Math 20630: Introduction to Mathematical Reasoning

Spring `21

Weekly schedule

Instructor: Jeffrey Diller (click for contact info, etc)

Time and place: MWF 11:40-12:30 PM, Hayes-Healy 129.

Math Bunker help: Sun-Thurs 7-9 in Hayes-Healy basement (recently former math library) or virtually via (url and pwd available in the contact file in Google Drive). The math bunker provides peer-help for proof-based math courses and is staffed by upper class math majors with a lot of experience with these. This has been a popular resource the past several years, and I highly encourage you to use it. If nothing else, you can go work on your homework in good & sympathetic company.

Office Hours:  (Note change to time and place as of 2/10) Mondays 5-6:30 PM. In person in Bond Hall 114 and virtually by Zoom—see contact file for url.

Textbook: An Introduction to Mathematical Thinking by William Gilbert and Scott Vanston. We'll also rely heavily on supplementary notes (available in our Drive folder) that I provide.  Reimburse me as your conscience dictates. That's a joke by the way.

If you’re interested in another take on this material, the book Mathematical Thinking: Problem-Solving and Proofs by D'Angelo and West is another textbook that has been used a lot for (other incarnations of) this course.  It's more ambitious than ours, even if you add in my supplementary notes and the style is somewhat different.

Why this course: Up til now, most of your mathematics courses have likely emphasized examples, computation, and intuitive understanding of mathematics. This course will emphasize careful mathematical arguments. By addressing questions about familiar things like numbers (Are there finite or infinitely many prime numbers? Do all rational numbers have rational square roots?) and sets (What does it mean for a set to have ``infinitely many'' elements? Do all sets with infinitely many elements have the same size?), we will see how it is that one justifies statements in mathematics. In a nutshell, the subject of this course is numbers, and its goal is to help you understand, invent, and present proofs.

What we'll cover: Course content falls roughly into four categories. We'll definitely cover the first three, though the first will be somewhat dispersed among the other two. The fourth category is a sort of grab bag that we'll reach into as much as we can.

In terms of the textbook, we will cover the following in more or less the order listed: chapter 2, sections 4.1 and 4.3, chapter 3, chapter 5 (we'll definitely need notes here, since this one is far to brief for our purposes), and sections 6.1-6.6. It'd be nice to spend time on chapters 7 and 8, too.

How you will be evaluated (note that because of the covid-compressed semester, I’m counting the hwk for a bit more and the final for a bit less than is my habit for this class):

Further Policies, Disclaimers and Fine Print