|
|
|
Schedule for Math 332, Fall 2006 (tentative)
(in pdf format,
ready to print)
| Week |
Day |
Ch. |
Topics |
| 8/24 – 25 |
1 |
|
Introduction (by Etienne
Rassart) |
| 8/28 – 9/1 |
2 |
1 |
Numbers, induction,
divisibility and primes |
|
3 |
|
The Euclidean algorithm |
| 9/3 – 9/8 |
4 |
|
The linear diophantine
equation |
|
5 |
2 |
Congruences, divisibility
tests |
| 9/11 – 9/15 |
6 |
|
Linear congruences, solving
them |
|
7 |
|
Chinese Remainder Theorem
and applications |
| 9/18 – 9/22 |
8 |
3 |
Fermat's little theorem and
Wilson's theorem |
|
9 |
|
Euler's theorem and the
Euler Φ-function |
| 9/25 – 9/29 |
10 |
|
Rings and Fields – Z/mZ |
|
11 |
5 |
Quadratic congruences |
| 10/2 – 10/6 |
12 |
|
Quadratic residues and the
law of Quadratic Reciprocity |
|
13 |
|
Quadratic Reciprocity |
| 10/9 – 13 |
|
|
FALL BREAK |
|
14 |
6 |
Order of an integer modulo p |
| 10/16 – 20 |
15 |
|
Primitive roots, power
residues, indices |
|
16 |
|
Existence of primitive roots |
| 10/23 – 27 |
17 |
7 |
Primes: Eratosthenes,
perfect and Fermat numbers, Mersenne |
|
18 |
|
The prime number theorem,
Dirichlet's thm., Goldbach conjecture |
| 10/30 – 11/3 |
19 |
8 |
Diophantine equations:
pythagorean triples and Fermat Last Thm. |
|
20 |
|
Sums of two squares |
| 11/6 – 10 |
21 |
9 |
Continued fractions: finite
and infinite |
|
22 |
|
Periodic continued fractions |
| 11/13 – 17 |
23 |
|
Rational approximations to
irrational numbers |
|
24 |
10 |
Pell's equation |
| 11/20 – 24 |
25 |
|
Pell's equation (continued) |
|
|
|
THANKSGIVING |
| 11/27 – 12/1 |
26 |
11 |
Gaussian integers |
|
27 |
|
Other quadratic extensions |
|
|
|