| Date |
Texbook sections/ Topics |
||
| 1 |
Tue Sep 5 |
Introduction: What is Number Theory?; 1.1 Induction | |
| 2 |
Thu Sep 7 | 1.2, Basis Representation Theorem; 2.1 Euclid's Division Lemma; 2.2 Divisibility | |
| 3 |
Tue Sep 12 |
2.2 Divisibility;
2.4 Fundamental Theorem of Arithmetic |
|
| 4 |
Thu Sep 14 |
3.1 Permuations and
Combinations; 3.4 Generating Functions |
|
| 5 |
Tue Sep 19 |
3.4
Generating Functions |
|
| 6 |
Thu Sep 21 |
HW 1 due; 4.1 Congruences;
4.2 Residue Systems |
|
| 7 |
Tue Sep 26 |
5.1 Linear Congruences
|
|
| 8 |
Thu Sep 28 |
HW 2 due; 5.2 Fermat's Little Theorem
and Euler's generalization of it; Wilson's theorem.
|
|
| 9 |
Tue Oct 3 |
Catch up; Review |
|
| 10 |
Thu Oct 5 |
Exam 1 |
|
| 11 |
Tue Oct 10 |
5.3 Chinese Remainder Theorem;
5.4 Polynomial Congruences |
|
| 12 |
Thu Oct 12 |
6.1 Combinatorial Study of
φ(n) |
|
| 13 |
Tue Oct 17 |
6.2 Formulas for d(n)
and
σ(n); 6.3 Multiplicative
Functions |
|
| 14 |
Thu Oct 19 |
HW 3 due; 6.4 Möbius Inversion |
|
| 15 |
Tue Oct 24 |
12.1 Introduction to Partitions; 12.2 Graphical Representations;
12.3 Euler's Partition Theorem
|
|
| 16 |
Tue Oct 26 |
HW 4 due;
13.1 Infinite Products as Generating Functions
|
|
| 17 |
Tue Oct 31 |
13.2 Series-Product Identities
|
|
| 18 |
Thu Nov 2 |
HW 5 due;
More on partition identities.
|
|
| 19 |
Tue Nov 7 |
Catch up; Review |
|
| 20 |
Thu Nov 9 |
Exam 2 |
|
| 21 |
Tue Nov 14 |
13.2 Series-Product
Identities |
|
| 22 |
Thu Nov 16 |
14.2 Euler's pentagonal number theorem
|
|
| 23 |
Tue Nov 21 |
Special Class in LSH B117
(Livingston
Campus) Ramanujan: The Man Who Loved Numbers |
|
| 24 |
Tue Nov 28 |
7.1 Reduced Residue Systems; 7.2
Primitive Roots mod p |
|
| 25 |
Thu Nov 30 |
HW 6 due; 8.1 Elementary properties of
π(n) |
|
| 26 |
Tue Dec 5 |
9.1 Euler's Criterion; 9.2 The
Legendre Symbol |
|
| 27 |
Thu Dec 7 |
9.3, 9.4 Quadratic Reciprocity |
|
| 28 |
Tue Dec 12 |
Catch up; Review |
|
| Mon Dec 18 8-11 AM |
Final Examination |