Math 230. Abstract and Discrete Mathematics

Spring 2015


The third midterm has been changed back to Friday April 10.
Here's a practice exam Midterm 3 from last year and its Solutions.

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.
For those interested in getting a head start on the next homework assignment (due April 15), the assignment is the following:
Homework 8 is due on April 15, 2015. It consists of cardinality problems
Homework 8
Homework 8 Solutions.

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.

Some extra notes regarding the Pigeonhole principle.

Midterm 2 Solutions.

I Prefer Pi by Borwein and Chapman. An article that includes a lot of results on π over the years. It includes a condensed version of the proof I gave in class that π is irrational, among many other beautiful results.

Practice Exam 2 and its
(Note: The solution to problem 4 is listed as 6, the solution to problem 5 is listed as 8 and the solution to problem 6 is listed as 7. The solutions to problem 7 can be found in the poker worksheet. The solution to part e of problem 5 is {3,10,17,24}. The solution to problem 8 is (m+1 choose 2) times (n+ 1 choose 2).

Poker Worksheet and
Poker Worksheet Solutions.

Induction Practice and
Induction Practice Solutions.

Access to the other homework assignments.

If you need a tutor to help, there is drop-in tutor help for this class in YH 107 or YH 118 at the following times (with the following tutors):


Mathematics: A Discrete Introduction by Edward R. Scheinerman.

The textbook is mandatory.

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, set theory and possibly graph theory too. 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.


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. The most recent homework will be posted in the announcements and a copy of all homeworks can be accessed here. 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 10 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 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 dates 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.

Accommodations Statement

If you believe that you need accommodations for a disability, please consult with The Learning and Teaching Center. Since accommodations may require early planning and are not retroactive, please contact the center as soon as possible. For details about the services for students with disabilities and the accomodations process, visit

You are also welcome to contact me privately to discuss your academic needs. However, all disability-related accommodations must be arranged through Teryn Robinson at the Learning and Teaching Center.

Last modified on May 5, 2015.