Lecture Schedule and Assignment
(This is tentative schedule. Check here
for frequent updates.)
| Date | Topic | Sections | Homework | Due Date |
| Week 1 | Feb 6 | |||
| Jan 28 | Introduction. Principle of mathematical induction |
1.1 | Page 6: 4, 9, 12, 13, 16, 18 Page 14: 2, 3, 5, 7 |
|
| Jan 30 | Euclid's division lemma | 2.1 | ||
| Week 2 | Feb 13 | |||
| Feb 4 | Divisibility. Linear Diophantine equation | 2.2 | Page 21: 1(d), 2, 4, 10, 12 Page 25: 1(d) Page 28: 6(b)(c), 9(b), 10 |
|
| Feb 6 | More on linear Diophantine equation Fundamental theorem of arithmetic |
2.3, 2.4 | ||
| Week 3 | Feb 20 | |||
| Feb 11 | Permutations and combinations Fermat's little theorem |
3.1, 3.2 | Page 33: 3, 5, 10, 13, 14 Page 38: 1, 3, 6 Page 40: 1, 2 |
|
| Feb 13 | Wilson's theorem, etc | 3.3, 3.5 | ||
| Week 4 | Feb 27 | |||
| Feb 18 | Generating functions Basic properties of Congruences |
3.4, 4.1 |
Page 43: 2, 5 |
|
| Feb 20 | Residue Systems Solving Linear Congruences. |
4.2, 5.1 | ||
| Week 5 | Mar 6 | |||
| Feb 25 | Fermat and Wilson Theorem (using congruences). Chinese remainder theorem | 5.2, 5.3 | Page 63: 3, 4, 6, 9, 11, 12, 16(c) Page 70: 1(c), 2, 6 |
|
| Feb 27 | Polynomial congruences. | 5.3, 5.4 | ||
| Week 6 | Mar 13 | |||
| Mar 4 | Midterm I | Page 73: 1, 6, 7, 8 Page 81: 1, 4, 11, 15 |
||
| Mar 6 | Combinatorial study of φ(n) | 6.1 | ||
| Week 7 | Mar 27 | |||
| Mar 11 | Formulae for d(n) and σ(n) Multiplicative arithmetic functions |
6.2, 6.3 | Page 84: 2, 3, 4, 5, 6 Page 90: 2, 5, 7, 8, 11 |
|
| Mar 13 | Möbius inversion formula | 6.4 | ||
| Week 8 | ||||
| Mar 18 | No Class (spring break) | |||
| Mar 20 | ||||
| Week 9 | Apr 3 | |||
| Mar 25 | Properties of reduced residue systems | 7.1 | Page 96: 6, 7 Page 99: 2, 3, 7, 8, 9, 10, 11, 12 |
|
| Mar 27 | Primitive roots modulo p | 7.2 | ||
| Week 10 | Apr 10 | |||
| Apr 1 | Elementary properties of π(x) | 8.1 | Page 104: 1, 2, 4, 6, 15, 16, 17, 18 Page 110: 2, 3 |
|
| Apr 3 | Tchebychev's theorem | 8.2 | ||
| Week 11 | Apr 17 | |||
| Apr 8 | Euler's criterion. Legendre Symbol | 9.1, 9.2 | Page 116: 1(c) Page 118: 2, 3 Page 124: 2, 3, 5 Page 127: 1, 2, 4, 5 |
|
| Apr 10 | Quadratic reciprocity law | 9.3, 9.4 | ||
| Week 12 | Apr 29 | |||
| Apr 15 | Applications of quadratic reciprocity law Review |
9.4, 10.1 | Page 132: 1, 2, 3, 4, 5 | |
| Apr 17 | Midterm II | |||
| Week 13 | ||||
| Apr 22 | Consecutive residues and non-residues | 10.1 | No Homework | |
| Apr 24 | Consecutive triples of quadratic residues Sum of two squares |
10.2, 11.1 | ||
| Week 14 | ||||
| Apr 29 | Sum of four squares | 11.2 | No Homework | |
| May 1 | Review | |||