Web site for MATH 3220: Discrete Structures II (Spring 2021)


This course is an introduction to discrete mathematics and discrete structures. The topics that it may examine include graph theory, trees, algebraic systems, Boolean algebra, groups, monoids, automata, machines, rings and fields, applications to coding theory, logic design, and sorting. Students who finish the course successfully will be able to apply discrete numerical methods to solve problems that arise elsewhere in mathematics and in computer science. There will be two 75-minute meetings each week.

I want all of you to succeed in this class; below you will find some tips for how you can help make this happen.


The course syllabus (it covers some of the same things as this web-page, but it covers other things too; you need to read both).

The list of topics covered in the course in Spring 2021 (same as Fall 2020).

The textbook for the course (Applied Discrete Structures 3rd edition, version 7, by Alan Doerr and Kenneth Levasseur).

Extra readings assigned throughout the semester include: review.pdf, mod.pdf, cong.pdf, gcd.pdf, isomorphism.pdf, order.pdf, vectors.pdf. eigen.pdf, boolean.pdf, and crt.pdf. You might also find pseudocode.pdf useful.

Lecture-by-lecture reading-and-thinking assignments (subject to continual update).

The Piazza page for the current semester of MATH 3220.

Lecture notes.

Lecture capture. Log in and select "MATH.3220-204 Discrete Structures II". Or click on this link.

Homework problems and solutions.

The UML tutoring page.

The Essence of Linear Algebra video series is a good intro to linear algebra (which is part of the syllabus of the course).

For the nuts and bolts of Gauss-Jordan elimination, try this Khan Academy video.

Francis Su's guidelines for good mathematical writing.

Dave Richeson's essays The Nuts and Bolts of Writing Mathematics and Editing a Very Poorly Written Proof.

My views about being wrong. See especially the section under the heading "MISTAKES INSIDE AND OUTSIDE THE CLASSROOM".


Professor James Propp

Piazza: https://piazza.com/uml/spring2021/math3220sec204

Email: JamesPropp at gmail dot com

Office: "ZoomSpace"

Drop-in Hours: Tuesdays and Thursdays, 11:30am to 12:15pm and 3:15pm to 4:00pm. Links for joining class meetings and drop-in hours are available at the Blackboard portal for the course. Meetings at times other than my drop-in hours can be arranged by appointment; see me after class, call me on the phone, or send me an email message.

Suggestions about how the course is being run are welcome at any time. If something isn't working for you, please don't wait until the end of the semester to tell me!


Meeting times: Tuesdays and Thursdays, 2:00 to 3:15 pm.

Meeting place: "Zoomspace"

Expectations: You're expected to attend classes, do the reading in advance, ask questions, and make serious attempts to answer questions raised by me or by other students during class. If you miss a class, it's your responsibility to make sure you obtain all information (course material, assignments, changes in exam dates, etc.) presented that day.

Exam dates: There will be three two-hour exams covering Chapters 9&10, Chapter 11, and Chapters 13&15, respectively. The first exam, covering chapters 9 and 10, will be Thursday, March 4 from 6:30 to 8:30 pm. The second exam, covering chapter 11, will be Thursday, April 1 from 6:30 to 8:30 pm. The third exam, covering chapters 13 and 15, will be held during exam period, on a date and at a time to be determined.


It's important that everyone take the same exams under the same conditions for maximum fairness and reliability of testing. I therefore don't give makeup exams unless you have a valid reason for missing the scheduled exam (for example, illness or a religious holiday), and I don't allow extra time on exams unless you have a note from Disability Services (see below). If you have to miss a scheduled exam, please let me know ahead of time if at all possible; I'm much more likely to be sympathetic if you call me the morning of the exam and say “I have the flu and can’t take the exam” than if you come in two days after the exam and say “I missed the exam. When can I take a makeup?”

You may not use a cell phone in any way during an exam.

Use of calculators is prohibited during exams.

You can always reschedule an exam that falls on a day that is a religious holiday for you, but you must make these arrangements ahead of time.


Tips on Preparing for Exams

  • Start studying for an exam at least one week ahead of time.
  • Begin by reviewing the homework problems for the sections that will be covered on the exam. Make sure you know how to solve each problem. If you can't solve a particular problem, make a note of the problem number and move on to the next problem; you can go back to the problem later with a fresh head (yours or someone else’s!).
  • Ask me or someone else for help on any homework problem that gave you trouble, then try to solve a similar problem from the textbook.
  • Get a good night’s sleep the night before the exam. You'll perform better if you are fresh and able to think clearly.

