Math 112: Studies in Mathematics
Information for StudentsCourse syllabus
Tutorial sections are mandatory. Tutorial is not "homework help" (although you can get help with your homework there) but will often cover new material not done in lectures, and review the material that was covered in the lecture. As you may have noticed, lectures move very quickly. Tutorial helps you find out if you've caught everything.
Bring your book! You will never need to bring it to lecture, but you will need it in tutorial.
Your tutor doesn't do most of the talking in tutorial, you do!! You, yes you, will be up there writing on the board like a PRO.
HomeworkReading 1: Russell's paradox
As if sets weren't confusing enough on their own, here's the story of how Bertrand Russell thought that he destroyed all of mathematics by defining a very special set. This is a one-page reading and we will discuss it in class on Friday.
HW due 10/3
HW due 10/10
Reading 2: Axioms
To discuss in class on October 12th. This reading consists of excerpts from two seminal (though relatively modern) papers in the field of philosophy of mathematics by Penelope Maddy and Solomon Feferman. Both deal with axioms in mathematics.
HW due 10/17
HW due 10/24
Reading 3: Well-Ordering
The story of the (highly contentious) well-ordering theorem, starring Georg Cantor and Ernst Zemelo.
On Friday in class we'll define what well-ordering means. This reading is to be done for Monday, October 24th.
HW due 10/31
Reading 4: Prime numbers
What we know (and what remains mysterious) about prime numbers.
HW due 11/7
HW due 11/21
This homework is long, so I recommend starting early. As of today (the 7th) you know enough to do all of the questions except for 6.8 and 6.9 from the book.
Reading 5: RSA Encryption
RSA encryption is the reason your internet is secure -- why you can check your e-mail and transfer money from your bank without being hacked. These two short articles explain the methodology and the mathematics behind this system of encoding information. Amazingly, it only uses prime numbers, modular arithmetic, and a little number theory.
We'll discuss this reading on Wednesday the 23rd, or in tutorials on the 22nd. It will be handed out in class sometime soon.
HW due 11/28
Reading 6: The continuum hypothesis-- how big is infinity?
Infinity comes in different sizes! This reading explains what it means to compare the size of two infinite sets and tells the story of the continuum hypothesis -- a question about the size of the set of real numbers and the size of the set of the natural numbers. Featuring some of our all-time favorite mathematicians: Cantor , Hilbert, and Godel, and with special guest appearances by Paul Cohen and two mathematicians who are too modern to have interesting wikipedia pages.