Lecture and Tutorial Contents - Winter 2011

References:

1) Textbook: Kenneth H. Rosen, Discrete Mathematics and Its Applications, Sixth Edition, McGraw Hill, 2007.
2) Lecture notes

Lecture and tutorial contents (the future material is tentative; further updates will reflect what was covered):

 1) Jan 7 Intro to Discrete Structures 01Introduction.pdf 2) Jan 11 Review of propositional logic. Ch 1.1, 1.2 02PropositonalLogic.pdf (sect 1,2,3) TUT1 (Jan 11) Tutorial: Propositional logic. (Tutorials in general solve selected exercises from the list on the side) Chapter 1.1: 1,3,6,12,13,23,29,38,52,63 Chapter 1.2: 7,9,14,26,34,38,57,60. 3) Jan 14 Predicate Logic. Ch. 1.3 03PredicateLogic.pdf (sect 1) 4) Jan 18 Predicate Logic. Ch 1.3,1.4 03PredicateLogic.pdf (sect 1-2) TUT2 (Jan 18) Tutorial: Predicate logic. Chapter 1.3: 5,6,9,12,16,20,28,30,33,39,43,46-49,53 Chapter 1.4: 6,9,14,19,24,27,30,31,34,37 5) Jan 21 Predicate Logic Ch 1.3, 1.4 03PredicateLogic.pdf (sect 2) 6) Jan 25 Predicate Logic; Rules of inference and proof methods 03PredicateLogic.pdf (sect 3) Ch. 1.5, 1.6, 1.7. 04InferenceRulesProofMethods.pdf (sect 1) TUT3 (Jan 25) Tutorial: Predicate Logic - Quiz#1 Exercises: some more exercises from TUT2; other selected. 7) Jan 28 Inference Rules and Proof Methods. Ch. 1.5, 1.6, 1.7. 04InferenceRulesProofMethods.pdf (sect 2) 8) Feb 1 Proof methods. Ch 1.6, 1.7 04InferenceRulesProofMethods.pdf (sect 3) TUT4 (Feb 1) Tutorial: Inference Rules; Quiz#2. Chapter 1.5: Ex. 24-31. 9) Feb 4 Number Theory (division, congruences, modular arithmetic) Ch 3.5, part of Ch 3.6 05NumberTheory.pdf (sect 1) 10) Feb 8A1 due Number Theory (Primes,GCD, Euclidean Algorithm) Ch 3.5, part of 3.6 05NumberTheory.pdf (sect 2) TUT5 (Feb 8) Tutorial: Number theory. Quiz#3 Chapter 3.4: 7, 9, 19, 21, 24, 28, 31 (tutorial focus here) (Other recommended practice: Chapter 3.5: 5, 10, 20, 22 Chapter 3.6: 23 Chapter 3.7: 19, 27, 49) 11) Feb 11 Number Theory (Extended Eucliden, Linear Congruences, Chinese Remainder Theorem.) Ch 3.7 05NumberTheory.pdf (sect 3) 12) Feb 15 Review/Catchup before midterm TUT6 (Feb 15) Tutorial: Review of last year's midterm Previous year midterm. 13) Feb 18 Midterm Test ROOM: MNT 203 (normal class time, different room) Feb 21-26 Study break - 14) Mar 1 Number Theory Fermat's Little Theorem, RSA cryptosystem Ch 3.7 05NumberTheory.pdf (sect 3) TUT7 (Mar 1) Tutorial: Solution of Midterm. Midterm solution 15) Mar 4 Induction. Ch 4.1 06Induction.pdf (sec 1) 16) Mar 8 Strong induction. Ch 4.2 06Induction.pdf (sec 2) TUT8 (Mar 8) Tutorial: Induction. Strong Induction. - Quiz#4 Chapter 4.1: 3, 13, 19, 32, 49 Chapter 4.2: 5, 11, 14, 23, 25, 29, 32 17) Mar 11 Recursive definitions and structural induction. Ch 4.3. 06Induction.pdf (sec 3) 18) Mar 15 Correctness of recursive algorithms. Program correctness and verification Ch 4.4, 4.5. 06Induction.pdf (sec 4) TUT9 (Mar 15) Tutorial: Structural induction, Program correctness and verification. Chapter 4.3: 5, 7, 22, 33. Chapter 4.5: 3,7 19) Mar 18 Recurrence relations. Ch 7.1, 7.2 07RecurrenceRelations.pdf 20) Mar 22 Recurrence relations and complexity of algorithms. Ch 7.2 TUT10 (Mar 22) Tutorial: recurrence relations Chapter 7.2: 3 (choose 1 or 2 parts), 11, 23, 28. 21) Mar 25 Recurrence relations. Ch 7.3 22) Mar 29 Recurrence relations Ch 7.3 TUT11 (Mar 29) Tutorial: recurrence relations Exercises 10, 11 (page 482; derive formula and prove, not using master theorem). 23) Apr 1 Graphs. Ch 9 (select). 08Graphs.pdf 24) Apr 5 Graphs and trees. Ch 9,10 (select). 08Graphs.pdf TUT12 (Apr 5) Tutorial: graph theory Exercises TBA. 25) Apr 8 Graphs and Trees Ch 9,10 (select). 08Graphs.pdf