  • Tips on Taking Exams


  • Read every question on the exam before you start working. This will give you a feel for how long the exam is and how you should pace yourself. It'll also give your subconscious mind a chance to start working on the questions.
  • If you're not sure what a question means, please ask me. I'm trying to see how well you know the material, not to trick you with ambiguous wording.
  • Show as much of your work as possible, in as clear a way as possible. Even if you get the wrong answer, I'll try to award you as much partial credit as I feel I can conscientiously give you, but it's hard for me to do this if you don't show your thought-processes.
  • Look at the point value of each question. Obviously, it's more important to do well on the questions that count the most than the ones that count the least.
  • It's generally best to do the easiest problem first, then the next easiest, and so on. You don't have to do the problems in the order they appear on the exam.
  • If you get stuck on one question, move on to the next. Come back later to the question that is giving you trouble.
  • Be aware of how much time you have left. Don't spend too much time on a single question. It's generally better to get partial credit on every question than full credit on a small number of questions.
  • If you have extra time, use it to check your work! Better still, if there's more than one natural approach to the problem, try to solve the problem with a different method; this can be a better way to catch mistakes than just re-reading your calculations. If you get the wrong answer with one approach but the right answer with the other approach, I'll give you nearly full credit (especially if you speculate intelligently on where you might have made an error).
  • If you get an answer that doesn't make sense but don't have time to trace where your error came from, don't just cross out your answer; explain why you think the answer you got looks wrong, and you may get some extra points for having good instincts.
  • Never be afraid to ask for extra paper. (If you want to write on the reverse side of a page, please write “see other side”.)


    It is forbidden to post homework questions online (not counting Piazza). Posting assigned questions to a website that permits plagiarism counts as a violation of academic integrity and could result in failing the course or expulsion from the university.

    Typically there'll be one homework assignment per week, due one week after it is assigned.

    In order for you to understand the material in this course, it's extremely important that you do the assigned homework problems. Working with your classmates can be a great help, and I strongly encourage it, subject to certain provisos (see below). I also urge you to ask questions about any problems that give you trouble.

    Homework will usually be due each week on Saturday. Your grade will be based on clarity as well as correctness, so neatness, grammar, and punctuation should not be neglected. Harder problems will in general be worth more points. However, it will not be possible to grade all problems. You are encouraged to give me feedback about the homework; for instance, if one of the problems was a huge time-sink, I want to know about it!

    Late homeworks will not be accepted.

    Each student will be allowed to skip one assignment without penalty, because the lowest homework score does not count toward the final grade. Don't use up your “free skip” too early in the semester!

    While you can discuss the exercises with classmates, the work you hand in should be your own write-up and not copied from someone else. When leaving a joint homework-solving session, don't carry away anything that doesn't fit in your own brain. Also, you must acknowledge who you worked with, even if the flow of help was one-sided (you helping another student). (If you didn't work with anyone, you must write “I worked alone on this assignment”.)

    Points may be deducted from students who repeatedly fail to state whom they worked with.

    Academic honesty in homeworks is expected. (E.g., if you use web-resources or tutors or collaborators of any kind, the role of their contribution must be acknowledged; you won't receive a lower grade for using such resources, but if the grader and I feel you're relying on them too heavily, we may require you to change your way of doing homework.) My expectations for appropriate ways of doing the homework will be discussed in class; in case you are in any doubt about what is expected, it is your responsibility to contact me for clarification.

    It is not required that you submit your solutions in LaTeX, but if you are planning to be a mathematician, scientist, or engineer, it's never too early to learn! LaTeX is free software that lets you typeset formulas about as fast as you can write them (with some practice). Composing your homework in LaTeX will help you pay attention to your communication of mathematics, and make it much easier to edit your work as you go along. There will be an initial hump of getting started, but after a couple of problem sets, using LaTeX will become quite natural. You'll probably still want to draw your diagrams and figures free-hand, but knowing how to write equations in LaTeX is a life-skill that will serve you well in later courses in which homeworks involve fewer pictures and more formulas.

    Also, you may want to use Mathematica as an aid to your learning. UML students will be able to download Mathematica as part of the campus license. You shouldn't use Mathematica as a substitute for being able to do the work yourself the old-fashioned way, but it's a great way to check your work. Also, Mathematica features many demonstrations (see http://demonstrations.wolfram.com/) that can bring course material to life in a vivid way.


    Regular attendance is expected. It is not part of the grading scheme, but class participation is. Class participation (measured by your section summaries as well as how much you contribute in class and on Piazza) only counts for 10 percent of your final grade, but when your other grades put you on the borderline between two grades, it can make a crucial difference.


    If you have any special needs, e.g., you need more time on exams because of a disability, I'll do my best to accomodate you. Please notify me at least two weeks in advance.