Week 1: Jan 04, Jan 06, Jan 08
Set Theory and Functions: read the handout Joy of Sets, Section 1.2 and Theorem 1.3.1 of LPV (the textbook Discrete Mathematics: Elementary and Beyond), and Chapter 4 of Hicks.
Read the handout Mathematical Hygiene. We will discuss some of these concepts throughout the course as needed.
Homework 1 due Jan 13
Week 2: Jan 11, Jan 13, Jan 15
Induction: Section 2.1 of LPV, Chapter 7 of Hicks
Homework 2 due Jan 20
Week 3: Jan 20, Jan 22
Pascal's triangle, counting, bijective proofs: Sections 1.7-1.8, 3.5-3.6 of LPV, Chapters 9, 10, 11 of Hicks
Note that we have been using ${{n}\choose{k}}$ for the binomial coefficient n choose k, whereas Hicks uses $C_{n,k}$.
Homework 3 due Jan 27. It is acceptable to leave binomial coefficients unsimplified.
The quiz Jan 27 will not be based on problems 4,5,9,
and will be similar to the other problems but not exactly the same as in previous weeks.
Week 4: Jan 25, Jan 27, Jan 29
More on binomial coefficients, binomial theorem, Fibonacci numbers: Sections 3.1, 4.1-4.3 of LPV
The Bean Machine
Homework 4 do not turn in. (This material will be covered on the midterm, so completing it may be a good way to study for the midterm.)
Week 5: Feb 01, Feb 03, Feb 05
Probability, poker, dice: Chapter 12 of Hicks.
Midterm: February 03. It will be in-class and 50 minutes long.
Try to arrive a few minutes early to class if possible so we can start exactly on the hour.
The midterm will cover all the material from class and on the homeworks up through February 1. The format will be similar to the last quiz, and about three times as long. I will not ask you to write proofs by induction, however I may test this material in other ways: for example, I will expect you to know what a statement is and what the statement (P(k) => P(k+1)) means. I may also ask a question similar to one of the statements from Homework 2 as a True/False question.
Extra Office Hours: Tuesday Feb 02, 12:30-2pm.
Week 6: Feb 08, Feb 10, Feb 12
Probability continued: poker, dice, birthday paradox: Chapters 12, 15, 16 of Hicks, Section 2.5 of LPV.
Homework 5 due Feb 17.
Week 7: Feb 15, Feb 17, Feb 19
Introduction to graph theory: vertex degrees, trees, paths, cycles: Sections 7.1-7.2, 8.1-8.2, 13.2 of LPV.
We will not follow LPV very closely for this topic.
Supplementary Wikipedia articles: Vertex degrees, Bipartite graphs, Kruskal's algorithm.
Homework 6 due Feb 24.
Week 8: Feb 22, Feb 24, Feb 26
Kruskal's algorithm for minimum-cost spanning tree, Euler's formula, platonic solids: Sections 9.1, 12.1-12.3 of LPV
Homework 7 due Mar 02.
The quiz Feb 24 will have a similar format to the midterm, with 3 true/false and 3 short answer that ask you to construct graphs with certain properties.
Week 9: Feb 29, Mar 02, Mar 04
Number theory: Primes, Euclidean algorithm, modular arithmetic: Chapters 17-18, 22-23 of Hicks, Sections 6.1-6.3 of LPV
Homework 8 due Mar 09.
Week 10: Mar 07, Mar 09, Mar 11
Euler's phi function, Fermat's little theorem, Public key cryptography: Chapters 24-25 of Hicks, Wikipedia article on Diffie-Hellman key exchange
Homework 9 do not turn in. Solutions to Homework 9
Week 11: Mar 14
Final review
Office Hours this week: Monday 10-11:30am, Wednesday 1-2:30pm.
The Final Exam is on Thursday, March 17, in RANDEL 121, from 3:30pm to 5:30pm. It will cover all the material from class and on the homeworks, with more emphasis on the material from weeks 5-10. The format of the final will be similar to the midterm and about 2-3 times as long.