# Math 145: Algebra (Fall 2018)

Instructor: David Jao

Office hours: TTh 2:00pm-3:00pm

### Teaching assistants

Christopher Leonardi | cfoleona
| MC 5494 | Office hours: Mon. 12:00pm-1:00pm and Tue. 4:00pm-5:00pm |

Luis Ruiz-Lopez | laruizlo
| MC 5486 | Office hours: Mon. and Wed. 12:30pm-2:30pm |

Michael Deveau | m2deveau
| MC 5019 | Office hours: Fri. 3:30pm-5:30pm |

### Announcements

Please join the discussion forum on Piazza (*https://piazza.com/uwaterloo.ca/fall2018/math145*) for assistance with the course, discussions of assignment problems and administrative issues.

The midterm examination is scheduled to take place on Saturday, October 20 in RCH 301 from 1:00pm to 2:50pm.

### Course materials

- Course outline (
*https:../../wiki/images/d/d1/MATH145-2018-outline.pdf*) - Sample midterm (
*https:../../wiki/images/7/79/MATH145-2018-midterm1.pdf*) - Sample midterm #2 (
*https:../../wiki/images/9/91/MATH145-2018-midterm2.pdf*) - Sample final exam #1 (
*https:../../wiki/images/5/56/MATH145-2018-final1.pdf*) - Sample final exam #2 (
*https:../../wiki/images/d/de/MATH145-2018-final2.pdf*)

### Assignments

- Assignment 1 (
*https:../../wiki/images/1/18/MATH145-2018-a1.pdf*) (due Wednesday, September 12 at 12:00pm)- Coq worksheet file (
*https:../../math145/2018/a1.v*) for assignment 1 - Installation instructions (
*https://coq.inria.fr/download*) for Coq - Coq cheatsheet (
*https:../../wiki/images/0/0b/Coq-cheatsheet.pdf*) and command reference

- Coq worksheet file (
- Assignment 2 (
*https:../../wiki/images/6/6e/MATH145-2018-a2.pdf*) (due Wednesday, September 19 at 12:00pm/2:30pm)- Coq worksheet file (
*https:../../math145/2018/a2.v*) for assignment 2

- Coq worksheet file (
- Assignment 3 (
*https:../../wiki/images/9/98/MATH145-2018-a3.pdf*) (due Wednesday, September 26 at 12:00pm/2:30pm)- Coq worksheet file (
*https:../../math145/2018/a3.v*) for assignment 3 - Coq worksheet file (
*https:../../math145/2018/a3_bonus.v*) for assignment 3 bonus question

- Coq worksheet file (
- Assignment 4 (
*https:../../wiki/images/2/2a/MATH145-2018-a4.pdf*) (due Wednesday, October at 12:00pm/2:30pm)- Coq worksheet file (
*https:../../math145/2018/a4.v*) for assignment 4 (incl. bonus question) - The quote on the assignment is from 算法統宗 (Suanfa_tongzong) (
*https://en.wikipedia.org/wiki/Suanfa_tongzong*) by 程大位 (Cheng Dawei) (*https://en.wikipedia.org/wiki/Cheng_Dawei*), page 111, chapter 4 (*https://archive.org/stream/02094086.cn#page/n110*).

- Coq worksheet file (
- Assignment 5 (
*https:../../wiki/images/3/30/MATH145-2018-a5.pdf*) (due Wednesday, October 17 at 2:30pm)- Coq worksheet file (
*https:../../math145/2018/a5.v*) for assignment 5 bonus question

- Coq worksheet file (
- Assignment 6 (
*https:../../wiki/images/a/ac/MATH145-2018-a6.pdf*) (due Wednesday, October 31 at 2:30pm) - Assignment 7 (
*https:../../wiki/images/6/63/MATH145-2018-a7.pdf*) (due Wednesday, November 14 at 2:30pm) - Assignment 8 (
*https:../../wiki/images/b/b8/MATH145-2018-a8.pdf*) (due Wednesday, November 28 at 2:30pm) - Assignment 9 (
*https:../../wiki/images/b/b2/MATH145-2018-a9.pdf*)

### Lecture materials

- September 7, 2018:
- Slides from lecture (
*https:../../wiki/images/2/26/MATH145-2018-lecture01.pdf*) - Coq demo (
*https:../../math145/2018/lecture01.v*) from lecture. (Use this file for learning purposes only. For assignment 1, please use the file posted above in the Assignments section.)

- Slides from lecture (
- September 10, 2018:
- Here is the unwieldy set theory axiom (
*https://en.wikipedia.org/wiki/Tarski%E2%80%93Grothendieck_set_theory#Implementation_in_Metamath*) mentioned in today's class (more properly called the Tarski-Grothendieck axiom). - For the one-axiom theory of equality, see Introduction to Mathematical Logic, by Mendelson. You can (legally) download a PDF from this link (
*https://link-springer-com.proxy.lib.uwaterloo.ca/book/10.1007%2F978-1-4615-7288-6*) if you have a UWaterloo library card. The axiom is Axiom S1 on page 117, and the proof of the "standard" equality axioms is on page 118, Proposition 3.2 (a), (b), and (c).

- Here is the unwieldy set theory axiom (
- September 14, 2018:
- Coq example (
*https:../../math145/2018/lecture04.v*) from lecture. You may copy material from this file into your assignment, but**DO NOT USE THIS ACTUAL FILE FOR YOUR ASSIGNMENT.**Use the assignment-specific worksheet posted above instead.

- Coq example (
- September 21, 2018:
- Coq example (
*https:../../math145/2018/lecture07.v*) from lecture. You may copy material from this file into your assignment, but**DO NOT USE THIS ACTUAL FILE FOR YOUR ASSIGNMENT.**Use the assignment-specific worksheet posted above instead.

- Coq example (
- September 28, 2018:
- Coq example (
*https:../../math145/2018/lecture10.v*) from lecture. You may copy material from this file into your assignment, but**DO NOT USE THIS ACTUAL FILE FOR YOUR ASSIGNMENT.**Use the assignment-specific worksheet posted above instead.

- Coq example (
- October 1, 2018:
- Coq example (
*https:../../math145/2018/lecture11.v*) from lecture. You may copy material from this file into your assignment, but**DO NOT USE THIS ACTUAL FILE FOR YOUR ASSIGNMENT.**Use the assignment-specific worksheet posted above instead.

- Coq example (
- October 5, 2018:
- Coq example (
*https:../../math145/2018/lecture13.v*) from lecture. You may copy material from this file into your assignment, but**DO NOT USE THIS ACTUAL FILE FOR YOUR ASSIGNMENT.**Use the assignment-specific worksheet posted above instead.

- Coq example (
- November 14, 2018:
- Slides about the RSA cryptosystem (
*https:../../wiki/images/6/69/MATH145-2018-rsa.pdf*)

- Slides about the RSA cryptosystem (