, algorithms for strings, trees and sequences. Applications to DNA and protein sequencing problems. Analysis and complexity of algorithms. Also listed as CMPS Lectures three hours a week. Vector fields, differential forms and exterior algebra. Introduction to manifolds and tangent bundles. Applications such as differential equations and the calculus of variations.
Intended for non-engineering students. Asymptotic solutions. Sturm-Liouville theory. Bessel and Legendre functions. This course may not be used to meet the level course requirements in any B. Math or B. Math Honours program in Mathematics and Statistics. Direct methods of solving a system of linear equations. Iterative techniques. Bounds for eigenvalues. Power method and deflation techniques of approximation. Emphasis is primarily on computational aspects.
Finite symmetry groups. Polynomials, unique factorization domains.
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