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 1.11.4. 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 23 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. Signup 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: 8474672272
• By foot: Locy Hall 202
