### Lecture and Tutorial Contents

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 5 Intro to Discrete Structures 01Introduction.pdf 2) Jan 8 Review of propositional logic. Ch 1.1, 1.2 02PropositonalLogic.pdf (sect 1,2) 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 12 Propositional logic: normal forms, boolean functions and circuit design. (See textbook 1.2 ex 42-61) 02PropositonalLogic.pdf (sect 3,4) 4) Jan 15 Predicate Logic. Ch. 1.3, 1.4 03PredicateLogic.pdf (sect 1) 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 19 Predicate Logic Ch 1.3,1.4 03PredicateLogic.pdf (sect 2,3) 6) Jan 22A1 posted Rules of inference and proof methods Ch 1.5,1.6,1.7 04InferenceRulesProofMethods.pdf (sect 1,2) TUT3 (Jan 25) LECTURE (PROF): Rules of Inference and proof methods Ch. 1.5, 1.6, 1.7. 04InferenceRulesProofMethods.pdf (sect 3) 7) Jan 26 Completing Inference Rules. Intro to Number Theory. Ch 1.7. Ch 3.4 05NumberTheory.pdf 8) Jan 29 Number Theory (divison, congruences, modular arithmetic) Ch 3.4 05NumberTheory.pdf (sect 1) TUT4 (Feb 1)A1 due Tutorial: Number theory. Chapter 3.4: 7, 9, 19, 21, 24, 28, 31 9) Feb 2 Number Theory (Primes, GDC, Euclidean algorithm) Ch 3.5, part of Ch 3.6 05NumberTheory.pdf (sect 2) 10) Feb 5 Number Theory (Primes,GCD, Euclidean Algorithm) Ch 3.5, part of 3.6 05NumberTheory.pdf (sect 2) TUT5 (Feb 8) LECTURE (PROF): Review before midterm. 11) Feb 9 MIDTERM EXAM. - 12) Feb 12 Number Theory (Extended Eucliden, Linear Congruences, Chinese Remainder Theorem.) Ch 3.7 05NumberTheory.pdf (sect 3) Feb 15-19 Study break - TUT6 (Feb 22) Tutorial: Number theory. Chapter 3.5: 5, 10, 20, 22 Chapter 3.6: 23 Chapter 3.7: 19, 27, 49 13) Feb 23 Number Theory (Lecturer: Sebastian Raaphorst) Fermat's Little Theorem, RSA cryptosystem Ch 3.7 05NumberTheory.pdf (sect 3) 14) Feb 26 Induction Review. (Lecturer: Sebastian Raaphorst). Ch 4.1 TUT7 (Mar 1) Tutorial: Induction. Chapter 4.1: 3, 13, 19, 32, 49 15) Mar 2 Induction. Ch 4.1 06Induction.pdf (sec 1) 16) Mar 5 Strong induction. Ch 4.2 06Induction.pdf (sec 2) TUT8 (Mar 8) Tutorial: Strong Induction. Chapter 4.2: 5, 11, 14, 23, 25, 29, 32 17) Mar 9 Recursive definitions and structural induction. Ch 4.3. 06Induction.pdf (sec 3) 18) Mar 12 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 16 Recurrence relations. Ch 7.1, 7.2 07RecurrenceRelations.pdf 20) Mar 19 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 23 Recurrence relations. Ch 7.3 22) Mar 26 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) Mar 30 Graphs. Ch 9 (select). 08Graphs.pdf Apr 2,5 holiday - 24) Apr 6 Graphs and trees. Ch 9,10 (select). 08Graphs.pdf 25) Apr 9 Graphs and Trees Ch 9,10 (select). 08Graphs.pdf TUT12 (Apr 12) Tutorial: graph theory Exercises TBA.