8/23-25

Integers: arithmetic and order

Sections 1, 2 from my notes; textbook sections 1.1, 2.1

The textbook takes the natural numbers rather than the integers as its starting point. Since I start with the integers, it’s probably easier to use my notes for this initial material. Also note that unlike the textbook, I include 0 among the natural numbers. This is a matter of convention over which mathematicians remain divided.

Homework 1 is now posted on canvas. Also, the Math Bunker opens for business in the basement of Hayes-Healy starting Sunday evening 7-9.

8/28-9/1

Least element (i.e. well-ordering) principle, b-ary expansions,

Notes sections 3, 4; textbook 1.4

9/4-9/8

Induction and the binomial theorem

Textbook 1.1, 1.2, 1.7

Take note: after trying out Hurley 153 for office hours, I’ve decided to move them to Hayes-Healy 129 (a regular classroom) instead.

9/11-9/15

Binomial Theorem

Divisibility, the Euclidean algorithm and prime factorization

Textbook 1.7

Notes section 5; textbook 1.5, 1.6, 2.2, 2.3

Here’s a youtube video explaining Euclid’s algorithm for finding greatest common divisors. Not too bad, but I’d be interested in alternatives, so tell me if you think you’ve got a nice one. If you’d like to wander a little further down the rabbit hole try searching “continued fractions and the euclidean algorithm”.

9/18-9/22

Linear Diophantine Equations

Sets, equivalence relations and congruence

Textbook 2.3

Notes section 6; textbook A.2, A.5, 2.4

9/25-9/29

More congruences

Textbook 2.5-2.7; notes section 7

Here’s a nice article about the Chinese Remainder Theorem from the online science magazine Quanta.

10/2-10/6

Fermat’s Little Theorem and RSA Encryption

Textbook 2.7

1^st midterm Wed, Oct 4

Here’s a Numberphile video about RSA. Numberphile is a great place to go for videos about all things mathematical. Other great video channels for math include 3Blue1Brown, Mathologer, TedEd Riddles, and Matt Parker's Standup + Maths.

10/9-10/13

Rational numbers

Pythagorean triples and Fermat’s Last Theorem

Notes, section 8; textbook 3.1, 3.2

textbook, pages 99-103

Fall break next week

PBS produced a show (an episode of the Nova series) about Andrew Wiles proof of Fermat’s Last Theorem called “The Proof”. It’s a lovely take on how math gets done.

10/23-10/27

Functions and cardinality

Textbook A3, A.4; (Appendix A in my notes gives a proof of the Cantor-Schroeder-Bernstein Theorem)

10/30-11/3

More cardinality

Real numbers, Sequences

Notes section 9; textbook 4.1-4.5

Notes sections 10, 11; textbook 5.1-5.3

11/6-11/10

More sequences

Math For Everyone Talk: Geometry from the Inside on Thurs Dec 9 at 5 PM in 101 Jordan, given by Stephen Trettel (University of San Francisco). Click the tile to see the poster and description. These talks are pitched at a general undergraduate audience and generally very entertaining.

11/13-11/17

Continuity

Notes sections 13, 14

2^nd midterm, Wed Nov 15

11/20

Continuity, return exam 2

2^nd midterm returned (I hope)

Thanksgiving break

11/27-12/1

Complex numbers

Textbook 6.1-6.5

12/4-12/6

Fundamental Theorem of Algebra. Wrapping up.

Notes section 15

Final exam 8-10 AM, Thursday, Dec 14 in 229 Hayes-Healy.