Section 001: Monday, Wednesday, Friday 9am - 9:50am, Drexel Plaza GL15

Section 004: Monday, Wednesday, Friday 1pm - 1:50pm, Peck Prblm Solving & Rsrch Cnt (PSRC) 214

Discrete Mathematics: Elementary and Beyond, by L. Lovász, J. Pelikán, and K. Vesztergombi (Drexel Library online copy)

Pirate This Discrete Math Book, by R. Andrew Hicks (Andrew Hicks is a professor at Drexel who wrote this book specifically for this class.)

A: 30%

B: 40%

C: 20%

D-F: 10%

This is not an absolute rule. If I think everyone is doing well, then higher grades than above will be given.

Students with special exam-taking requirements or time conflicts should contact me by January 20.

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.