Josh Laison
Math 251: Foundations of Advanced Mathematics

Course Procedures

Neat mathy links:
Twin primes and the The Bounded Gaps Between Primes Polymath project
Godel's Incompleteness Theorem

Course calendar:
Monday Wednesday Friday
Week 1 Jan 18: First day of class! Jan 20: Reading: Sections 1.1, 1.2
Exercises: Section 1.2. 4(4), 4(5), 5(4), 5(5), 11(2) (either edition)
Presentation notes: At least 5 from the Mathematical statements handout.
Jan 22: Martin Luther King, Jr. Day Celebration
No class today!
Week 2 Jan 25: If you have a laptop, bring it to class. Create an account on sharelatex or download and install MikTex and WinEdt or one of these.
LaTeX documentation, resources, and symbol finder

Sample LaTex document

Jan 27: Read Section 1.3. Don't worry about memorizing the names of the facts 1.3.1 and 1.3.2, but verify that they make sense logically to you. The terms you do want to memorize are "contrapositive" and "converse".
Exercises: Section 1.3 Exercises 5(all parts), 8(2), 8(4), 8(5), 11(all parts) (either edition)
Jan 29: Read Sections 1.4 and 1.5. Again don't worry about memorizing the names of the rules of inference in 1.4, but verify that they make sense logically to you.
Exercises: Section 1.4 Exercise 4 (all parts) (Explain the fallacies informally. Which step does not follow from the previous step, and why?
Section 1.5 Exercise 6 (parts 2, 4, 5) (either edition)
Week 3 Feb 1: No assignments. Feb 3: Read Sections 2.1, 2.2, and 2.3.
Exercies: Section 2.2 Exercise 1 (parts 2 and 3), Section 2.3 Exercise 1 (parts 2 and 3) (either edition).
For each part, your answer should have the form, "At the beginning of the proof, assume.... At the end of the proof, conclude.... "
Feb 5: Written problems #1 due.
Week 4 Feb 8: Read sections 2.4 and 2.5.
Exercises: Section 2.4: 1 (parts 1 and 3), Section 2.5: 4 (all parts) (either edition).
Presentation notes: At least 5 from the Proof techniques handout.
Feb 10: TBA Feb 12: Quiz #1 today.