1 |
Aug 19 |
Introduction; Induction; Basis representation |
1.1,1.2 |
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2 |
Aug 21 |
Basis representation; Divison lemma; Greatest common divisors |
1.2,2.1 |
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- |
HW1 assigned. |
3 |
Aug 26 |
Euclid's algorithm; Linear combinations |
2.2 |
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- |
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4 |
Aug 28 |
Linear Diophantine equations; Fundamental theorem of arithmetic; Combinatorics |
2.3,2.4,3.1 |
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5 |
Sep 4 |
Combinatorics; Fermat's Little Theorem |
3.1,3.2 |
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HW2 assigned. |
6 |
Sep 9 |
Wilson's Theorem; Congruences |
3.3,4.1 |
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7 |
Sep 11 |
Residue Systems; Riffling |
4.2,4.3 |
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8 |
Sep 16 |
Linear Congruences; Fermat and Wilson II; Chinese Remainder Theorem |
5.1-5.3 |
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- |
HW3 assigned. |
9 |
Sep 18 |
Polynomial Recurrences; Euler's Phi Function |
5.4,6.1 |
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- |
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10 |
Sep 23 |
Arithmetic Functions; Mobius Inversion |
6.2,6.3,6.4 |
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- |
- |
11 |
Sep 25 |
Mobious Inversion; Primitive Roots |
6.4,7.1 |
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- |
HW3 due. |
12 |
Sep 30 |
Primitive Roots |
7.1,7.2 |
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- |
Midterm assigned. |
13 |
Oct 2 |
Prime Numbers |
7.2,8.1 |
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- |
Midterm due. |
14 |
Oct 7 |
Prime Numbers: Chebyshev's Theorem |
8.1,8.2 |
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15 |
Oct 9 |
Prime Numbers: Bertrand's Postulate |
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- |
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16 |
Oct 16 |
Quadratic Reciprocity: Euler's Criterion and Gauss's Lemma |
9.1,9.2 |
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- |
HW4 assigned. |
17 |
Oct 21 |
Quadratic Reciprocity: Legendre Symbols (-1/p) and (2/p) |
9.3 |
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- |
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18 |
Oct 23 |
Quadratic Reciprocity Law: Proof |
9.3 |
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- |
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19 |
Oct 28 |
Quadratic Reciprocity Law: Applications |
9.4 |
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- |
HW4 due. |
20 |
Oct 30 |
Quadratic Reciprocity Law: Proof |
9.3 |
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21 |
Nov 4 |
Distribution of Quadratic Residues |
10.1,10.2 |
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- |
HW5 assigned. |
22 |
Nov 6 |
Distribution of consecutive QR triples; Sums of squares |
10.2,11.1 |
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- |
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23 |
Nov 11 |
Sums of squares |
11.1,11.2 |
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- |
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24 |
Nov 13 |
Partitions |
12 |
- |
- |
HW5 due. |
25 |
Nov 18 |
Partitions II |
12 |
- |
- |
- |
26 |
Nov 20 |
Generating Functions |
13.1 |
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- |
HW6 assigned. |
27 |
Dec 2 |
Partition Generating Functions; Jacobi's Triple Product Identity |
13.2 |
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28 |
Dec 4 |
JTPI Proof; Euler's Pentagonal Number Theorem |
13.2,14.2 |
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29 |
Dec 18 |
Final Exam |
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