| WEEK 1 | W, Sep 5 computation vs. abstraction; odd2 = 8k+1; examples not a proof; idea of induction/descent |
F, Sep 7 examples of failed conjectures, sample induction proof, list of applications of number theory |
M, Sep 10 §1.1 divisibility |
| WEEK 2 | W, Sep 12 §1.2 primes |
F, Sep 14 §§1.3, 1.4 gcd, Eucl alg |
M, Sep 17 §1.5 Fund Thm of Arithmetic |
| WEEK 3 | W, Sep 19 §2.1 congruences |
F, Sep 21 §2.1 operations with congruences and congruence classes; computing ab mod m; solving linear congruences |
M, Sep 24 Ch 1 assigned exercises due. §6.1 lin Diophantine eqs in 1 or 2 variables |
| WEEK 4 | W, Sep 26 §2.2 linear congruences |
F, Sep 28 §2.3 Chinese Remainder thm |
M, Oct 1 Last day to drop without instructor's signature. §2.1 rep’n of integers in different bases, divisibility tests |
| WEEK 5 | W, Oct 3 §2.4, 2.5 Wilson’s thm, Fermat's thm, pseudoprimes |
F, Oct 5 EXAM 1 on Ch 1 and 2.1–2.3 |
M, Oct 8 §§2.1, 2.6 repunits; Euler’s thm |
| WEEK 6 | W, Oct 10 Returned Exam 1, discussed it. §3.1 arithmetic fcns, multiplicativity |
F, Oct 12 §§3.1, 3.3, 3.4, 3.2 f multiplicative ⇒ F(n) = ∑d | n ƒ(d) is multiplicative; number and sum of divisors, calculation of Euler’s phi fcn |
M, Oct 15 §§3.2, 3.5 Euler's φ fcn, perfect numbers |
| WEEK 7 | W, Oct 17 §§3.5, 3.6 perfect numbers, Möbius inversion |
F, Oct 19 §§3.6, 4.1 Möbius inversion, quadratic residues |
M, Oct 22 §§4.1, 4.2 quadratic residues, Legendre symbol |
| WEEK 8 | W, Oct 24 §§4.2, 4.3 Legendre symbol, quadratic reciprocity |
F, Oct 26 Ch 2, 3 assigned exercises due. §4.2 analog of Gauss’ lemma; calculation of (2/p) |
M, Oct 29 QUIZ 1 on Ch 2, 3. determination of integers n such that φ(n) = 4 |
| WEEK 9 | W, Oct 31 Returned Ch. 2, 3 exercises §§4.3 pf of quadratic reciprocity (QR) |
F, Nov 2 §§4.2, 4.3 calculation of (3/p) with & without QR |
M, Nov 5 §4.1 gen’l quadratic congruences with prime modulus |
| WEEK 10 | W, Nov 7 §5.1 order of an integer, primitive roots |
F, Nov 9 Ch 4 assigned exercises due. §5.1 powers of prim rt form complete reduced residue set; order of ai in terms of order of a |
M, Nov 12 EXAM 2 on §§2.4–4.3 |
| WEEK 11 | W, Nov 14 §§5.1, 5.2 m has prim rt ⇒ m has φ(φ(m)) prim rts; Lagrange’s thm |
F, Nov 16 §5.2 prim rts for primes |
M, Nov 19 §5.3 prim rt thm (start) |
| WEEK 12 | W, Nov 21 §5.3 prim rt thm (conclusion) |
M, Nov 26 §5.4 indices, nth power residues |
W, Nov 28 §5.4 indices, nth power residues (cont’d) |
| WEEK 13 | F, Nov 30 Decimal fractions handout §§6.2, 6.3 nonlinear Diophantine eqs, Pythagorean triples |
M, Dec 3 QUIZ 2 on Ch 5. Ch 5 assigned exercises due. §§6.3, 8.3 Pyth triples, converse of Fermat’s thm |
W, Dec 5 Returned Quiz 2. Divisibility handout. §§6.3, 7.1 Pyth triples w given leg or hypotenuse; rat’l/irrat’l numbers |
| WEEK 14 | F, Dec 7 Student evaluations §7.1 decimal fractions |
M, Dec 10 EXAM 3 on Ch 5 and §§6.2, 6.3, 8.3 |
W, Dec 12 Ch 6–8 assigned exercises due. §7.1 decimal fractions |
| FINAL EXAM SLOT |
Th, Dec 21 Final exam slot 8:00–10:30 a.m. 171 Edu Returned assigned exercises for Ch 6–8. Handout: divisibility tests in base b. Decimal fractions; identification nos and check digits |