8/25-27

Integers: arithmetic and order

Sections 1 and 2 from my notes

Skim chapter 1 (especially 1.1, 1.4 and 1.6) from the textbook.

Notes and homework available in Google Drive folder. I aim to post each homework by (at the latest) the Thursday before it’s due. Please email me if you’re not finding it by then.

(8/25) The first hwk is now posted.

8/30-9/3

Well-ordering principle, b-ary expansions,

Sections 3, 4, and 5 from my notes.

Textbook sections 2.1, 2.4

Note that after I collect each homework, I upload solutions to all but the revision problem. You can find these in the Drive homework folder.

9/6-9/10

Divisibility and the Euclidean algorithm

Diophantine equations, prime factorization

Notes, section 5.

Textbook sections 2.2, 2.3, 2.5

On 9/6 I (think I) shared an “individual” Google Drive folder with each of you. All graded/commented homework solutions will be returned to this, so email me know if you didn’t get an invitation/can’t see the folder.

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”.

9/13-9/17

Sets, equivalence relations and congruence

Notes, section 6.

Textbook sections 1.3, 3.1, 3.3

Revision for the problem on the 1^st hwk due at the same time as hwk 3. The link for the Google form is in the contact info file.

9/20-9/24

More congruences

Textbook sections 3.2, 3.4-3.6

Notes, section 7

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

9/27-10/1

RSA Encryption

Rational numbers

Textbook 7.3 and 7.4

Notes, section 8

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.

10/4-10/8

Induction and the binomial theorem

Textbook 4.1 and 4.3

1^st midterm, Wed Oct 6

10/11-10/15

Functions

Textbook 6.1-6.5

Fall break next week

10/25-10/29

Cardinality, real numbers

Text 6.6; also see Appendix A in my notes for a proof of the Cantor-Schroeder-Bernstein Theorem

11/1-11/5

Sequences,

Notes, sections 9,10 (the textbook doesn’t cover sequences)

11/8-11/12

sequences/continuity

Notes, section 11

Notes, sections 13, 14

11/15-11/19

Complex numbers

Text 8.1-8.7

2^nd midterm, Wed Nov 17

I’ll be at a conference in Canada this week. I’ll zoom record lectures in advance and my graduate student will proctor the midterm. Monday office hours will happen at the usual time but by Zoom (use the link in the Drive contacts file).

11/22

Finish unfinished business re continuity or complex numbers, answer hwk 10 questions.

2^nd midterm returned (I hope)

Thanksgiving break

11/29-12/3

Fundamental Theorem of Algebra

Notes, section 15

Hwk 10 will be due Monday 11/29

12/6

Wrapping up.

(Final) homework 11 due Monday 12/6

Final exam 8-10 AM, Monday, Dec 13 in 129 Hayes-Healy.