Mathematics 211 Course Page

# Math 211

## Algebraic Methods

### Fall/Winter 2021/2022

List of Assignments       List of Overheads       List of Handouts       List of MAPLE Solutions       Further Reading       News

 Time: Tu 11:30, Wed 13:30, Fr 12:30 (Fall term), Mo 10:30, Wed 9:30, Fr 8:30 (Winter term) Place: Room 210, Walter Light Hall (Fall term), Online/Room 128, JEF (Winter term)
 Instructor: Dr. Ernst Kani Room 211, Jeffery Hall Telephone: 533-2435 Email: kani@mast.queensu.ca
 Office hours (Fall): Tu 12:30 - 13:00 Wed 14:30 - 15:20 Fr 13:30 - 14:30
 Marking scheme: Assignments October Mid-term test Christmas exam March Mid-term test Final exam 15.0% 7.5% 30.0% 7.5% 40.0% _______ 100.0%

 Assignments: Due Fridays at 12:30 MAPLE Lab: Wed 15 September, 2021, 13:30-14:30 (in class) Mid-term tests: Wed 20 October, 2021, 13:30-14:20 (in class) Wed 02 March, 2022, 9:30-10:20 (in class) Christmas exam: 16 December 2021, 9:00-11:00 (online) Final exam: 18 April, 9:00-12:00 Textbook: E. Kani, N. J. Pullman, N. M. Rice, Algebraic Methods, Queen's University, 2021. (Course Reader) PC software: MAPLE - available for free from Queen's website. (Log in to MyQueensU and go to Software Centre.)

### Course Outline

 Integers: - Greatest common divisor (gcd), Euclidean algorithm (ch. 1) - Linear Diophantine equations (ch. 1) - Modular arithmetic (ch. 2) - Public key cryptography (ch. 2) Polynomials: - Review of complex numbers (ch. 3) - Gcd, Euclidean algorithm (ch. 3) Approximation: - Data fitting: Lagrange interpolation formula,                     Least square approximation (ch. 4) Matrices: - Matrix polynomials, discrete linear systems (ch. 5) - Applications of Jordan canonical form (ch. 6,7) - Powers of matrices, stochastic matrices (ch. 7) Groups: - Permutation groups, cycles, Burnside's theorem,   application to colouring problems (ch. 8)