Math 250, Fall 2022

Math 250 -- Fall 2022

Foundations of Mathematics
Emory University


Lecture Room:	E308a MSC
Lecture Time:	TuTh 2:30-3:45
Final Exam:	TBA
Instructor:	David Zureick-Brown ("DZB")
Office:	W430 MSC
Phone:	(608) 616-0153
Email:	dzureic@emory.edu

Text:	"An Introduction to Abstract Mathematics", Bond and Keane
Office Hours:	Mon 4:30-5:30 (tentative, via Zoom, link is on the syllabus)

About this course

"There are two situations when it's good to know what's under the hood of a car: one is when it breaks, the other is when you need to make a new car. Neither of them should prevent you from getting behind the wheel and learning to drive. And if you know what a car does and when it breaks, you'll be surprised by how much more sense the fancy technology under the hood will make.

That said, a lot of great math has been done by digging around under the hood." -- Dmitry Vaintrob

Syllabus

We will cover the following topics.

Logic -- statements, negation, converse, etc.
Sets, relations, functions -- the building blocks of mathematics
Techniques of proof -- proof by contradiction, induction; non-constructive proofs, "consider a minimal X" proofs, pigeonhole principle
Cardinality -- different sizes of infinity
Numbers -- what they are, transcendental numbers vs. algebraic numbers (i.e., the difference between pi and 2^(1/2))
Mathematical prose and rigor-- how to write mathematics correctly and in complete sentences.

Here is an official pdf of the syllabus for this course.

Homework

The homework assignments are available at this link, and will be updated after each lecture.

Assignments should be turned in via Canvas, as pdfs, produced by LaTeX.