Math 300 (73) Foundations of Higher Mathematics

Overview

This course is an introduction to mathematical reasoning and proof. It is designed to make students think about mathematics in different ways than before. We discuss basic principles of logic and various proof techniques, and give applications of these tools.

• Syllabus

• Tips on homework and presentations

Reading assignments

Each week, you will be assigned several sections of reading from the book. These should be read before class, and you should have read at least the first section of the assignment before Monday's class. (For the first week, this should be done by Tuesday.) For further information on reading, refer to the tips on homework and presentation.

• Week 1: Sections 1.1-1.4. The preface, esp. pp ix–x, of this book may give you some further motivation.

• Week 2: Sections 2.1 and 2.2

• Week 3: Sections 2.3 and 3.1

• Week 4: Sections 3.2 and 3.3

• Week 5: Section 4.1

• Week 6: Sections 4.2 and 5.1

• Week 7: Sections 5.2 and 6.1

• Week 8: Sections 6.2 and 6.3

We're about to finish THREE rounds of presentations. This article may be a fun read as we reflect and look beyond the set of sets.

Homework

• Problem Set 1: 1.1.3beh, 1.2.13c, 1.3.3bcd, 1.3.15

• Problem Set 2: 1.4.21, 1.4.8, 2.1.4efh, 2.1.20bdf

• Problem Set 3: 2.2.18, 2.2.22, 2.3.26, 2.3.D1

• Problem Set 4: 3.1.16, 3.1.22, and this

• Problem Set 5 (due April 29): 3.3.12, 3.3.18, 3.3.22

• Problem Set 6: 4.1.12 (*Is the assumption of associativity necessary?), 4.1.34, 4.2.4bd, 4.2.16

• Problem Set 7

• Problem Set 8: 6.1.14, 6.1.17, 6.2.11

Presentations

We will have 2-3 presentations per class. This means that your presentation should be about ten to fifteen minutes – no longer! We will go through the topics in the order of the following list, with the first presentation occurring on Monday, April 6. Sign-up opens after the first class.

• Topics 1 (#4 restated)

• Topics 2

• Topics 3

Exams

Here are some sample questions for the midterm exam. Solutions (#1c updated)

Here is the midterm exam, with solutions.

Contact information

If you have questions or comments, please contact me. My contact information is as follows.

• By email: zyf@math.northwestern.edu

• By phone: 847-467-2272

• By foot: Locy Hall 202