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: 5,6,9,12,16,20,28,30,33,39,43,46-49,53 |
|
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 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 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 |
|
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). |