20150120  lecture: logic & sets   lecture notes
 introduction and motivation
 review of logical formulas
 review of set theory

20150122  lecture: logic & sets   lecture notes
 logical quantifiers
 comprehensions
 set products & relations
 equivalence relations

20150127
  
20150129  lecture: modular arithmetic   lecture notes
 set quotients
 congruence classes of integers
 operations on congruence classes

20150130 11:59 PM EDT
 assignment  
20150203  lecture: modular arithmetic   lecture notes
 algebra of congruence classes
 solving equations over ℤ/mℤ
 Euclid's lemma
 ℤ/pℤ as a set of permutations
 generating random numbers

20150205  lecture: modular arithmetic   lecture notes
 greatest common divisor
 more on random numbers
 infinitude of primes

20150210
  
20150212  lecture: modular arithmetic   lecture notes
 generating prime numbers
 Fermat's little theorem
 Fermat primality test
 detecting probable primes
 generating probable primes

20150213 11:59 PM EDT
 assignment  
20150217 Monday sched.
  
20150219  lecture: modular arithmetic   lecture notes
 multiplicative inverses in ℤ/mℤ
 Chinese remainder theorem (CRT)
 applications of CRT
 computing CRT solutions

20150224  lecture: modular arithmetic   lecture notes
 Bézout's identity
 extended Euclidean algorithm
 more applications of CRT
 Euler's totient function
 Euler's theorem

20150226  lecture: review  
20150227 11:59 PM EDT
 assignment  
20150303 Tuesday 9:3510:35 AM  midterm exam  
20150305  lecture: modular arithmetic   lecture notes
 review of midterm solutions
 more on the totient function
 more on multiplicative inverses

20150310  recess  
20150312  recess  
20150317  lecture: complexity   lecture notes
 computational complexity
 efficiency vs. intractability
 intractable problems
 factoring
 computing φ
 RSA problem (e roots)
 discrete logarithm problem

20150319  lecture: complexity   lecture notes
 computing square roots in ℤ/mℤ
 congruent squares problem
 Hensel's lemma

20150324  lecture: complexity   lecture notes
 applications of intractability
 basic proof of identity
 DiffieHellman protocol
 RSA and Rabin encryption

20150326  lecture: complexity   lecture notes
 efficient arithmetic algorithms
 addition and multiplication
 gcd and inversion
 modular exponentiation
 solving CRT systems

20150327 11:59 PM EDT
 assignment  
20150331  lecture: algebraic structures   intractability review examples
 proving unsolvability
 history of algebraic structures
 algebra of permutations
 shift permutations on ℤ/mℤ
 multiplicationinduced

20150401 Wednesday sections  quiz  
20150402  lecture: algebraic structures   lecture notes
 algebraic closures
 algebra of permutations
 swap permutations
 decomposing into swaps
 isomorphisms and examples
 homomorphic encryption

20150407  lecture: algebraic structures   lecture notes
 compression as an isomorphism
 more on generators
 linear congruence theorem

20150409  lecture: algebraic structures   lecture notes
 CRT as an isomorphism
 CRT isomorphism applications
 generators, and closures
 generalized CRT

20150413 11:59 PM EDT
 assignment  
20150414  lecture: algebraic structures   lecture notes
 more on generalized CRT
 other algebraic structures
 algebra of data structures
 distributed storage
 compression

20150416  lecture: algebraic structures   lecture notes
 more CRT and applications
 more on isomorphisms
 subgroups
 hidden subgroup problem

20150421  lecture: algebraic structures   lecture notes
 Shor's algorithm
 unreliability and errors
 direct products
 structural induction
 fundamental theorem of arithmetic

20150423  lecture: algebraic structures  
20150428  lecture: review  
20150430  lecture: review  
20150506 Wednesday 9:0011:00 AM EPC 205  final exam  