20160119  lecture: logic & sets   lecture notes
 introduction and motivation
 review of logical formulas
 review of set theory

20160121  lecture: logic & sets   lecture notes
 logical quantifiers
 comprehensions
 set products & relations

20160126  lecture: logic & sets   lecture notes
 reflexivity, symmetry, & transitivity
 equivalence relations
 set quotients

20160128  lecture: modular arithmetic   lecture notes
 congruence classes of integers
 operations on congruence classes
 solving equations over ℤ/mℤ
 algebra of congruence classes

20160201 11:59 PM EST
 assignment  
20160202  lecture: modular arithmetic   lecture notes
 more algebra of congruence classes
 Euclid's lemma
 solving equations & Euclid's lemma

20160204  lecture: modular arithmetic   lecture notes
 ℤ/pℤ as a set of permutations
 generating random numbers
 greatest common divisor
 generalized Euclid's lemma
 finding coprimes

20160209  lecture: modular arithmetic   lecture notes
 more on finding coprimes
 linear congruential generators
 infinitude of primes
 Fermat's little theorem
 Fermat primality test

20160211  lecture: modular arithmetic   lecture notes
 detecting probable primes
 generating probable primes
 multiplicative inverses in ℤ/mℤ
 Chinese remainder theorem (CRT)
 applications of CRT

20160216 11:59 PM EST Monday sched.
 assignment  
20160218  lecture: modular arithmetic  
20160223  lecture: modular arithmetic   lecture notes
 Bézout's identity
 extended Euclidean algorithm
 Euler's totient function
 Euler's theorem

20160225  lecture: review  
20160226 11:59 PM EST
 assignment  
20160301 Tuesday 9:3510:35 AM  midterm exam  
20160303  lecture: modular arithmetic   review of midterm solutions
 lecture notes
 more on Euler's totient function
 closure of (ℤ/mℤ)*

20160308  recess  
20160310  recess  
20160315  lecture: complexity   lecture notes
 problem complexity
 efficient arithmetic algorithms
 addition, multiplication
 modular exponentiation

20160317  lecture: complexity   lecture notes
 efficient arithmetic algorithms
 division and modulus
 gcd and inversion
 solving CRT systems
 efficiency vs. intractability

20160322  lecture: complexity   lecture notes
 complexity reductions
 intractable problems
 factoring
 computing φ
 RSA problem (e roots)
 discrete logarithm problem
 computing square roots in ℤ/mℤ

20160324  lecture: complexity   lecture notes
 congruent squares problem
 Hensel's lemma
 Rabin encryption

20160328 11:59 PM EDT
 assignment  
20160329  lecture: complexity   lecture notes
 applications of intractability
 RSA and Rabin encryption
 DiffieHellman protocol
 more random number generators

20160330 Wednesday sections  quiz  
20160331  lecture: algebraic structures   lecture notes
 algebra of permutations
 swap & adjacent swap
 shift/cyclic
 multiplicationinduced
 decomposition into swaps
 examples of isomorphisms

20160405  lecture: algebraic structures   lecture notes
 more isomorphisms and examples
 homomorphic encryption

20160407  lecture: algebraic structures   lecture notes
 compression as an isomorphism
 generators and closures
 linear congruence theorem (LCT)

20160411 11:59 PM EDT
 assignment  
20160412  lecture: algebraic structures  
20160414  lecture: algebraic structures   lecture notes
 more on the CRT isomorphism
 generalized CRT practice
 applications of the LCT

20160419  lecture: algebraic structures   lecture notes
 algebraic properties
 subgroups
 direct products of groups

20160421  lecture: algebraic structures   polynomials in ℤ/mℤ
 representing groups as functions
 Shor's algorithm

20160426  lecture: review  
20160427 11:59 PM EDT
 assignment  
20160428  lecture: review  
20160503 Tuesday 9:0011:00 AM EPC 205  final exam  