Math 230. Abstract and Discrete Mathematics

Fall 2019


Cardinality Lecture Notes. We covered a few things extra in class and we have not covered everything on these notes yet. We will cover everything in these notes and more. Another good resource to read on cardinality is Chapter 13 in the open textbook The Book of Proof by Richard Hammack. The chapter is here.

An excerpt of the comic book Logicomix relevant to the infinite hotel example I mentioned in class.

Different proof of Cantor-Bernstein. This is another proof of Cantor-Bernstein. A very nice proof. I suggest you spend some time thinking of why the author had to go through so much trouble to get to the proof at the end. I also suggest you fill out the details in the write up. Another famous proof can be found in Wikipedia Schroder-Bernstein-Cantor theorem.

The third midterm is Wednesday Wednesday December 4. To prepare for the midterm, I recommend working on the following:

Some extra notes regarding the Pigeonhole principle.

The second midterm is Wednesday October 30. To prepare for the midterm, I recommend working on the following:

Poker Worksheet and
Poker Worksheet Solutions.

Induction Practice and
Induction Practice Solutions.

The first midterm is Wednesday October 2. To prepare for the midterm, I recommend working on the following:

Access to the homework assignments.


Mathematics: A Discrete Introduction by Edward R. Scheinerman.

The textbook is mandatory.

Course Description

Topics covered include logic and proofs, set theory, relations, cardinal numbers, countable and uncountable sets, permutations and combinations, graph theory, and group theory. Prerequisite: Mathematics 110. (Under the Forester Fundamental Curriculum, this course meets the Quantitative Reasoning requirement. Under the old GEC, this course meets the Natural Science & Mathematics requirement.)

Topics we will cover

The main goal of the class is to learn how to do mathematical proofs. We will learn several proof techniques and on the way we will use these techniques on different subjects of mathematics such as number theory, combinatorics, and set theory. We will also cover several important abstract concepts such as relations, functions and partially ordered sets.

The sections in the book that will be covered are:

1-12, 22, 20, 14-17, 19, 24-26, 54-56.

The reason the numbering is bizarre is that this is the order I like to teach the class.

Student Learning Outcomes

Main Goals: Secondary Goals:


The course grade will be based on:
Quizzes 20%,
Midterms 45% (15% each),
Final Exam 35%.

Homework and Quizzes

There will be written homework roughly every week. A copy of all homeworks can be accessed here. The dates of the quizzes will be updated as the semester progresses. Collaboration in the homework is permitted. The homework won't be turned in, instead there will be quizzes to test you on the homework exercises. There will be approximately 9 quizzes throughout the semester (roughly every week). The quizzes will consist of 2 or 3 problems which will be similar to the questions assigned on the homework assignment that week (but not necessarily identical).


There will be three midterms and one final exam. On the midterms and the final exam you must work on the problems on your own. No collaboration permitted in the exams.

The tentative dates for the midterms are:


Students are expected to come to every lecture and every exam.

If the dates of the exams conflict with Lake Forest approved events, inform me as soon as possible.

Academic Honesty Policy

The student is expected to be honest with their work. I will penalize any student that copies or uses a cell phone to look for answers in an exam or quiz. I encourage students to be familiar with the college's Academic Honesty Policy to see the possible sanctions for academic dishonesty.

Accommodations Statement

If you are a student who needs an accommodation because of a disability or medical or psychological condition that limits your ability to fully participate in this course, please contact Kara Fifield, Director of Disability Services, to document your disability with the College and with the professor of this course. Academic accommodations should be reasonable and not alter the fundamental nature of this course. Because it can take a week or more to arrange requested accommodations, you are encouraged to establish your semester accommodations as early in the semester as possible. Contact Kara Fifield by email or phone: or 847-735-5167. For more information about services for students with disabilities at Lake Forest College, see:

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Kara Fifield.

Last modified on November 12, 2019.