This is the web page for sections 3 and 4 of Math 311w taught by Tim Reluga in the autumn of 2015.

This course introduces students to the use of mathematics as language. Using a theorem-proof framework much like that used in Euclid’s geometry textbook 2, 400 years ago, we will study elementary number theory, modular arithmetic, set theory, formal logic, groups, and other discrete-math topics. The course will include several writing assignments to help students develop their own communications skills.

Textbook and partial solutions courtesy of Gary Mullen.

*Office Hours moved to Tuesday afternoons, 2:30 - 4:30*

**The final exam is Thursday, December 17th, 8 am - 9:50 am, in 112 Bouckhout Lab**1st review session Saturday, 10 am - noon, McAllister 106.

Tuesday, Dec 15th, I'll be in my office 10 am - noon and 1 - 3 pm.

The division theorem will be one of the problems on the exam.

More practice problems in preparation for the final exam.

- For 8/23 -- Read Section 1.1.
- Practice homework: Section 1.1, problems 1-7 (updated)
- Online pratice: A
- Extra practice on the division theorem
- Simple online gcd practice

- For 8/31 -- Read Section 1.2.
- For 9/9 -- Read Section 1.3
- Practice homework: Section 1.3, problems 2,3,4,6,8
- Extra proof practice using GCD theorems reference sheet.
- Interactive Eratosthenes' sieve

- For 9/14 -- Read Section 1.4.
- Practice homework: Section 1.4, problems 1,2,3,5,6,7
- Extra problems for Section 1.4: A

- For 9/21 -- Read Section 1.5.
- Practice homework: Section 1.5, problems 1-5

- 9/28 - Exam 1, in-class
- For 10/2 -- Read section 1.6.
- Practice homework: Section 1.6, problems 1,2,3,5,6,7,8.
- Extra problems
- Handout for RSA theorems
- Martin Hellman's and Martin Gardner's classic articles on public-key encryption.

- For 10/12 -- Read section 2.1
- Read section 2.2
- Practice homework: Section 2.2, problems 1,2,4,5,6,7,8,9.
- Extra problems A

- For 10/23 -- Read section 2.3
- Practice homework: Section 2.3, problems 1,2,3,4,6,7,9
- these extra problems, updated to include partial answers (2015/10/31).
- Sochi medal counts

- For 11/4 -- Read section 3.1
- Practice homework: Section 3.1, problems 1,2,3,4
- Online pratice: A, B, C
- More pratice: Making truth-tables, Translating truth-tables
- A handout on common logic rules.
- Use deduction to prove (p → r) ∧ (q → r) = (p ∨ q) → r .
- Use deduction to prove ((p → q) ∧ (q → r)) → (p → r) .

- For 11/9 -- Read section 3.2
- Practice homework: Section 3.2, all problems

- For 11/16 -- Read section 4.3 on groups
- For 11/20 -- Read section 5.1 on order, and subgroups
- Problems 1, 3, 6-10

- For 11/30 -- Read section 5.2 on Cosets, orbits, and Lagrange's theorem
- Problems 1, 2, 3

- For 12/2 -- Read section 5.3 on group isomorphisms
- Problems 1,3-7

- Quiz 1, section 4, 2015-09-02 and answers
- Quiz 1, section 3, 2015-09-09 and answers
- Quiz 2, section 4, 2015-09-16 and answers
- Quiz 2, section 3, 2015-09-23 and answers
- Quiz 3, section 4, 2015-10-07 and answers
- Quiz 3, section 3, 2015-10-14 and answers
- Quiz 4, section 4, 2015-10-21 and answers
- Quiz 4, section 3, 2015-10-28 and answers
- Quiz 5, section 4, 2015-11-11 and answers
- Quiz 5, section 3, 2015-11-18 and answers
- Quiz 6, section 4, 2015-11-18 and answers
- Quiz 6, section 3, 2015-11-18 and answers
- Bonus Quiz, sections 3 and 4, due 2015-11-30.

- List of theorems on GCD's and Prime numbers
- List of theorems regarding congruence classes
- List of theorems regarding order and RSA
- List of logic identies

- The limits of reason, an article by Gregory Chaiton
- think like a mathematician
- An attack on contrapositives, which, however doubtfully, assumes we're smart enough to guess the ways of the world.
- Solution of the Kadison-Singer conjecture.
- (2015-11-19) Einstein's proof of the pythagorean theorem
- (2015-11-13) Breaking news! Looks like graph isomorphisms may not be has hard to calculate as we thought they were!
- Breaking news on public key encryption based on the Diffie-Hellman key exchange protocol here, with the mathy version here.
- Flatland: The Movie official trailer.
- The Beauty of Polynomial Roots
- My explanation of circle-squaring
- New foundations for math?
- If you are interested in some programming practice, you might want to check out Project Euler, which is a self-taught course in mathematical problem-solving using programming.
- Popularizers of mathematics
- Erica Klarreich's excellent mathematics writting
- Martin Gardner, math's best friend
- Ian Stewart, another great mathematics writter.

- Visual Explanations of some simple mathematical concepts (with atleast 1 mistake in the exponential growth example).
- Another why python post
- Learn the command line