1 |
Aug 18 |
Introduction; Induction |
1.1,1.2 |
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- |
HW1 assigned. |
2 |
Aug 20 |
Basis representation; Division definition |
1.2,2.1 |
- |
- |
HW Workshop at 5pm |
3 |
Aug 25 |
GCDs and integral linear combinations |
2.2 |
- |
- |
- |
4 |
Aug 27 |
Euclidean algorithm; Linear Diophantine equations |
2.2,2.3 |
- |
- |
HW Workshop at 5pm |
5 |
Sep 1 |
Fundamental Theorem of Algebra; Combinatorics |
2.4,3.1 |
- |
- |
HW1 due; HW2 assigned. |
6 |
Sep 3 |
Fermat's Little Theorem; Congruences |
3.2,4.1 |
- |
- |
- |
7 |
Sep 8 |
Residue Systems; Riffling |
4.2,4.3 |
- |
- |
- |
8 |
Sep 10 |
Linear Congruences; Fermat and Wilson |
5.1-5.3 |
- |
- |
- |
9 |
Sep 15 |
Chinese Remainder Theorem; Polynomial Recurrences; Euler's Phi Function |
5.3,5.4,6.1 |
- |
- |
HW2 due; HW3 assigned this evening. |
10 |
Sep 17 |
Inclusion/Exclusion; Arithmetic Functions |
6.2,6.3 |
- |
- |
- |
11 |
Sep 22 |
Arithmetic Functions; Mobius Inversion |
6.3,6.4 |
- |
- |
- |
12 |
Sep 24 |
Mobius Inversion; Primitive Roots |
6.4,7.1 |
- |
- |
- |
13 |
Sep 29 |
Primitive Roots II |
7.1 |
- |
- |
HW3 due. HW4 assigned. |
14 |
Oct 1 |
Existence of primitive roots modulo p; prime numbers |
7.2,8.1 |
- |
- |
- |
15 |
Oct 6 |
Midterm (Chapters 1 to 6) |
- |
- |
- |
- |
16 |
Oct 8 |
Prime Numbers |
8.2 |
- |
- |
- |
17 |
Oct 15 |
Prime Numbers: Chebyshev's Theorem |
8.2 |
- |
- |
HW5 posted. |
18 |
Oct 20 |
Prime Numbers: Chebyshev's Theorem II |
8.2 |
- |
- |
- |
19 |
Oct 22 |
Prime Numbers: Bertrand's Postulate |
8.2 |
- |
- |
- |
20 |
Oct 27 |
Quadratic Reciprocity: Euler's Criterion and Gauss's Lemma |
9.1,9.2 |
- |
- |
- |
21 |
Oct 29 |
Quadratic Reciprocity: Legendre Symbols (-1/p) and (2/p) |
9.3 |
- |
- |
- |
22 |
Nov 3 |
Quadratic Reciprocity Law: Proof |
9.3 |
- |
- |
HW5 due. HW6 assigned. |
23 |
Nov 5 |
Quadratic Reciprocity Law: Proof II; quadratic congruences |
9.3 |
- |
- |
- |
24 |
Nov 10 |
Consecutive Residues |
10.1-10.2 |
- |
- |
- |
25 |
Nov 12 |
Consecutive Residues II; sums of two squares |
10.2,11.1 |
- |
- |
- |
26 |
Nov 17 |
Lagrange's four square theorem I |
11.2 |
- |
- |
HW6 due. |
27 |
Nov 19 |
Lagrange's four square theorem II |
11.2 |
- |
- |
HW7 assigned (as of Tues. Nov 24). |
28 |
Dec 1 |
Partitions; Euler's Partition Theorem |
12 |
- |
- |
- |
29 |
Dec 3 |
Generating Functions |
13.1 |
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- |
- |
30 |
Dec 8 |
Lattice Points |
15 |
- |
- |
HW7 due. |
- |
Dec 15 |
Final Exam: Tues. Dec 15, 3pm-5pm |
- |
- |
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