| Date |
Topic |
Read |
Exercises |
| Jan. 20 |
Axioms, Well-ordering |
|
Appendix A (p. 518): 1a, 2a, 8(extra credit).
Also, what are:
Also(ex.cred.)Show that if n>2, n! is the sum
of at most n of its proper factors.
|
| Jan. 22 |
Induction |
App. A
1.2 |
1.2: 6, 7, 13, 17
Leftover extra credit--App.A #8,
and now: if n>2, n! is the sum
of exactly n of its proper factors.
|
| Jan. 27 |
Divisibility, Binomial Coeff's |
1.4
App. B |
(all for next Mon., not Wed.)
App.A: 2b
1.4: 5ad, 7, 8, 46
2.1: (do before quiz) 3
App.B: 2, 3d, 5, 6 |
| Jan. 29 |
Primes |
3.1 |
3.1: 6, 14ab, 24 |
| Feb. 3 |
Greatest Common Divisor
Euclidean Algorithm |
3.2
3.3 |
(all for Mon., 2/10)
leftover: 3.1 #24
3.2: 2f,15,16,22,(ex.cr.)25
3.3: 1c,2d,3c,4d,5b
ex.cr.: Can n+2, n^2+n+1 be both cubes?
(that's a correction; it was n+3 etc.) |
| Feb. 5 |
more gcd, E.alg.
Fundamental Theorem (3.4) |
3.4 |
3.4: 1e, 35, 60 |
| Feb. 10 |
irrationals (3.4) and special primes (3.5)
|
3.4
3.5 |
3.4: 30d,32c,33a,36,
44 (any method),45,46,52
and leftover 60;
3.5: 15 |
| Feb. 12 |
balance of 3.4, 3.5 | | (No new homework) |
| Feb. 17 | Snow Day |
| Feb. 19 |
Congruences (4.1) |
4.1 |
Self-scheduled exam due 2/24
+ (for March 3):
4.1: 1ag, 3, 4, 6ab, 8, 17, 19,
28ac, 33, 34 |
| Feb. 24 |
more congruences
and linear congruences |
|
4.2: 1ab, 2cd, 5, 6;
also, construct charts of
inverses mod 13 and mod 16 |
| Feb. 26 |
Linear Congruences (4.2)
Check digits and ISBNs |
4.2
(and maybe peek at 5.5) |
|
| Mar. 3 |
Chinese Remainder Thm. (4.3)
Wilson's Theorem (6.1) |
4.3 to start of
computational app;
start 6.1 |
(to turn in 3/17)
4.3: 3, 4b, 7, 10, 12; also read (don't turn in) 15, 19.
6.1: 2, 4. HINT on 4
|
| Mar. 5 |
Fermat's Little Theorem |
6.1 |
6.1: 12, 15, 19 (combines Chinese + Fermat),
and 35 (combines Wilson + Fermat) |
| Mar. 10-12 | Hooray! Spring Break! |
| Mar. 17ff |
Euler's Thm on phi(n) | 6.3 |
6.3: 1ace, 5, 15 (that's 15, not 13);
also: Find phi(n) for n=11, 25, 360, 3599
(hint: 3600 is a square)
also: Find primitive roots for p=11, 19, 31
also: Find ALL the primitive roots for p=13
|
| Mar. 19 | NO CLASS |
| Mar. 24 |
Quadratic residues |
11.1 | 11.1: 1d, 3, 5a, 7, 13ac |
| Mar. 26 |
Quadratic reciprocity |
11.2 | 11.2: 1acf, 2, 4, 6 |
| Mar. 31 |
Pythagorean triples |
13.1 | 13.1: 1, 9(hard!!) |
| Apr. 2 |
Fermat's Last Theorem |
13.2 | 13.2: 3 |
| Apr. 7 |
Sums of squares |
13.3 | 13.3: 1c, 2aei, 3d
Don't forget: Fermat's Last Tango, 7pm Apr. 8, rm.338 |
| Apr. 9 |
More sums of squares; review |
|
exam (due Apr. 14) |
| Cryptology (Ch. 8, part)
incl. RSA | |
RSA handout |
| Recognizing primes (6.2 etc.) |
| Factoring (up to quad. sieve) |
| maybe...
Multiplicative Functions (Ch. 7) |
| Continued Fractions (Ch. 12) |