Plan for Math 124, Fall 2001^{1}

Date  Note Reading  Subject
W Sept 12  D7–8, Kix–4  Overview 1: What is This Course About?
F Sept 14  D16–31  Primes 1: Prime Factorization
M Sept 17  D179–181, P1–13 Computing 1: Introduction to Computing and PARI
W Sept 19 hwk D35–38  Primes 2: The Sequence of Prime Numbers
F Sept 21  D41–48  Congruences 1: Fermat’s Theorem
M Sept 24  D48–51  Congruences 2: Chinese RT, Wilson’s Theorem, Prime Modulus
W Sept 26 hwk D51–56  Congruences 3: Equations Modulo N
F Sept 28  D206–209  Cryptography 1: Intro to Public-key Crypto. (Diffie-Helman)
M Oct 1  D210–211  Cryptography 2: The RSA Cryptosystem
W Oct 3  hwk www.rsa.com  Cryptography 3: RSA in Practice
F Oct 5  D59–62  Quadratic reciprocity 1: Primitive Roots
M Oct 8  holiday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
W Oct 10 hwk D63–70  Quadratic reciprocity 2: The Reciprocity Law
F Oct 12 D70–74 Quadratic reciprocity 3: The Proof
M Oct 15  Overview 2: Midterm Review
W Oct 17 hwk  Midterm
F Oct 19  G145–152  Computing 2: Programming in PARI
M Oct 22  D78–89  Continued Fractions 1: Introduction, Basic Facts
W Oct 24 hwk D89–93  Continued Fractions 2: Infinite Continued Fractions
F Oct 26  D94–104  Continued Fractions 3: Quadratic Irrationals
M Oct 29  D104–111  Continued Fractions 4: Pell’s Equation
W Oct 31 hwk D115–120  Quadratic Forms 1: Sums of Two Squares
F Nov 2  D129–133  Quadratic Forms 2: Equivalence of Quadratic Forms
M Nov 5  D133–138  Quadratic Forms 3: Discriminants
W Nov 7  hwk D140–145  Quadratic Forms 4: Reduced Positive Definite Forms
F Nov 9  D159–162  Elliptic Curves 1: Trivial Notions 1
M Nov 12  holiday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
W Nov 14 hwk K17–20  Elliptic Curves 2: Basic Notions 1
F Nov 16  D162–165, K25–32 Elliptic Curves 3: Basic Notions 2
M Nov 19 P21–24, G76–82 Computing 3: Computing with Elliptic Curves using PARI
W Nov 21 hwk D165–168  Elliptic Curves 4: Elliptic Curves over Finite Fields
F Nov 23  holiday . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
M Nov 26  Elliptic Curves 5: Elliptic Curve Factorization 1
W Nov 28 hwk  Elliptic Curves 6: Elliptic Curve Factorization 2
F Nov 30 D168–170 Elliptic Curves 7: Fermat’s Last Theorem
M Dec 3  Elliptic Curves 8: The ABC-Conjecture
W Dec 5  hwk K20–24  Elliptic Curves 9: The Congruent Number Problem
F Dec 7  W1–5  Elliptic Curves 10: The Birch and Swinnerton-Dyer conjecture 2
M Dec 10  Computing 4: Empirical Evidence for the BSD Conjecture
W Dec 12  Overview 3: Final Review

D: Davenport, K: Kato et al., P: PARI tutorial, G: PARI guide, W: Wiles

1Remember that this plan is only a plan, not a contract.