Lectures for Mathematics 361, Spring 201819
 M 1/28: Overview: Z[i], sums of two squares
 T 1/29: Pythagorean triples; start Euclidean rings
 W 1/30: More Euclidean rings
 F 2/1: Finish Euclidean rings; Euler's proof that \sum 1/p
diverges, start arithmetic functions and Dirichlet series
 M 2/4: More arithmetic functions and Dirichlet series
 T 2/5: Homework preview session (questiondriven)
 W 2/6: [Assignment 1 due]
Euclid's lemma, lcm, (Z/nZ,+,.), (Z/nZ)^x, Euler's rule, Fermat's
Little Theorem
 F 2/8: [Add/sectionchange deadline]
ax+ny=b, ax=b(n); algorithms, Ruby code
 M 2/11: SunZe Theorem
 T 2/12: Hensel's Lemma
 W 2/13: [Assignment 2 due]
Zp as a limit; completion of a metric space
 F 2/15: Finitelygenerated abelian groups, (Z/pZ)^\times, padic
geometry, Z/p^eZ~Zp/p^eZp
 M 2/18: (Z/p^eZ)^\times for p odd, (Z/2^eZ)^\times, when is
(Z/nZ)^\times cyclic; start quadratic reciprocity
 T 2/19: The Bernoulli numbers, power sums, and zeta values
 W 2/20: [Assignment 3 due]
Euler's lemma; coin flips by telephone; Gauss's lemma
 F 2/22: (5/p) by Gauss, Legendre's formulation of QR
 M 2/25: Euler QR <=> Legendre QR, Legendre QR by lattice points,
Jacobi symbol
 T 2/26: Homework discussion
 W 2/27: [First quiz due]
Algebraic numbers and algebraic integers, (2/p) again
 F 3/1: QR by Gauss sums, start the sign of the Gauss sum
by Fourier analysis
 M 3/4: [NoW drop deadline]
Sign of the Gauss sum by Fourier analysis
 T 3/5: Gloss Fourier analysis; ringquotients require ideals
 W 3/6: [Assignment 5 due]
Start finite fields
 F 3/8: Finish finite fields, preview homework
 M 3/11: Characters, N(x^e=u)
 T 3/12: Gauss sums, Jacobi sums, counting formulas, quadratic
example
 W 3/13: [Assignment 6 due]
Analysis of Jacobi sums, start cubic example
 F 3/15: Finish cubic example, revisit quadratic example,
preview homework
 M 3/18: Start arithmetic of D=Z[\omega]: unique factorization, units,
primes, factorization of rational primes, primary primes
 T 3/19: Arithmetic of D: review, residue fields
 W 3/20: [Assignment 7 due]
Cubic character, its properties, state cubic reciprocity
 Second quiz out  due 4/3
 F 3/22: Prove cubic reciprocity
 Spring break week
 M 4/1: Examples of cubic reciprocity
 T 4/2: Fermat for n=3
 W 4/3: [Second quiz due]
Start Dirichlet's theorem on arithmetic progressions
 F 4/5: (No meeting  Qual break)
 M 4/8: [Withdraw/leave deadline]
Finish Dirichlet's theorem on a.p.'s, preview discussion
 T 4/9: Mellin transform, continuation and functional equation
for EulerRieman zeta
 W 4/10: [Assignment 10 due]
Review Riemann's proof, start Dirichlet Lfunctions
 F 4/12: More on Dirichlet Lfunctions, start uniform description
of local factors
 M 4/15: Review, start local factors again
 T 4/16: Finish local factors, factorization of Gauss sums
 W 4/17: [Assignment 11 due]
Quadratic fields, through norm
 F 4/19: More on quadratic fields, through quadratic character
 M 4/22: More on quadratic fields, through fundamental domain
 T 4/23: More on quadratic fields, through lattice results
 W 4/24: More on quadratic fields, through L(1,\chi)
 F 4/26: Quadratic fields: lattice points in a disk,
estimate A_n for Dedekind zeta
 M 4/29: Finish ideal class number formula for imaginary
quadratic fields; mention cyclotomic zeta
 T 4/30: Start real quadratic units
 W 5/1: More real quadratic units, evaluations
 F 5/3: (No meeting)
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