Math 115, Summer 2012. James McIvor.

Schedule of Lectures

Please check this page regularly for updates. Reading assignments are to be done BEFORE the lecture.

Lecture No.

Date

Title

Reading

Lecture Notes

1 June 18 Introduction. Divisibility. Ideals. 1.1,1.2 Lecture 1
2 June 19 GCD and Ideals. 1.2, notes Lecture 2
3 June 20 LCM. Primes, Unique Factorization. 1.2,1.3 Lecture 3
4 June 21 Congruences and Their Properties. 2.1 Lecture 4
5 June 25 Fermat's Little Theorem. Wilson's Theorem. 2.1 Lecture 5
6 June 26 Fermat's Thm on Sums of Squares 2.1 Lecture 6
7 June 27 Chinese Remainder Thm 2.3 Lecture 7
8 June 28 Algebraic Perspective: Rings 2.10, 2.11, notes Lecture 8
9 July 2 More Algebra 2.10,2.11,notes Lecture 9
10 July 3 Hensel's Lemma, Reduction of Modulus 2.5,2.6 Lecture 10
11 July 4 Holiday - No Class
12 July 5 Prime Modulus 2.7 Lecture 12
13 July 9 Primitive Roots 2.8 Lecture 13
14 July 10 Quadratic Residues 3.1 Lecture 14
15 July 11 Gauss' Lemma 3.1 Lecture 15
16 July 12 Quadratic Reciprocity 3.2 Lecture 16
17 July 16 Quadratic Forms 3.4 Lecture 17
18 July 17 Review
19 July 18 Midterm Exam
20 July 19 Quadratic Forms II 3.4,3.5 Lecture 20
21 July 23 Quadratic Forms III - The Reduction Theorem 3.5,3.6 Lecture 21
22 July 24 Applying the Reduction Theorem 3.7 Lecture 22
23 July 25 Diophantine Eqns - Linear Equations 5.1,5.2 Lecture 23
24 July 26 Pythagorean Triples 5.3 Lecture 24
25 July 30 The "Method of Descent" 5.4, notes Lecture 25
26 July 31 Rational Points on Curves 5.6 Lecture 26
27 Aug 1 The Projective Line 5.6, notes Lecture 27
28 Aug 2 The Projective Plane 5.6, notes Lecture 28
29 Aug 6 Elliptic Curves I 5.7 Lecture 29
30 Aug 7 Elliptic Curves II 5.7, notes Lecture 30
31 Aug 8 Review
32 Aug 9 Final Exam