Final grades are now posted. I am in my office Friday, 1-3 pm if you want to pick up your exam before break. Otherwise, you are welcome to pick it up after break.

This is the web page for section 4 of Math 311w taught by Tim Reluga in the autumn of 2017.

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 millenia ago, we will study elementary number theory advances from ancient times to our current technological age. Theories of modular arithmetic, set theory, formal logic, groups, and other discrete-math topics will be covered, with applications to encryption and digital information encoding. The course will include several writing assignments to help students develop their communications skills.

Course syllabus, including class data, contact information, office hours, and grading policies (subject to change)

Textbook and partial solutions courtesy of Gary Mullen.

Information on our weekly essays

- For 8/21 – Read Section 1.1.
- Textbook practice: Section 1.1, problems 1-7
- Online pratice: A
- Extra practice on the division theorem
- Simple online gcd practice
- A longer explanation of circle-squaring

- For 8/28 – Read Section 1.2.
- For 9/6 – 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 9/11 – Read Section 1.4.
- Practice homework: Section 1.4, problems 1,2,3,5,6,7
- Extra problems for Section 1.4: A

- For 9/18 – Read Section 1.5.
- Practice homework: Section 1.5, problems 1-5

- For 9/25 – Read section 1.6.
- Practice homework: Section 1.6, problems 1,2,3,5,6,7,8.
- Extra problems
- Handout for RSA theorems

- 9/29 - Exam 1, in-class
- For 10/4
- Martin Hellman’s and Martin Gardner’s classic articles on public-key encryption.

- For 10/6 – 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) . (A solution)

- For 10/9 – Read section 3.2
- Practice homework: Section 3.2, all problems

- For 10/13 – Read section 2.1
- For 10/18 – 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.

- 11/3, second midterm in class
- For 11/10 – Read section 4.3, Groups
- For 11/17 – Read section 5.1 on subgroups and order
- Practice homework: Section 5.1, problems 1, 3, 6-10

- For 12/1 – Read section 5.2 on Cosets, orbits, and Lagrange’s theorem
- Practice homework: Section 5.2, problems 1, 2, 3

- 12/12(Tuesday), 8 am - 9:50, final exam will be in Willard room 73.

- Quiz 1 answers
- Quiz 2 answers
- Quiz 3 answers
- Quiz 4 answers
- Quiz 5 answers
- Quiz 6 answers
- Quiz 7 answers

- 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
- Midterm 1 Practice Exam
- Final exam proof practice 1
- Final Extra practice problems

New tricks for factoring numbers quickly by hand. This includes a way to check for divisibility by 7!

A new Mersenne prime has been found.

- 3-valued logic used in SQL databases!
Scariest scifi film of the year Careful what world you dream of creating.

- Some students have found Socratica’s videos on symmetry groups useful.
- On the word “because” in math, an interesting recent essay by Barry Mazur. I think an explanation is really just a convenient concept from which many important related ideas can be directly deduced by something resembling gradient descent. Barry’s openning, throw-away-line, that classical mechanics is “only understood as a consequence of quantum mechanics”, reveals a fundamentally different perspective, and that modern AI proves a powerful counterpoint to.
- An idea for a dynamic math notation called magic paper.
- US Elliptic curver reputation in shambles from things dating back to this kind of thing
- Eugenia Cheng’s recent video essay math is amazing, which is a great conversation starter since there are a number of misleading comments and a general underappreciation of the beauty of useful things. I was annoyed enough to write a rebuttal.
- the mythical mobius bagel discussed in the wsj.
- In Praise of Proofs by Contradiction that Aren’t by Evelyn Lamb, 2014
- The logic of computing the seemingly uncomputable
- 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.
- Einstein’s proof of the pythagorean theorem
- 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
- 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).