Math 17
An Introduction to Mathematics Beyond Calculus

Last updated June 27, 2012 12:25:54 EDT

## Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly.
On the other hand, the weekly syllabus contained in the Homework Assignments page will always be accurate.

Lectures Sections in Text Brief Description
1/4   Introduction, Elliptic curves in Fermat's Last Theorem, Congruent Numbers, and Cryptography
1/6   Congruent numbers and rational points on conics; algebraic versus geometric structure on sets
1/8   Rational curves and intersections; Bachet's duplication formula
1/11   Rational points on the unit circle: Pythagorean triples, congruent numbers
1/13   Well ordering, division algorithm, greatest common divisors and divisibility properties
1/15   Euclid's algorithm, Bezout's theorem, congruences
1/18   No Class Martin Luther King day (class moves to x-hour)
1/19 (x-hour)   congruences and equivalence relations; Caesar cipher
1/20   Affine ciphers, general linear congruences
1/22   Z_n as a ring, U_n as a group
1/25   Groups, orders of elements
1/27   More on groups, Euler's theorem, Fermat's little theorem
1/29   Applications, fast modular exponentiation
2/1   Public Key Cryptography, RSA
2/3   Public Key Cryptography
2/8   Fundamental Theorem of Finite Abelian Groups, Projective space
2/9 (x-hour)   Projective space and relating points on affine and projective curves
2/10   Elliptic curves and the addition law
2/12   No class: Snow Day (aka Winter Carnival)
2/15   Elliptic curves and the addition law
2/17   Pollard p-1 factoring algorithm
2/19   Lenstra's elliptic curve method of factorization
2/22   Congruent number problem and elliptic curves
2/24   Congruent numbers and Tunnel's theorem; some complex analysis
2/26   Elliptic Curves over C
3/1   Elliptic Functions and Weierstrass function, wrap up
3/3   Student Presentations
3/5   Student Presentations
3/8   Student Presentations

T. R. Shemanske
Last updated June 27, 2012 12:25:54 EDT