20140902  lecture: logic & sets   lecture notes
 introduction and motivation
 review of logical formulas
 review of set theory

20140904  lecture: logic & sets   lecture notes
 logical quantifiers
 comprehensions
 set products & relations
 equivalence relations

20140909  lecture: modular arithmetic   lecture notes
 set quotients
 congruence classes of integers
 operations on congruence classes

20140910 11:59 PM EDT
 assignment  
20140911  lecture: modular arithmetic   lecture notes
 algebra of congruence classes
 solving equations over ℤ/mℤ
 Euclid's lemma

20140916  lecture: modular arithmetic   lecture notes
 ℤ/pℤ as a set of permutations
 generating random numbers
 greatest common divisor
 more on random numbers

20140918  lecture: modular arithmetic  
20140923  lecture: modular arithmetic   lecture notes
 Fermat primality test
 detecting probable primes
 generating probable primes
 multiplicative inverses in ℤ/mℤ

20140925  lecture: modular arithmetic   lecture notes
 Chinese remainder theorem (CRT)
 applications of CRT
 computing CRT solutions

20140926 11:59 PM EDT
 assignment  
20140930  lecture: modular arithmetic   lecture notes
 more on CRT solutions
 Bézout's identity
 extended Euclidean algorithm
 computing CRT solutions

20141001    all sections and OHs cancelled

20141002  lecture: modular arithmetic   lecture notes
 more applications of CRT
 Euler's totient function
 Euler's theorem

20141007  lecture: modular arithmetic   lecture notes
 applications of Euler's theorem
 computing inverses
 efficient exponentiation

20141009  lecture: complexity   lecture notes
 efficient arithmetic algorithms
 addition and multiplication
 gcd and inversion
 modular exponentiation
 solving CRT systems

20141010    extra OHs: 2  4 PM (CS lab)

20141014 11:59 PM EDT (Monday sched.)
 assignment  
20141016  lecture: review  
20141021 Tuesday 3:354:35 PM  midterm exam  
20141023  lecture   review of midterm solutions
 efficiency vs. intractability

20141028  lecture: complexity   lecture notes
 efficiency vs. intractability
 intractable problems
 factoring
 computing φ
 RSA problem (e roots)
 discrete logarithm problem
 computing square roots in ℤ/mℤ

20141030  lecture: complexity  
20141104  lecture: complexity   lecture notes
 applications of intractability
 basic proof of identity
 DiffieHellman protocol
 RSA encryption protocol
 Rabin encryption protocol

20141106  lecture: algebraic structures   more on the Rabin protocol
 proving unsolvability
 encryption & Shamir secret sharing
 other protocol variants
 DiffieHellman example
 Hensel's lemma example

20141110 11:59 PM EDT
 assignment  
20141111  lecture: algebraic structures   lecture notes
 history of algebraic structures
 algebra of permutations
 swap permutations
 decomposing into swaps
 shift permutations on ℤ/mℤ
 multiplicationinduced
 examples of isomorphisms

20141112 Wednesday sections  quiz  
20141113  lecture: algebraic structures   lecture notes
 more on isomorphisms
 homomorphic encryption
 compression as an isomorphism

20141118  lecture: algebraic structures   lecture notes
 more on generators
 linear congruence theorem
 CRT as an isomorphism
 CRT, generators, and closures

20141120  lecture: algebraic structures   lecture notes
 more on generalized CRT
 CRT isomorphism applications
 other algebraic structures
 algebra of data structures
 distributed storage
 compression

20141125  lecture: algebraic structures   lecture notes
 more CRT and applications
 more on isomorphisms
 subgroups
 hidden subgroup problem

20141126 11:59 PM EDT
 assignment  
20141127  recess  
20141202  lecture: algebraic structures   lecture notes
 more on generators & subgroups
 direct products
 structural induction
 fundamental theorem of arithmetic

20141204  lecture: review  
20141209  lecture: review  
20141215 11:59 PM EDT
 assignment  
20141218 Thursday 3:005:00 PM  final exam  