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