Math 217M: Introduction to Mathematical Proof (Fall 2024)

• See here for the syllabus.

Announcements

• No class Wednesday 10/16.

• (9/23) Here is the definition sheet for this week and next.

• (9/20) Here is the worksheet from today.

• (9/16) Here are the notes for this week.

• (9/6) Here is the worksheet from today.

Take-home final

Here is the take-home final. It is due by Monday, October 21st. Please either email me a scan of your final or drop it off at my office.

Problem sets

• Week 6 (Due Monday 10/14) Exercises 11.20, 11.21, 11.22 (p. 131) and 3.1, 3.2, 3.4. High Pass: All chapter 11 exercises and at least two chapter 3 exercises. Pass: At least four exercises in total, with at least two from chapter 11.

• Week 5 (Due Monday 10/7) Exercises 11.1, 11.2, 11.4, and 11.5 from the textbook (p. 130). Read Chapter 3 (“Number Theory”) of the textbook, and pick one of the lemmas in section 3.3 to write up your own proof of. You should read the book’s proof, but the proof you write should be in your own words and reflect your own understading. High Pass: All chapter 11 exercises and the chapter 3 proof. Pass: All chapter 11 exercises.

• Week 4 (Due Monday 9/23). See page 11 of here. High Pass: All five problems. Pass: At least two parts of problem 1 and at least three of the remaining problems.

• Week 3 (Due Monday 9/16). See here. High Pass: Problems 1 through 3, and four of Problems 4 through 7. Pass: At least four problems in total, with at least one of Problems 1 and 2 and at least two of Problems 4 through 7. High Pass: Problems 1 through 3, and two of the remainder. Pass: Three total, with at least one from 1 or 2.

• Week 2 (Due Monday 9/9). Exercises 4.1, 4.3, 4.4, 4.7, 4.10, 4.14, 4.18 from the textbook (p. 38). High Pass: At least 6 exercises. Pass: At least 4 exercises.

• Week 1 (Due Monday 9/2). Exercises 1.1, 1.3, 1.4, 1.5, 1.9, 1.10, and 2.1 from the textbook (p. 8 and p. 14). High Pass: At least 6 exercises. Pass: At least 4 exercises.

Reading assignments

• By Wednesday 8/28: read A Note to the Student from the textbook and the mathematical habits at the end of chapter 1.

• By Friday 8/30: look at the table of contents and the topics for chapters 3, 5, 7, 9, 10, 12, 13, 14, and 15 so we can decide as a class which of them we will look at this semester.

Resources for writing mathematics

Writing

• From Francis Su at Harvey Mudd College.

• From Kevin Lee at UC Davis.

• From Kevin Houston at University of Leeds.

• A blog post by Terence Tao at UCLA.

• A book by Donald Knuth, Tracy Larrabee, and Paul Roberts.

Using LaTeX

• A set of LaTeX tutorials.

• A handly tool for figuring out the command for a math symbol.

Schedule and topics

This is a seven week half-semester course. The schedule is organized on a weekly basis. Mondays and Wednesdays will be used for lecture and Fridays will be used for group activities and presentations.

The schedule below is tentative; we might have small adjustments in the dates.

• Week 1: What is a proof and why do we care? [Chapters 1 and 2]

• Week 2: Induction, part 1 [Chapter 4]

• Week 3: Induction, part 2 [Chapter 4]

• Week 4: Logic

• Week 5: Functions and relations [Chapter 11]

• Week 6: Functions and relations [Chapter 11]

• Week 7: Wrapup and final

  (No class Wednesday 10/16.)

Chapters 1, 2, 4, and 11 comprise the core topics for the class. The other chapters are each about a different area of mathematics. As a class we will choose three chapters from 3, 5, 7, 9, 10, 12, 13, 14, and 15 to look at.