The following is a tentative schedule for the course. Please check back regularly for updates as the term progresses.
| Day | Date | Brief Description |
|---|---|---|
| 1 | 13 Sep (M) | The integers; divisors and multiplies |
| 2 | 15 Sep (W) | GCD and Euclidean algorithm |
| 3 | 17 Sep (F) | Consequences of the Euclidean algorithm; Fundamental Theorem of Arithmetic |
| 4 | 20 Sep (M) | Primes |
| 5 | 22 Sep (W) | Perfect numbers and sum-of-divisors theorem |
| 6 | 24 Sep (F) | Residues and congruences |
| 7 | 27 Sep (M) | Units; Fermat's little theorem |
| 8 | 29 Sep (W) | Euler's totient function; Chinese Remainder theorem |
| 9 | 2 Oct (F) | More CRT; RSA cryptography |
| 10 | 4 Oct (M) | Primality testing |
| 11 | 6 Oct (W) | Order and primitive roots |
| 12 | 8 Oct (F) | Exam 1 |
| 13 | 11 Oct (M) | Primitive roots mod p |
| 14 | 13 Oct (W) | Primitive roots mod n |
| 15 | 15 Oct (F) | Quadratic residues |
| 16 | 18 Oct (M) | Quadratic reciprocity and applications |
| 17 | 20 Oct (W) | Proof of quadratic reciprocity; Generalized quadratic reciprocity |
| 18 | 22 Oct (F) | Which numbers are sums of two squares?, I |
| 19 | 25 Oct (M) | More sums of squares; Pythagorean triples and the unit circle |
| 20 | 27 Oct (W) | Gaussian integers, I |
| 21 | 29 Oct (F) | Exam 2 |
| 22 | 1 Nov (M) | Gaussian integers, II |
| 23 | 3 Nov (W) | Gaussian integers, III |
| 24 | 5 Nov (F) | Pell's equation and diophantine approximation, I |
| 25 | 8 Nov (M) | Pell's equation and diophantine approximation, II; Continued Fractions, I |
| 26 | 10 Nov (W) | Continued fractions, II |
| 27 | 12 Nov (F) | Arithmetic Functions, I |
| 28 | 15 Nov (M) | Arithmetic Functions, II |
| TBD | Final Exam |