### Lecture and Tutorial Contents - Winter 2012

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 01Introduction.pdf 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 02PropositonalLogic.pdf 3) Jan 16 Predicate Logic. Ch 1.3 03PredicateLogic.pdf (sect 1) TUT2 (Jan 17) Tutorial: Predicate logic. Quiz#1 Chapter 1.3: 5,6,9,12,16,20,28,30,33,39,43,46-49,53 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. 24-31. 8) Feb 2 Number Theory (division, congruences) Ch 1.6-1.7, part of Ch 3.4 ending (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 19-25 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 4.7-27, 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 07RecurrenceRelations.pdf 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). 08Graphs.pdf 23) Apr 2 Graphs and trees. Ch 9,10 (select). 08Graphs.pdf TUT12 (Apr 3) Tutorial: graph theory Exercises TBA. 24) Apr 5 Graphs and Trees Ch 9,10 (select). 08Graphs.pdf