Week 1:  
Friday, September 2nd  Introduction. Sets: Venn
diagrams; set identities. 

Wednesday, September 7th  Logic: propositional calculus; logical operators.  
Friday, September 9th 
Logic: The conditional and biconditional (equivalence) statements.  
Week 2: 
Reading: Notes on logic by Jacques Verstraete are posted here. Also compare with Rosen. 

Monday, September 12th  Logic: tautologies and contradictions. Examples of Direct Proofs and Proof by Contradiction.  Assignment
1 assigned. 
Wednesday, September 14th  Logic: combinatorial circuits; circuit complexity.  
Friday, September 16th  Asymptotic Bounds. Polynomial and Exponential Time Algorithms.  
For more background on the topic of this and the next lecture see these notes (especially Section 5).  
Week 3: 

Monday, September 19th  Example: P and NP.  
Wednesday, September 21st  Arrow's impossibility
theorem. See these
notes. 

Friday, September 23rd  Logic: predicate calculus.

Assignment 1 due. 
Week 4: 

Monday, September 26th  Logic: proofs by induction.  
Wednesday, September
28th 
Number Theory: prime factorisation.  
Friday, September 30th  Number Theory: applications
of unique prime factorizations. 

Week 5: 

Monday, October 3rd  Number Theory: Greatest
common divisiors. 
Assignment 2 assigned. 
Wednesday, October 5th  Number Theory: Euclid's Algorithm.  
Friday, October 7th  Number Theory: Modular arithmetic.  
Week 6: 

Monday, October 10th  Thansgiving. No lecture. 

Wednesday, October 12th  Number Theory: Modular
arithmetic and prime fields. 
Assignment 2 due. 
Friday, October 14th  Assignment 3 assigned. 

Week 7: 

Monday, October 17th  Number Theory: Modular Equations.  
Wednesday, October 19th  Number Theory: Fermat
Test, MillerRabin Test, Recognizing Primes. 

Friday, October 21st  Example: cryptography.  
Week 8: 

Monday, October 24th 
Example:
RSA encryption.


Wednesday, October 26th  Combinatorics: functions, counting.  
Friday, October 28th  Combinatorics: subsets; the Binomial theorem.  
Week 9: 

Monday, October 31st  Combinatorics: Pascal's triangle.  Assignment 3 due, assignment 4 assigned. 
Wednesday, Nov 2nd 
Combinatorics: solving recurrence equations.  
Friday, November 4th  Combinatorics: inclusionexclusion.  
Week 10: 

Monday, November 7th  Combinatorics: inclusionexclusion; the derangement problem.  
Wednesday, November 9th  Combinatorics: inclusionexclusion; Euler's function.  
Friday November 11th.  Combinatorics: the Multinomial theorem.  
Week 11: 

Monday, November 14th  Graph Theory: the Handshaking lemma. Euler circuits.  Assignment 4 due, assignment 5 assigned. 
Wednesday, November 16th  Graph Theory: Hamiltonian cycles.  
Friday, November 18th.  Graph Theory: trees.  
Week 12: 

Monday, November 21st  Graph Theory: representing spanning trees.  
Wednesday, November 23rd  Graph Theory: counting spanning trees.  
Friday, November 25th  Graph Theory: planar graphs.  
Week 13: 

Monday November 28th  Graph Theory: graph coloring; characterising bipartite graphs.  Assignment 5 due. 
Wednesday, November 30th 
Graph Theory: the 4color theorem; the 5color theorem.  
Friday, December 2nd  Game Theory 

Week 14:  
Monday, December 5th 
Review 

Thursday, December 22nd 
FINAL EXAM 