01204211-58
Announcements
Activities
- 8/20: Activity 1 - Logic 1
- 8/27: Activity 2 - Logic and Proofs
- 9/3: Activity 3 - Induction 1
- 9/10: Activity 4 - Counting 1
- 10/4: Homework 5 - Counting 2
- 10/8: Homework 6 - Number theory 1
- 10/15: Activity 7 - Number theory 2 -- Due date: 14 Dec 2015
- 11/26: Activity 8 - Polynomials and Graph theory 1 -- Due date: 14 Dec 2015
- 12/9: Homework 9 - Graph theory 2 -- Due date: 18 Dec 2015
- 12/9: Homework 10 - Graph theory 3 -- Due date: 21 Dec 2015
Topics
| Week/number | Topics | Handouts | Links |
|---|---|---|---|
| 1/1 | Introduction, Propositions | handout1 | |
| 1/2 | Quantifiers | handout2 | Clips: part1, part2, part3, part4 |
| 2/1 | Inference rules Proof techniques 1 |
handout3 handout4 |
|
| 2/2 | Proof techniques 2 | handout5 | Clips: part1, part2, part3 |
| 3/1 | Induction 1 | handout6 | |
| 3/2 | Induction 2 | handout7 | Clips: part1, part2, part3 |
| 4/1 | Induction 3 Counting 1 |
handout8 handout9 |
|
| 4/2 | Counting 2 | handout10 | Clips: part1, part2, part3, part4 |
| 5/1 | Counting 3 | handout11 | |
| 5/2 | The pigeonhole principle and the birthday problem | handout12 | Clips: part1, part2, part3, part4 |
| 6/1 | Binomial Coefficients 1 | handout13 | |
| 6/2 | Binomial Coefficients 2 Fibonacci sequence |
handout14 handout15 |
Clips (binomial coefficients 2): part1, part2 |
| 7/1 | Primality testing 1 | handout16 | |
| 7/2 | Primality testing 2 | handout17 | |
| 8/1 | Primality testing 3 | handout18 | |
| 8/2 | Modular arithmetic 1 | External materials: Lecture notes from Berkeley CS70 Fall15, Chapter 4 sections 4.5 - 4.6 from MIT 6.042 OCW | |
| 9/1 | Modular arithmetic 2 (RSA) | External materials: Lecture notes from Berkeley CS70 Fall15, | |
| 9/2 | Modular arithmetic 3 (Modular multiplicative inverses) | Clips: part1, part2, part3, part4 External materials Chapter 4 sections 4.1 - 4.3 from MIT 6.042 OCW | |
| 10/1 | Polynomials | External materials: Lecture notes from Berkeley CS70 Fall15 | |
| 10/2 | (no class - commencements) | ||
| 11/1 | Graphs 1 - Introduction & degrees | Materials from LPV Ch.7 sections 7.1 - 7.2. Available in this free manuscript as Ch.9, sections 9.1 - 9.2. | |
| 11/2 | (cancelled) | ||
| 12/1 | Graphs 2 - Eulerian walks | Materials from LPV Ch.7.3. | |
| 12/2 | (no class - open house) | ||
| 13/1 | Graphs 3 - Trees | Materials from LPV Ch.8. Available in this free manuscript as Ch.10. | |
| 13/2 | Reviews with activities 8 | ||
| 14/1 | (cancelled) | ||
| 14/2 | Graphs 4 - Euler's formula | Materials from LPV Ch.12. | |
| 15/1 | Graphs 5 - Matching | Materials from LPV Ch.10. Available in this free manuscript as Ch.12. | |
| 15/2 | (make-up) Graphs 6 - Coloring | Materials from LPV Ch.13. |
Additional links
The outline of the course is inspired mainly by CS70 at Berkeley (See the recent course homepage.) More over, the course borrows a lot of exposition from other sources listed below.
- CS70: Discrete mathematics and probability theoryat Berkeley
- Mathematics for Computer Science at MIT OCW.
- Lovasz, Pelikan, Vesztergombi. Discrete Mathematics: Elementary and Beyond. Springer, 2003. See Lovasz and Vesztergombi's lecture notes (dmbook.ps)
- Matousek and Nestril. Invitation to Discrete Mathematics. 2nd Edition. Oxford Press, 2008.
- Rosen. Discrete Mathematics and Its Applications. Mcgraw-Hill.
