Note: this is an archived version of the course page. The formatting has been simplified and student comments have been erased.
In this course we will learn the basics in a few different areas of mathematics: number theory, discrete math, set theory, and if time permits, group theory. Meanwhile, we will explore the concept at the heart of modern mathematics: proof. The syllabus and homework appear below.
Important note: you are invited and encouraged to share your thoughts, questions, and comments with the class by writing comments on this web site. You can openly discuss homework problems as well as any other course-related matter. But be please be aware that your comments will be public on the web. I will remove inapproprate comments, and I am happy to remove any of your comments on request.
Course title: Discrete and foundational mathematics
Meeting times: M,W,F 9–10:15am
Meeting place: MG-120
Instructor office: MG 237-A
Office hours: M 4:30 and Th 10:30 (subject to change), and by appointment
Textbook: “Proof”, by Esty and Esty
Written work: Book problems and other worksheets will be collected regularly. In total, this will be worth about 25% of your grade. I’ll drop your lowest homework.
Exams: There will be four midterms and a final. Each midterm will be worth about 15% and the lowest will be dropped. The final will be worth about 25%.
Participation: You will have chances to participate in class discussions as well as online discussions. This will be worth about 5% of your grade. Don’t stress out too much about this—if you show up to class and bring your brain, you should get full credit here.
Midterm ch. 1: September 21
Midterm ch. 2: October 10
Midterm ch. 3: November 2
Midterm ch. 4: November 16
Final exam: December 17 from 12–2pm
Comment on this post! Due Wednesday, August 29.
Your first assignment is to write a short comment below which will tell us a little about yourself. Sign in using your real name and your BSU email address (it will not be published). Be sure to include at least the following information, and anything else you care to tell us.
It may take a few hours for your post to appear since I will have to approve it. But from then on, you should be in the system for good.
Here’s what you need to do to get ready for Friday’s lecture.
Read § 1.2 and be ready to ask any questions you have about the section. You are also free to write questions or remarks in the comments below. Then take a look at problems A1–A32 and be ready to discuss them in class.
Note: you don’t actually have to do all of these problems. After a while they all start to get really easy. Do enough so that you are comfortable with the concepts.
On sections 6.1 and 1.2, due Wednesday, September 5.
§ 6.1: A1, B5
§ 1.2: B5, B6, B9, B10, B22, B23, B24, B33, B34, C4
Read the first two pages of § 1.3, and be ready to discuss problems A1–A12 in class. That’s it!
Read the rest of § 1.3, and be ready to discuss problems A13–A35 or so. If anything seems weird about these problems, please ask a question in the comments below! (Remember, participation counts, and web participation is one way to do it.)
Assignment on sections 1.3, 1.4 due Wednesday, September 12.
§ 1.3. B1, B2, B10, B15, B19, B22, B23, B28
§ 1.4. B2, B3, B14, B15, B16, B20, B25
Start reading § 1.4 and be prepared to answer the first few ‘A’ problems!
On § 1.5 and § 1.6, due Wednesday, September 19.
§ 1.5. B3, B4, B11, B13, B27
§ 1.6. B2, B3, B4, B5, B6, B7, B33, B35, B41, B42, B43, B48, B49, B50
Read § 1.5 and be ready to talk about the “A” exercises!
Homework 5 on sections 2.1–2.2 and part of section 2.3. Due Wednesday, October 3.
§2.1. B3, B9, B10, B13, B14, B19
§2.2. B3, B4, B23, B24, B25, B26, B27, B28, B37, B41, B42, B84, C9, C10, C11
§2.3. B3, B6, B7, B21, B23, B25, B63, C1, C5
Take a look at the ‘A’ problems from §2.1 and §2.2.
On sections 2.3, 2.4, and 2.5. Due Wednesday, October 10.
§2.3. B15, B17, B34, B35, B44, B45, B46, B47
§2.4. B13, B29, B30, B31, B32
§2.5. B6, B15, B16, B17, B18, B25, B26
On sections 3.1 through 3.3 This will be due Monday, October 22.
§ 3.1. B18, B19, B20, B21, B22, B23, B40
§ 3.2. B11, B12, B13, B14, B16, B36, B37
§ 3.3. B10, B23, B24, B84
On Sections 3.4 and 3.5. Due on Monday, October 29.
§ 3.4. B4, B5, B6, B8, B9, B11, B22
§ 3.5. B1, B2, B4, B5, B6, B12, B13, B14, B15, B16, B18, B19, B34
On Chapter 6. Due Monday, November 12.
§ 6.1. B20–B26, B30, C1
§ 6.2. A9, A10, A13, A15, A17, B8, B13, B14
§ 6.3. A1, A2, A6, B3, B4, B14
Oh, and start reading Section 6.2. Try to get up through the definition of “Greatest Common Divisor”, which is the main theme of the chapter. Also check out the compainion Theorem 6.
Due Monday, December 10.
Read Chen’s article, and write careful and complete solutions to the 14 problems at the end. You will be graded on proof-writing as well as correctness. You are welcome to share your insights with your classmates, but as always, turn in your own writing.
Because of its length, this will be counted as two homeworks.
PS: here is a link to his discrete math notes.
Please use these exercises on planar graphs to help with your studies for the final exam: ws7.pdf