Math 20630: Introduction to Mathematical Reasoning

Fall `21

Weekly schedule

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

Time and place: MWF 8:20-9:10 in Hayes-Healy 129.

Math Bunker help: Sunday-Thursday, 7pm-9pm (also 9pm-10pm on Wednesdays) in Hayes-Healy basement (room in the SE corner). The math bunker provides peer-help for proof-based math courses and is staffed by upper cle to work on your homework in good company.

Office Hours:  Mondays 5-6:30 PM in Hayes-Healy 125. Note: this room is technically reserved til 5 PM for math dept colloquia. Most weeks I expect it’ll be empty by 5, but if you arrive and find the room occupied, just hang on outside til it empties out and/or I arrive.

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. The preass 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 thervious sentence is a joke, by the way.

Some other (purely optional) sources:

If you look at any of these, I’d like to hear what you think. The second one in particular looks to me like a contender for textbook in future instances of this course.

Why this course: Up til now, most of your math classes have probably emphasized examples, computation, and intuitive understanding. 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