Math 230. Abstract and Discrete Mathematics

Fall 2015


Homework 9. The last homework will not be tested on a quiz. It will however appear in the final. It consists of the the following exercises:
54.1, 54.2, 54.3, 54.4, 54.8.
55.1, 55.2, 55.5, 55.7.
56.1, 56.5.
Suggested extra work:
After 54.4, think about the width of the poset defined in 54.3 for any n (Hint: Consider n even and n odd separately).
54.9 is a very good exercise to get more practice with posets.
56.7 is "alphabetical" ordering in disguise (this ordering has the more technical name of "lexicographic ordering").
Homework 9 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.

Homework 8 is due on Friday Dec. 4, 2015. It consists of cardinality problems
Homework 8
and problems 25.16 and 25.17.
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.

Practice Exam 3. These are a few problems you can work on to prepare for the third midterm. Most of the problems are from the textbook and the solutions are in the back of the book.

Some extra notes regarding the Pigeonhole principle. This chapter is from the book Problem Solving Strategies by Arthur Engel.

The N is a Number documentary is a biography of Paul Erdős. I highly recommend watching the snippet of the video starting in the 25th minute. It gives a nice proof of the party problem mentioned in class.

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
Practice Exam 2 Solutions.
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).

Induction Practice and
Induction Practice Solutions.

Poker Worksheet and
Poker Worksheet Solutions.

First midterm moved to be on Monday September 21.
We will do review on Friday. I suggest trying the following practice exam prior to Friday's class.
Practice Exam 1 Solutions.

Self-Explaining Booklet, is a short file with tips that can help you read proofs better.

Chapter 1. Read sections 1 through 5 in the chapter during the weekend.

The other homework assignments can be found below:
Homework Assignments


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


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.

Past Courses

I've taught this course several times. For those of you wishing to move at a faster pace, you can do so by looking at the homework assignments and midterms from previous courses. The homework assignments are essentially the same as in past years as I provide the solutions to each assignment before it is due (the idea is that you can read the solution and check your work as you prepare for the quizzes). The midterms are different each time, but share a structure, so you can test yourself with past midterms.
Here are the links to previous iterations of this course:
Fall 2013
Spring 2014
Spring 2015.

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 December 4, 2015.