Lectures for Mathematics 361, Spring 202122
 M 1/24: Overview: Z[i], sums of two squares
 T 1/25: Pythagorean triples; start Euclidean rings
 W 1/26: More Euclidean rings
 F 1/28: Finish Euclidean rings; start Euler's proof that \sum 1/p
diverges
 M 1/31: Arithmetic functions and Dirichlet series
 T 2/1: More arithmetic functions and Dirichlet series
 W 2/2: [Assignment A due]
Euclid's lemma, lcm, (Z/nZ,+,.), (Z/nZ)^x, Euler's rule, Fermat's
Little Theorem
 F 2/4: [Add/sectionchange deadline]
ax+ny=b, ax=b(n); algorithms, Ruby code
 M 2/7: SunZe Theorem
 T 2/8: Hensel's Lemma
 W 2/9: [Assignment B due]
Zp as a limit; completion of a metric space
 F 2/11: Finitelygenerated abelian groups, (Z/pZ)^\times, padic
geometry, Z/p^eZ~Zp/p^eZp
 M 2/14: (Z/p^eZ)^\times for p odd, (Z/2^eZ)^\times, when is
(Z/nZ)^\times cyclic
 T 2/15: The Bernoulli numbers, power sums, and zeta values
 W 2/16: [Assignment C due] Start
quadratic reciprocityEuler's criterion, Gauss's lemma
 F 2/18: (5/p) by Gauss, Legendre's formulation of QR
 M 2/21: Euler QR <=> Legendre QR, Legendre QR by lattice points,
Jacobi symbol
 T 2/22: Algebraic numbers and algebraic integers
 W 2/23: [First quiz due]
Algebraic numbers and algebraic integers, (2/p) again
 F 3/25: QR by Gauss sums, sign of the Gauss sum by Fourier analysis
 M 2/28: [NoW drop deadline] Gloss
Fourier analysis
 T 3/1: Start finite fields
 W 3/2: [Assignment D due]
Finish finite fields
 F 3/4: Characters, N(x^e=u), orthogonality of characters
 M 3/7: Gauss sums, Jacobi sums, counting formula
 T 3/8: Invoke table of Jacobi sum values, quadratic example in
two ways, start establishing table of Jacobi sum values
 W 3/9: [Assignment E due]
Finish Jacobi sum values, cubic example and its modularity
 Second quiz out  due 3/16
 F 3/11: Start arithmetic of D=Z[\omega]: unique factorization,
units, primes, factorization of rational primes, primary primes
 M 3/14: Arithmetic of D, continued
 T 3/15: Arithmetic of D, continued
 W 3/16: [Second quiz due]
Prove cubic reciprocity
 F 3/18: (No meeting)
 Spring break week
 M 3/28: Examples of cubic reciprocity
 T 3/29: Fermat for n=3
 W 3/30: [Assignment F due]
Start Dirichlet's theorem on arithmetic progressions
 F 4/1: (No meeting  Qual break)
 M 4/4: [Withdraw/leave deadline]
Finish Dirichlet's theorem on a.p.'s, preview discussion
 T 4/5: Mellin transform, continuation and functional equation
for EulerRieman zeta
 W 4/6: [Assignment G due]
Review Riemann's proof, start Dirichlet Lfunctions
 F 4/8: More on Dirichlet Lfunctions, start uniform description
of local factors
 M 4/11: Review, start local factors again
 T 4/12: Finish local factors, factorization of Gauss sums
 W 4/13: [Assignment H due]
Quadratic fields, through norm
 F 4/15: More on quadratic fields, through quadratic character
 M 4/18: More on quadratic fields, through fundamental domain
 T 4/19: More on quadratic fields, through lattice results
 W 4/20: More on quadratic fields, through L(1,\chi)
 F 4/22: Quadratic fields: lattice points in a disk,
estimate A_n for Dedekind zeta
 M 4/25: Finish ideal class number formula for imaginary
quadratic fields; mention cyclotomic zeta
 T 4/26: Start real quadratic units
 W 4/27: More real quadratic units, evaluations
 F 4/29: (No meeting)
 M 5/9: [Term project due at noon]
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