Math 220, Fall 2023

Math 220 -- Fall 2023

Mathematical Reasoning and Proof
Amherst College


Lecture Room:	Seeley Mudd 204
Lecture Time:	MWF 1-1:50
Final Exam:	TBA
Instructor:	David Zureick-Brown ("DZB")
Office:	Seeley Mudd 502
Phone:	(413) 542-2595
Email:	dzureickbrown@amherst.edu

Text:	"How to Prove It: A Structured Approach" 3rd Edition by Daniel J. Velleman
Office Hours:	Monday 3-4 (in person)
	Thursday 2:30-3:30 (zoom)
	Thursday 3:30-5:30 (in person)

About this course (a quote from a former student):

"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, contrapositive, quantifiers.
Mathematical prose and rigor -- how to write mathematics correctly and in complete sentences.
Techniques of proof -- ``direct'' proofs, proof by contradiction, induction, proof by ``cases''.
Sets, relations, functions -- the building blocks of mathematics.
Some additional topics (e.g., cardinality, different sizes of infinity).

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

Homework

The homework assignments are available at this link, and will be updated regularly.

Assignments should be turned in via Gradescope, as a single file.