Math 230. Abstract and Discrete Mathematics

Spring 2014


Read Sections 54, 55 and 56. In particular read the portion in section 54 titled "Notation and Language" carefully. It's important to understand that to avoid confusion in the classroom next week.

Homework 9 (the last homework is due on Friday April 25, 2014. 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 8 is due on April 16, 2014. It consists of the problems on this pdf
Solutions to the cardinality homework.

Midterm 3 Solutions.

There will be no class on Monday March 31. Instead of class, I will ask you to read these notes on cardinality:
Cardinality Notes.

Some extra notes regarding the Pigeonhole principle.

Homework 7 is due on April 2, 2014:
25.6, 25.9, 25.16, 25.18,
26.7, 26.9, 26.10.
Also do 26.1 to practice.

The N is a Number Documentary mentioned in class. Check out the 25th minute bit on Ramsey theory.

Homework 6 is due on Wednesday March 26, 2014:
24.1, 24.2, 24.5, 24.6, 24.8, 24.14, 24.16, 24.17, 24.20.

The Fermat's Last Theorem BBC Documentary mentioned in class.

Homework 5 is due on Wednesday March 19, 2014:
22.16, 22.17
20.4, 20.5, 20.9, 20.10, 20.13.
21.3, 21.7, 21.9.

Midterm 2 and its

Induction Practice and its

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 hands 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 Hands worksheet and its

I wrote a brief piece mentioning the extended Newton binomial theorem and how it can be used to approximate the square root of 2. You can find the article here.

Midterm 1 and its

First practice exam and its

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 homework problems (depending on the homework assignment).


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 April 18, 2014.