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 22 A1 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. |