References:
1) Textbook: Kenneth H. Rosen, Discrete Mathematics and Its Applications, Sixth Edition, McGraw Hill, 2007
(or Seventh edition, 2012). Edition 6 has been voted as the official edition for the course; all references are based
on 6th edition.
2) Lecture notes
Lecture and tutorial contents (the future material is tentative; further updates will reflect what was covered).
Bold indicates material that has been confirmed and updated. The rest is just a tentative outline.
Date 
Topic 
Slides 
1) Jan 9 
Intro to Discrete Structures 

TUT1 (Jan 10) 
Tutorial: Propositional logic. (Tutorials in general solve selected exercises from the list on the side) 
(references to exercises in 6th edition): Chapter 1.1: 1,3,6,12,13,23,29,38,52,63 Chapter 1.2: 7,9,14,26,34,38,57,60. 
2) Jan 12 
Review of propositional logic. 
Ch 1.1, 1.2 
3) Jan 16 
Predicate Logic. 
Ch 1.3 03PredicateLogic.pdf (sect 1) 
TUT2 (Jan 17) 
Tutorial: Predicate logic. Quiz#1 
Chapter 1.3: 5,6,9,12,16,20,28,30,33,39,43,4649,53 
4) Jan 19 
Predicate Logic 
Ch 1.3, 1.4 03PredicateLogic.pdf (sect 2) 
5) Jan 23 
Predicate Logic 
03PredicateLogic.pdf (sect 3) 
TUT3 (Jan 24) 
Tutorial: Predicate Logic  Quiz#2 
Exercises: some more exercises from TUT2; Chapter 1.4: 6,9,14,19,24,27,30,31,34,37 
6) Jan 26 
Rules of Inference 
Ch. 1.5 04InferenceRulesProofMethods.pdf (sect 1,2) 
7) Jan 30 
Proof methods. 
Ch 1.6, 1.7 04InferenceRulesProofMethods.pdf (sect 3) 
TUT4 (Jan 31) 
Tutorial: Inference Rules; Quiz#3. 
Chapter 1.5: Ex. 2431. 
8) Feb 2 
Number Theory (division, congruences) 
Ch 1.61.7, part of Ch 3.4 ending 04InferenceRulesProofMethods.pdf (sect 3) 05NumberTheory.pdf (sect 1) 
9) Feb 6 
Number Theory (Modular arithmetic) 
Ch 3.4 05NumberTheory.pdf (sect 1) 
TUT5 (Feb 7) 
Tutorial: Number theory. Quiz#4 
Chapter 3.4: 7, 9, 19, 21, 24, 28, 31 (tutorial focus here) (Other recommended practice in numbr theory: Chapter 3.5: 5, 10, 20, 22 Chapter 3.6: 23 Chapter 3.7: 19, 27, 49) 
10) Feb 9 
Number Theory (Primes,GCD, Euclidean Algorithm) 
Ch 3.5, part of 3.6 05NumberTheory.pdf (sect 2) 
11) Feb 13` 
Number Theory (Extended Eucliden, Linear Congruences, Chinese Remainder Theorem.) 
Ch 3.7 05NumberTheory.pdf (sect 3) 
TUT6 (Feb 14) 
Tutorial: Review of last year's midterm 

12) Feb 16 
Number Theory Chinese Remainder Theorem, Fermat's Little Theorem 
Ch 3.7 05NumberTheory.pdf (sect 3) 
Feb 1925 
Study break 
 
13) Feb 27 
RSA cryptosystem and review. 
Ch 3.7 05NumberTheory.pdf (sect 3) 
TUT7 (Feb 28) 
Tutorial: More Number Theory Exercises. 
Number Theory: exercise on solving congruences and inverses, exercise 4.727, exercise on RSA. 
14) Mar 1 
Midterm test. 
ROOM: MRT250 and MRT252 
15) Mar 5 
Induction and Strong induction. 
Ch 4.1, 4.2 06Induction.pdf (sec 1,2) 
TUT8 (Mar 6) 
Tutorial: Induction. Strong Induction.  
Chapter 4.1: 3, 13, 19, 32, 49 Chapter 4.2: 5, 11, 14, 23, 25, 29, 32 
16) Mar 8 
Recursive definitions and structural induction. 
Ch 4.3. 06Induction.pdf (sec 3) 
17) Mar 12 
Correctness of recursive algorithms. Program correctness and verification 
Ch 4.4, 4.5. 06Induction.pdf (sec 4) 
TUT9 (Mar 13) 
Tutorial: Structural induction, Program correctness and verification. 
Chapter 4.3: 5, 7, 22, 33. Chapter 4.5: 3,7 
18) Mar 15 
Recurrence relations. 
Ch 7.1, 7.2 
19) Mar 19 
Recurrence relations and complexity of algorithms. 
Ch 7.2 
TUT10 (Mar 20) 
Tutorial: recurrence relations 
Chapter 7.2: 3 (choose 1 or 2 parts), 11, 23, 28. 
20) Mar 22 
Recurrence relations. 
Ch 7.3 
21) Mar 26 
Recurrence relations 
Ch 7.3 
TUT11 (Mar 27) 
Tutorial: recurrence relations 
Exercises 10, 11 (page 482; derive formula and prove, not using master theorem). 
22) Mar 29 
Graphs. 
Ch 9 (select). 
23) Apr 2 
Graphs and trees. 
Ch 9,10 (select). 
TUT12 (Apr 3) 
Tutorial: graph theory 
Exercises TBA. 
24) Apr 5 
Graphs and Trees 
Ch 9,10 (select). 