Math 230. Abstract and Discrete Mathematics

Fall 2024

Instructor: Enrique Treviño
Lectures: MWF 2:30pm to 3:50pm in BR 253
Office Hours: MTWF 11:00-11:30am and R 9am-11:30am, and by appointment.
Office: Brown Hall 123
Email:
Phone Ext.: #6187

Announcements

The third midterm is Wednesday November 20. The main topics for the midterm are proof by contradiction, functions, composition of functions, and pigeonhole principle. The section on cardinality would show up in the true-false section of the midterm. To prepare for the midterm, I recommend working on the following:

Practice Exam 3.
The solutions to the questions from the book are in the back of the back. For the other problems, you can ask in the review session.
Midterm 3 Fall 2013 and its
Solutions.
Midterm 3 Spring 2014 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.

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.

Documentary of Paul Erdos called "N is a number". Check out minute 25 to get another explanation of the party problem.

Some extra notes regarding the Pigeonhole principle.

The second midterm is Wednesday October 23. To prepare for the midterm, I recommend working on the following:

Practice Exam 2 and its
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).
Midterm 2 Fall 2013 and its
Solutions.
Midterm 2 Spring 2014 and its
Solutions.

Induction Practice
Induction Practice Solutions.

Poker Worksheet
Poker Worksheet Solutions.

The first midterm is Monday September 16. To prepare for the midterm, I recommend working on the following:

Practice Exam 1 and its
Solutions.
Midterm 1 Fall 2013 and its
Solutions.
Midterm 1 Spring 2014 and its
Solutions.

Announcements for the class will be posted here.

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

Access to the homework assignments.

Textbook

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.

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 (possibly in a different order) are:

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

Student Learning Outcomes

Main Goals:

Understand what a mathematical proof is.
Learn how to write your own proofs.
Understand sets and set notation.
Learn to use mathematical induction.

Secondary Goals:

Learn to prove by contradiction.
Learn what an equivalence relation is.
Learn binomial coefficients.
Learn what a mathematical definition is.
Learn what functions are. Furthermore, learn how to prove a function is (or isn't) onto, is or isn't one-to-one.
Learn what posets are.
Learn about cardinality.
Learn boolean algebra and truth tables.

Grading

The course grade will be based on:
Homework 10%,
Midterms 60% (20% each),
Final Exam 30%.

Homework

There will be written homework roughly every week. A copy of all homework assignments can be accessed here. Collaboration in the homework is permitted. The homework will be graded based on whether it is submitted or not, it will not be graded. Solutions to the homework are available here.

Exams

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:

The first midterm will be on Monday September 16.
The second midterm will be on Wednesday October 23.
The third midterm will be on Wednesday November 20.
The final exam will be on Wednesday December 11 from 1:30pm to 4:30pm.

Attendance

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.

Description of instructional time and expectations:

This course meets 3 times per week for 4 to 4.5 hours per week. The course carries 1.0 course credit (equivalent to four semester credit hours). Students are expected to devote a minimum of 12 hours of total work per week (in-class time plus out-of-class work) to this course.

Academic Honesty

Please read the College's information on Academic Honesty. If a student cheats in an exam, quiz or homework assignment, I will proceed with charging the student with the Academic Honesty Judicial Board. The usual (first) penalty is a 0 in the assignment on which the cheating occured plus some ethics lectures the student would take. The second penalty is usually suspension.

Academic Resources, Protocols, and Policies

Click here: Academic Resources, Protocols, and Policies

Last modified on November 14, 2024.