Josh Laison
Math 251: Foundations of Advanced Mathematics


                               (Christina, Katie, Harbour, Boyuan, Elizabeth, Chase, Stefan, Jackson, Keith, Keeton, Amanda, Zech, Sasha, Jamie, Carlos)

                               (Kaitlin, Ivy, Eric, Matt, Sophia, Dylan, Alexa, Mylinh, Sarah, Caleb, Andy, Allie, Kyle)

Course Procedures

Neat mathy links:
Twin primes and the The Bounded Gaps Between Primes Polymath project
Godel's Incompleteness Theorem and accompanying cartoons
The Erdos Number project
Fermat's Last Theorem
The Classification of Finite Simple Groups and the Monster Group
The On-Line Encyclopedia of Integer Sequences
Counterexamples in Analysis
Topology joke

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: Read Section 2.6. No reading exercises. Feb 12: Quiz #1 today.
Week 5 Feb 15: Skim Section 6.3. No reading exercises. Feb 17: No assignments. Feb 19: Written problems #1 final draft due.
Presentation notes: At least 3 from the Induction handout.
Week 6 Feb 22: Reading: Sections 3.1, 3.2, 3.3.
First edition: Section 3.2 Exercise 2 (all parts), 4 (parts 1 and 2),
    Section 3.3 Exercise 2 (parts 1 and 2), 4 (parts 3 and 4).
Second edition: Section 3.2 Exercise 3 (all parts), 5 (parts 1 and 2),
    Section 3.3 Exercise 2 (parts 1 and 2), 4 (parts 3 and 4).
Feb 24: No assignments. Feb 26: Written problems #2 due.
Presentation notes: At least 5 from the Set Identities handout.
Week 7 Feb 29: Reading: Section 3.4
Exercises Section 3.4 1(1), 1(2), 2(1), 2(2). (either edition)
Mar 2: Reading: Sections 4.1 and 4.2.
Section 4.1 Exercises 1 (all parts), 3 (all parts), Section 4.2 exercises 2(1,5).
(either edition, but note differences in notation in Section 4.2.)
Mar 4: Quiz #2 today.
Week 8 Mar 7: No assignments. Mar 9: Written problems #2 final draft due. Mar 11: Presentation notes: At least 3 from the Image and Inverse Image handout.
Week 9 Mar 14: Reading: Sections 4.3 and 4.4. Note that we won't cover commutative diagrams and right and left inverses in this course, so you can skip those parts of section 4.3 if you like.
Section 4.3 Exercises 1(4), 2(1), 2(2), Section 4.4 Exercise 2 (all parts)
(either edition)
Mar 16: Written problems #3 due. Mar 18: No assignments.
SPRING BREAK! SPRING BREAK! SPRING BREAK!
Week 10 Mar 28: Reading: Section 5.1.
Exercises 3 (parts 1,2,3,4), 4 (parts 1,5,6). (either edition)
Mar 30: Reading: Section 5.3
1st Edition: Section 5.3: 1 (parts 1,2,6), 10 (parts 1,2,3).
2nd Edition: Section 5.3: 1 (parts 1,2,6), 8 (parts 1,2,3).
Apr 1: No class today!
Week 11 Apr 4: Reading: Section 5.2
Exercises Section 5.2: 1 (parts 1,2,3), 2 (parts 1,2), 3. (either edition)
Apr 6: No assignments. Apr 8: Quiz #3 today.
Week 12 Apr 11: Written problems #3 final draft due.
Presentation notes: At least 3 from the Modular Arithmetic handout.
Apr 13: Reading: Section 7.1.
Exercises: Section 7.1 2 (parts 1, 3, 5), 3 (parts 1, 2). (either edition)
Apr 15: Reading: Section 7.2. No reading problems.
Written problems #4 due.
Week 13 Apr 18: Presentation notes: At least 5 from the Groups handout. Apr 20: SSRD, no class today! Apr 22: Reading: Section 7.8 (Warning: this section is only in the 2nd edition)
Exercises 6, 7, 8.
Week 14 Apr 25: No assignments. Apr 27: Presentation notes: At least 3 from the Sequences handout. Apr 29: Written problems #5 due.
Week 15 May 2: Last day of class!
May 11: Last day to schedule final exam.