20150903  lecture: logic & sets   lecture notes
 introduction and motivation
 review of logical formulas
 review of set theory

20150908  lecture: logic & sets   lecture notes
 logical quantifiers
 comprehensions
 set products & relations
 equivalence relations

20150910  lecture: modular arithmetic   lecture notes
 set quotients
 congruence classes of integers
 operations on congruence classes
 solving equations over ℤ/mℤ

20150914 11:59 PM EDT
 assignment  
20150915  lecture: modular arithmetic   lecture notes
 algebra of congruence classes
 Euclid's lemma
 ℤ/pℤ as a set of permutations
 generating random numbers

20150917  lecture: modular arithmetic   lecture notes
 greatest common divisor
 generalized Euclid's lemma
 finding coprimes
 more on random numbers

20150922  lecture: modular arithmetic   lecture notes
 generating prime numbers
 Fermat's little theorem
 Fermat primality test
 detecting probable primes
 generating probable primes

20150924  lecture: modular arithmetic   lecture notes
 multiplicative inverses in ℤ/mℤ
 Chinese remainder theorem (CRT)
 applications of CRT

20150929  lecture: modular arithmetic   lecture notes
 computing CRT solutions
 more on CRT solutions
 Bézout's identity
 extended Euclidean algorithm

20150930 11:59 PM EDT
 assignment  
20151001  lecture: modular arithmetic   lecture notes
 practice computing CRT solutions
 efficiency of Euclidean algorithm
 using Bézout's identity
 more applications of CRT

20151006  lecture: modular arithmetic   lecture notes
 Euler's totient function
 Euler's theorem
 applications of Euler's theorem
 computing inverses
 efficient exponentiation

20151008  lecture: complexity   lecture notes
 problem complexity
 efficient arithmetic algorithms
 addition, multiplication
 modular exponentiation
 division

20151013 Monday sched.
  
20151014 11:59 PM EDT
 assignment  
20151015  lecture: complexity   lecture notes
 efficient arithmetic algorithms
 modulus
 gcd and inversion
 solving CRT systems
 efficiency vs. intractability
 intractible problems
 RSA problem (e roots)
 discrete logarithm problem

20151020  lecture: review  
20151022 Thursday 3:354:35 PM  midterm exam  
20151027  lecture   review of midterm solutions
 lecture notes
 computing square roots in ℤ/mℤ
 congruent squares problem

20151029  lecture: complexity   lecture notes
 Hensel's lemma
 complexity reductions
 other intractable problems

20151103  lecture: complexity   lecture notes
 more complexity reductions
 applications of intractability
 basic proof of identity
 DiffieHellman protocol
 RSA encryption protocol
 Rabin encryption protocol

20151105  lecture: complexity   lecture notes
 RSA and DiffieHellman examples
 more on the Rabin protocol
 more on random number generators
 other protocol variants

20151110  lecture: algebraic structures   lecture notes
 algebra of permutations
 swap permutations
 decomposing into swaps
 shift permutations on ℤ/mℤ
 multiplicationinduced
 examples of isomorphisms

20151111 11:59 PM EDT
 assignment  
20151112  lecture: algebraic structures   lecture notes
 more on isomorphisms
 homomorphic encryption
 compression as an isomorphism
 generators of algebraic structures

20151117  lecture: algebraic structures  
20151118 Wednesday sections  quiz  
20151119  lecture: algebraic structures   lecture notes
 linear congruence theorem
 CRT as an isomorphism
 generalized CRT

20151124  lecture: algebraic structures   lecture notes
 more on generalized CRT
 groups and subgroups
 hidden subgroup problem

20151126  recess  
20151130 11:59 PM EDT
 assignment  
20151201  lecture: algebraic structures   lecture notes
 more on groups and subgroups
 direct products of groups
 more applications

20151203  lecture: algebraic structures   lecture notes
 other algebraic structures
 algebra of data structures
 distributed storage
 compression
 structural induction
 fundamental theorem of arithmetic

20151208  lecture: review  
20151210  lecture: review  
20151215 11:59 PM EDT
 assignment  
20151217 Thursday 3:005:00 PM CAS 316  final exam  