Monday, Wednesday, Friday 1:00pm - 1:50pm, University Crossings 151

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.)

Students with special exam-taking requirements or time conflicts should contact me by October 4.

Week 1: Sep 23, Sep 25, Sep 27

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 October 2

Week 2: Sep 30, Oct 02, Oct 04

Induction: Section 2.1 of LPV, Chapter 7 of Hicks

Homework 2 due October 9

Week 3: Oct 07, Oct 09, Oct 11

Pascal's triangle, counting, bijective proofs, binomial theorem : Sections 1.7-1.8, 3.5-3.6, 3.1 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 October 16. It is acceptable to leave binomial coefficients unsimplified.

Week 4: Oct 16, Oct 18

Probability, poker, dice: Chapter 12 of Hicks.

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: Oct 21, Oct 23, Oct 25

Probability continued: poker, dice, birthday paradox: Chapters 12, 15, 16 of Hicks, Section 2.5 of LPV.

Midterm: October 23. It will be in-class and 50 minutes long.

Try to arrive a couple minutes early to class if possible so we can start exactly on the hour.

The midterm will cover all the material from class up through Oct 21 and homeworks 1-4. The format will be similar to the last quiz, and about three times as long.

Week 6: Oct 28, Oct 30, Nov 01

Introduction to graph theory: vertex degrees, trees, paths, cycles: Sections 7.1-7.2, 8.1-8.2, 13.2 of LPV.

Homework 5 due November 06.

Week 7: Nov 04, Nov 06, Nov 08

Trees, Kruskal's algorithm: Sections 8.1-8.2, 9.1 of LPV.

We will not follow LPV very closely for this topic.
Supplementary Wikipedia articles: Vertex degrees, Bipartite graphs, Kruskal's algorithm.

The quiz November 06 will cover probability.

Homework 6 due November 13.

Week 8: Nov 11, Nov 13, Nov 15

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 Nov 20.

Week 9: Nov 18, Nov 20, Nov 22

Number theory: Primes, Euclidean algorithm, modular arithmetic: Chapters 17-18, 22-23 of Hicks, Sections 6.1-6.3 of LPV

Homework 8 due Dec 04.

Week 10: Nov 25

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 with solutions Do not turn in. This will be good practice for the final.

Week 11: Dec 02, Dec 04, Dec 06

Previous week continued, final review

I will be gone December 2-4 and Elaine will cover class. Monday will be a final review, mainly several practive problems to work on and go over in class. Wednesday will cover Diffie-Hellman key exchange.
There will be a quiz in class on December 4.
I will not have office hours on Dec 4th, but office hours will be 11:30-12:30 as usual on Dec 6th.

Graph theory practice questions from old quizzes:
Old Quiz 5
Old Quiz 6

The Final Exam is on Monday, December 9, in Lebow 241, from 10:30am to 12:30pm. It will cover all the material from class and on the homeworks, with more emphasis on the material from weeks 5-11. The format of the final will be similar to the midterm and about 2-3 times as long.

Students requesting accommodations due to a disability at Drexel University need to request a current Accommodations Verification Letter (AVL) in the ClockWork database before accommodations can be made. These requests are received by Disability Resources (DR), who then issues the AVL to the appropriate contacts. For additional information, visit the DR website at drexel.edu/oed/disabilityResources/overview/, or contact DR for more information by phone at 215.895.1401, or by email at disability@drexel.edu.