Math 221: Discrete Mathematics

Winter 2016

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

Course Description: This course covers a range of topics in Discrete Mathematics including set theory, induction, counting, number theory, graphs, and cryptography. The goal is to teach students basic methods of mathematical thinking, mainly logical, combinatorial, and algorithmic, which will be of great importance in their future work in pure Mathematics or (especially) in its applications to Computer Science, Engineering, and other areas.
Prerequisites: Math 220 or CS 270 or ECE 200.
Office Hours: Korman 275, Monday 10am-11:30am, Wednesday 11:00am-12:30pm.
Textbooks: We will use a combination of the following texts:
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.)
• 10% Homework
• 20% Weekly quizzes
• 30% Midterm
• 40% Final
• Grade Distribution: Grades will curved so that approximately the top 30% of the class receive A's, the next 40% B's, etc. as indicated below:
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.
Exam Policy: No books or electronic devices are allowed on the midterm or exam. No collaboration is permitted at the midterm or exam. THERE WILL BE NO MAKE-UPS FOR EXAMS.
The midterm will be in-class on February 03; it will be 50 minutes long.
Students with special exam-taking requirements or time conflicts should contact me by January 20.
Quiz Policy: Quizzes will be given in class most Wednesdays, and will be similar to some of the homework questions due that day. They will be about 15 minutes long. There will be about 8 quizzes total and the lowest quiz grade will be dropped to compute the quiz grade. Same rules as the exams apply. THERE WILL BE NO MAKE-UPS FOR QUIZZES.
Homework Policy: You may consult each other and the textbook above. List all people and sources who aided you and whom you aided, and write up the solutions independently, in your own language. It is easy nowadays to find solutions to almost anything online. DO NOT consult such solutions until after turning your homework. Solutions to homeworks will be posted on this website and/or discussed in class. Late homeworks will not be accepted.
Homework Help: Math Resource Center (Korman 247)
Important University Policies:

Disability Resources

Course Drop Policy

Code of Conduct

Please visit this site frequently for new information. Updates to the syllabus and reading assignments, homeworks, homework solutions, and practice exams will be posted here as the course progresses.

Syllabus

Since we are using multiple textbooks, there will be some overlap with the reading assignments. The most important/relevant sources will be listed first.

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.

Outcomes: Students must understand basic mathematical language including sets and functions, apply mathematical induction, count or enumerate objects using various combinatorial formulas, operate with discrete structures including graphs and permutations, and describe simple algorithms.