The following is the syllabus that I currently have planned for the
semester. Like all plans, this is subject to change, and at any given
time, we may be a bit off from it.
| Week | Starts | Sections | Topic |
|---|---|---|---|
| 1 | Jan. 12 | 1.1 | Mathematical Induction |
| 1.2 | Basis Representation Theorem | ||
| 2.1 | The Division Lemma | ||
| 2 | Jan. 19 | 2.2 | Divisibility |
| 3 | Jan. 26 | 2.3 | Linear Diophantine Equations |
| 2.4 | Fundamental Theorem of Arithmetic | ||
| 4.1 | Introduction to Congruences | ||
| 4 | Feb. 2 | 4.2 | Residue Systems |
| 5.1 | Linear Congruences | ||
| 5.2 | Fermat's and Wilson's Theorems | ||
| 5 | Feb. 9 | 5.2 (cont.) | Fermat's and Wilson's Theorems |
| 5.3 | Chinese Remainder Theorem | ||
| 5.4 | Polynomial Congruences | ||
| 6 | Feb. 16 | FIRST MIDTERM: MON. FEB. 16, IN CLASS | |
| 7.1 | Reduced Residue systems | ||
| 7.2 | Primitive Roots Modulo p | ||
| 7 | Feb. 23 | 7.2 (cont.) | Primitive Roots Modulo p |
| Primitive Roots Modulo Non-primes | |||
| SPRING BREAK -- MARCH 1-7 -- NO CLASSES | |||
| 8 | Mar. 8 | 9.1 | Quadratic Residues |
| 9.2 | The Legendre Symbol | ||
| 9.3 | Quadratic Reciprocity | ||
| 9 | Mar. 15 | 9.3 (cont.) | Quadratic Reciprocity |
| SECOND MIDTERM: WED. APR. 18, IN CLASS | |||
| 9.4 | Applications of Quadratic Reciprocity | ||
| 10 | Mar. 22 | 10.1 | Consecutive Residues and Nonresidues |
| 10.2 | Consecutive Triples of Quadratic Residues | ||
| 11 | Mar. 29 | 10.2 (cont.) | Consecutive Triples of Quadratic Residues |
| 6.1 | Euler's Phi-Function | ||
| 6.2 | The Functions d(n) and sigma(n) | ||
| 12 | Apr. 5 | 6.3 | Multiplicative Functions |
| 6.4 | The Mobius Inversion Formula | ||
| 13 | Apr. 13 | 8.1 | Elementary Properties of Pi(x) |
| 14 | Apr. 19 | 8.2 | Tchebychev's Theorem |
| To Be Announced | |||
| 14 | Apr. 26 | To Be Announced | |
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