Math 230. Abstract and Discrete Mathematics

Fall 2013


Practice Exam for the final exam.
Solutions to the final practice exam.
Recall that the final exam is on Wednesday December 18 from 1:30pm to 4:30pm.

Poset Worksheet Solutions.

Midterm 3 and its Solutions.

Homework 9 Solutions.

No class on Friday November 22 and on Wednesday November 27.

Practice Exam for the third midterm and its Solutions.

Solutions to the poker hands worksheet.

Cardinality Lectures.

Homework 9 is due on Wednesday November 20, 2013:
Read sections 24, 25, 26 and 17. Do the following exercises:
24.17, 24.20,
25.6, 25.9, 25.16, 25.18,
17.4, 17.18, 17.32.
I highly recommend working on the following problems for practice: 24.23, 24.24, 26.1, 26.13, 17.1, 17.3, 17.5, 17.33.
I also highly recommend trying the exercises in the cardinality lectures.

Solutions to Homework 8.

Midterm 2 and its Solutions.

Homework 8 is due on Wednesday November 6, 2013:
Read section 24 and do the following exercises:
24. 1, 24.2, 24.5, 24.6, 24.8, 24.14, 24.16.

Practice Exam 2 Solutions

Class canceled (no exam) on Friday October 25. The exam will now be on Monday October 28.

The second practice exam is here. The solutions will be posted on Friday at 1pm.

Click the links for solutions to Homework5 and Homework 6.

Homework 7 is due on Wednesday October 23, 2013:
Read Sections 14, 15 and 16.
14.1, 14.3 (no need to prove here), 14.5, 14.6, 14.10 (proofs required in 14.6 and 14.10).
15.1, 15.3 (no proof required here), 15.7, 15.8.
16.1, 16.10, 16.15.
Also read (but don't turn in) exercises 14.17 and 15.15.

The induction practice worksheet is here.
The solutions are here.

Homework 6 is due on Wednesday October 16, 2013:
22.16, 22.17
20.4, 20.5, 20.9, 20.10, 20.13.
21.3, 21.7, 21.9.
In the problems from section 21 you are allowed to prove it in a different way (for example, induction) if you prefer.

Read Section 22 carefully.

Homework 5 is due on Wednesday October 9, 2013:
22.4,22.5, 22.6, 22.7, 22.9, 22.14.

Midterm 1,
and its Solutions. (Note, the solutions are for the first draft for the exam. Problem 8b in the pdf is problem 7b in the actual exam, problems 9 and 10 in the pdf are problems 8 and 9 in the actual exam, also I should note the solution that appears in 8b which is for 7b of the exam should be 0 instead of 100!/(101).)

Twin Prime Hero. This is a link to the article "Twin-Prime Hero", an interview with Yitang Zhang, the mathematician who made a big breakthrough in number theory this year. The interview is short and interesting, I highly recommend reading it. For more links on the result of Zhang, check out the Media section in the following wiki:

Practice Exam for the first midterm.
Solutions to the practice exam.
Cheat Sheet that will be provided in the first midterm (might be edited a bit by the time it will be provided).

I have posted solutions to homeworks 2, 3 and 4:
Solutions HW 2,
Solutions HW 3,
Solutions HW 4.

Read Section 12 carefully.

Homework 4 is due on Wednesday September 25, 2013:
11.1, 11.2, 11.4, 11.7.
12.1, 12.5, 12.9, 12.12, 12.21, 12.24, 12.30 (a and c).

Read Sections 8, 9, 10, 11 and 12.

Homework 3 is due on Wednesday September 18, 2013:
From chapter two, turn in solutions of
8.2, 8.4, 8.8, 8.10, 8.15,
9.2, 9.5, 9.7, 9.9, 9.11,
10.1, 10.4, 10.9, 10.14.

There will be drop-in tutor help for this class in YH 107 or YH 118 at the following times (with the following tutors): This link opens the Mathematica program I wrote in class to find that 496 is the next perfect number after 28. The file can be open in 2 ways, either you download Mathematica and open it there or you download Wolfram's cdf player (use this link). With Wolfram's cdf player you can see the file online but you can't edit it or play around with the numbers.

Read Sections 5, 6 and 7 for Friday's class.

Homework 2 is due on Wednesday September 11, 2013:
From chapter one, turn in solutions of
5.1, 5.7, 5.11, 5.18, 5.23
6.1, 6.3, 6.6, 6.9 and 6.13.
7.1, 7.6, 7.10, 7.11(a, c, e), 7.13, 7.17.

I uploaded the first chapter to the textbook here for those that tried to get the book from the library (the library should have a copy of the book soon).

Mathematics: A Discrete Introduction by Edward R. Scheinerman.

The textbook is mandatory.

Topics we will cover

The main goal of the class is to teach how to do mathematical proofs, for this, one needs to know what a proof is. We will learn the importance of definitions, how to do proofs, many 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.


The course grade will be based on:
Homework 25%,
Midterms 45% (15% each),
Final Exam 30%.


There will be written homework due 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, but you are not allowed to copy someone else's work. The solutions must be written individually. You have to mention on your problem set the names of the students that you worked with.


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.
Classes will be canceled on September 20, November 22 and November 27. I will remind you of this in the Announcement section.

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 December 9, 2013.