Math 221: Discrete Mathematics

Professor: Jonah Blasiak

Fall 2021

Tuesday, Thursday 2:00pm - 3:20pm, Academic Building 219
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, Tuesday 3:30pm-5pm, Friday 12pm-1pm.
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.)
Grade Breakdown:
  • 10% Homework
  • 20% Weekly quizzes
  • 30% Midterm
  • 40% Final
    • Grading Policy:
  • A: 80-100%
  • B: 60-80%
  • C: 40-60%
  • D-F: 0-40%
    • Exam Policy: No books or electronic devices are allowed on the midterm or exam. No collaboration is permitted on the midterm or exam. THERE WILL BE NO MAKE-UPS FOR EXAMS. The midterm will be in-class on October 21; it will be 80 minutes long.
    Students with special exam-taking requirements or time conflicts should contact me by October 1.
    Quiz Policy: Quizzes will be given in class most Thursdays, 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. No books or electronic devices are allowed on quizzes. No collaboration is permitted on quizzes. 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.
    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: Sep 21, Sep 23
    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 September 30

    Week 2: Sep 28, Sep 30
    Induction: Section 2.1 of LPV, Chapter 7 of Hicks
    Homework 2 due October 7

    Week 3: Oct 05, Oct 07
    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
    Homework 3 due October 14.

    Week 4: Oct 12, Oct 14
    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 19, Oct 21
    Probability continued: independence, lottery games: Chapters 12, 15, 16 of Hicks, Section 2.5 of LPV.
    Midterm: October 21 in class.

    Week 6: Oct 26, Oct 28
    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 04.

    Week 7: Nov 02, Nov 04
    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.
    Homework 6 due November 11.

    Week 8: Nov 09, Nov 11
    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 18.

    Week 9: Nov 16, Nov 18
    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 02.

    Week 10: Nov 23
    Euler's phi function, Fermat's little theorem, Public key cryptography: Chapters 24-25 of Hicks, Wikipedia article on Diffie-Hellman key exchange

    Week 11: Nov 30, Dec 02
    Previous week continued, final review

    Homework Help: Math Resource Center (Korman 247)
    Important University Policies:

    Academic Dishonesty

    Course Drop Policy

    Code of Conduct

    Disability Resources:
    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.
    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.