Lectures for Mathematics 361, Fall 201617
 Monday, 8/29: Overview: Z[i], sums of two squares
 Tuesday, 8/30: Pythagorean triples; start Euclidean rings
 Wednesday, 8/31: More Euclidean rings
 Friday, 9/2: Finish Euclidean rings; Euler's proof that \sum 1/p diverges
 Monday, 9/5: Labor Day Holiday
 Tuesday, 9/6: Homework preview session (questiondriven)
 Wednesday, 9/7: [Assignment 1 due]
Arithmetic functions and Dirichlet series
 Friday, 9/9: [Add/sectionchange deadline]
Totient via inclusionexclusion, start congruences,
I&Rex1.8 <=> ax=b(n)
 Monday, 9/12: Finish ax=b(n); algorithms, Ruby code
 Tuesday, 9/13: [Assignment 2 due] SunZe Theorem
 Wednesday, 9/14: Hensel's Lemma
 Friday, 9/16: Compactness of Zp; start (Z/p^eZ)^\times
 Monday, 9/19: Discuss homework
 Tuesday, 9/20: [Assignment 3 due]
(Z/p^eZ)^\times for p odd
 Wednesday, 9/21: (Z/2^eZ)^\times, when is (Z/nZ)^\times cyclic;
start quadratic reciprocity
 Friday, 9/23: Euler's lemma; coin flips by telephone; Gauss's lemma
 Monday, 9/26: (5/p) by Gauss, Legendre's formulation of QR
 Tuesday, 9/27: Euler QR <=> Legendre QR, Legendre QR by lattice points,
Jacobi symbol
 Wednesday, 9/28: Homework discussion
 Friday, 9/30: [Assignment 4 due]
Algebraic numbers and algebraic integers, (2/p) again
 Monday, 10/3: QR by Gauss sums, start the sign of the Gauss sum
by Fourier analysis
 Tuesday, 10/4: [NoW drop deadline]
Sign of the Gauss sum by Fourier analysis
 Wednesday, 10/5: Gloss Fourier analysis; ringquotients require ideals
 Friday, 10/7: [First quiz due]
Start finite fields
 Monday, 10/10: Finish finite fields, preview homework
 Tuesday, 10/11: Characters, N(x^e=u)
 Wednesday, 10/12: [Assignment 6 due]
Gauss sums, Jacobi sums, counting formulas,
quadratic example
 Friday, 10/14: Analysis of Jacobi sums, start cubic example
 Fall break week
 Monday, 10/24: Finish cubic example, revisit quadratic example,
preview homework
 Tuesay, 10/25: Start arithmetic of D=Z[\omega]: unique factorization, units,
primes, factorization of rational primes, primary primes
 Wednesday, 10/26: [Assignment 7 due]
Arithmetic of D: review, residue fields
 Friday, 10/27: Cubic character, its properties, state cubic reciprocity
 Monday, 10/31: Prove cubic reciprocity
 Tuesday, 11/1: Examples of cubic reciprocity
 Wednesday, 11/2: [Assignment 8 due]
Fermat for n=3
 Second quiz out  due 11/9
 Friday, 11/4: Start Dirichlet's theorem on arithmetic progressions
 Monday, 11/7:
 Tuesday, 11/8: [Withdraw/leave deadline]
Finish Dirichlet's theorem on a.p.'s, preview discussion
 Wednesday, 11/9: [Second quiz due]
Mellin transform, continuation and functional equation
for EulerRieman zeta
 Friday, 11/11: Review Riemann's proof, start Dirichlet Lfunctions
 Monday, 11/14: More on Dirichlet Lfunctions, start uniform description
of local factors
 Tuesday, 11/15: Review, start local factors again
 Wednesday, 11/16: [Assignment 10 due]
Finish local factors, factorization of Gauss sums
 Friday, 11/18: Quadratic fields, through norm
 Monday, 11/21: More on quadratic fields, through quadratic character
 Tuesday, 11/22: More on quadratic fields, through fundamental domain
 Wednesday, 11/23: [Assignment 11 due]
More on quadratic fields, through lattice results
 Friday, 11/25: Thanksgiving Holiday
 Monday, 11/28: More on quadratic fields, through L(1,\chi)
 Tuesday, 11/29: Quadratic fields: lattice points in a disk,
estimate A_n for Dedekind zeta
 Wednesday, 11/30: Finish ideal class number formula for imaginary
quadratic fields; mention cyclotomic zeta
 Friday, 12/2: Start real quadratic units
 Monday, 12/5: More real quadratic units, evaluations
 Tuesday, 12/6: No meeting (college on Thursday schedule)
 Wednesday, 12/7:
Assignments

Materials

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