September 9
Lecture 10
Quadratic reciprocity and its applications
quadratic reciprocityJacobi symbolsum of two squares
What we covered
Lectures
This page records what we actually covered after each class meeting, with links to the corresponding lecture notes.
September 4
Lecture 9
The law of quadratic reciprocity
quadratic reciprocitycounting lattice points
September 2
Lecture 8
Gauss's lemma (cont.)
Gauss's lemma2 modulo p
August 31
Lecture 7
Gauss's lemma
Wilson's theoremfloor functionGauss's lemma
August 28
Lecture 6
Euler's criterion and its applications
quadratic residues & nonresiduesEuler's criterionLegrendre symbol-1 modulo p
August 26
Lecture 5
Quadratic residues and nonresidues
polynomial congruencesLagrange's theoremquadratic congruencesquadratic residues & nonresidues
August 24
Lecture 4
Euler's theorem and linear congruence equations
residue classesEuler's totient functionEuler's theoremFermat's little theoremlinear congruences
August 21
Lecture 3
Review of unique factorization (complete), review of Euclidean algorithm and congruences
FTAUFDEuclidean domainEuclidean algorithmcongruences
August 19
Lecture 2
Review of unique factorization (cont.)
FTAidealsPIDgcdBézout's lemmaEuclid's lemma
August 17
Lecture 1
Course introduction and review of unique factorization
syllabusdivisibilityunitsprimes and compositesFTAdivision algorithm
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