Math 221: Discrete Mathematics

Professor: Jonah Blasiak

Fall 2023

Monday, Wednesday, Friday 1:00pm - 1:50pm, Pearlstein Business Center 207
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 241 Monday 2pm-3pm, Tuesday 4:30pm-6:00pm.
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 November 01; it will be 50 minutes long.
    Students with special exam-taking requirements or time conflicts should contact me by October 11.
    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. 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 textbooks 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 (https://www.math.drexel.edu/~jblasiak/DiscreteMathematics221Fall2023.html) frequently for new information. Updates to the syllabus and reading assignments, homeworks, 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 27, Sep 29
    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 Oct 04

    Week 2: Oct 02, Oct 04, Oct 06
    Induction: Section 2.1 of LPV, Chapter 7 of Hicks
    Homework 2 due October 11

    Week 3: Oct 11, Oct 13
    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 18.
    It is acceptable to leave binomial coefficients unsimplified.

    Week 4: Oct 16, Oct 18, Oct 20
    Probability, poker, dice: Chapter 12 of Hicks.
    The Bean Machine
    Homework 4 due October 25.

    Week 5: Oct 23, Oct 25, Oct 27
    Probability continued: independence, lottery games: Chapters 12, 15, 16 of Hicks, Section 2.5 of LPV.
    Homework 5 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 6: Oct 30, Nov 01, Nov 03
    Introduction to graph theory: vertex degrees, trees, paths, cycles: Sections 7.1-7.2, 8.1-8.2, 13.2 of LPV.
    Midterm: November 1st.
    The midterm 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 the material from homeworks 1-5 and in class up through but not including graph theory. The format will be similar to the quizzes, and about 3-4 times as long.

    Week 7: Nov 06, Nov 08, Nov 10
    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 15.
    No quiz or homework due on Nov 08.

    Week 8: Nov 13, Nov 15, Nov 17
    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 29.

    Week 9: Nov 20
    Number theory: Primes, Euclidean algorithm, modular arithmetic: Chapters 17-18, 22-23 of Hicks, Sections 6.1-6.3 of LPV.

    Week 10: Nov 27, Nov 29, Dec 01
    Euler's phi function, Fermat's little theorem, Public key cryptography: Chapters 24-25 of Hicks.
    Homework 8 due Dec 06.
    Wikipedia article on Diffie-Hellman key exchange

    Week 11: Dec 04, Dec 06, Dec 08
    Previous week continued, final review
    Homework 9 with solutions Do not turn in. This will be good practice for the final.
    Graph theory practice questions from old quizzes: Old Quiz 5 Old Quiz 6
    Office Hours next week: Monday December 11 from 2-3pm.

    The Final Exam is on Tuesday December 12, in NSBITT 125, from 1pm to 3pm. It will cover all the material from class and on the homeworks, with more emphasis on the material from weeks 6-11. The format of the final will be similar to the midterm and about 2-3 times as long.

    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.