Math 251: Foundations of Advanced Mathematics

(back row: Nathan, Reese, Josh, Sam, Max, Carson, Joseph, George, Tyler, Blake, Samuel)

(front row: Colin, Beka, Megan, Stephan, Derek, Hongyuan)

- Course Procedures
**LaTex Resources:**- To install LaTeX on Windows, first download MikTex (the "small MikTex installer" should be fine), and then download WinEdt.
- Or if you want a free version try one of these or MonkeyTex or TexLive .
- For Macintosh, use MacTex or TexShop.
- A sample LaTex document written by me. This should have examples of most things that you'd like to know how to do.
- The Not-So-Short Introduction to LaTeX
- A List of LaTex resources
- A List of Tex resources
- Search for symbols in LaTex
- Browse a whole lot of symbols in LaTex (Warning, large PDF file)
**Links:**- Hilbert's Problems

- The Clay Millennium Problems

- The Erdös Number Project

**Course calendar:**Monday Wednesday Friday **Week 1****Aug 28:**First day of class.**Aug 30:**Reading: Sections 1.1, 1.2

Section 1.2 Exercises 4(4), 4(5), 5(4), 5(5), 11(2)

Presentations: Mathematical statements handout**Week 2****Sep 2:**Labor day, no class.**Sep 4:**Reading: Section 1.3

Section 1.3 Exercises 5(1), 5(3), 5(4), 8(5), 11(2), 11(4)**Sep 6:**No assignments.**Week 3****Sep 9:**Reading: Sections 1.4, 1.5

Section 1.5 Exercises 2(1), 5(3), 5(4), 6(2), 6(4)**Sep 11:**No assignments.**Sep 13:**Reading: Sections 2.1, 2.2, 2.3

Section 2.2 exercises 1(2), 1(3), Section 2.3 exercises 1(2), 1(3).**Week 4****Sep 16:**Homework #1 due today.

Reading: Sections 2.4, 2.5

Section 2.4 Exercise 1(3), Section 2.5 Exercises 1(2), 1(3)**Sep 18:**Quiz #1 today.

No reading assignments.**Sep 20:**No assignments.**Week 5****Sep 23:**No reading assignments.

Presentations: Proof techniques handout.**Sep 25:**Reading: Section 2.6, exercises 1(4), 1(6), 1(7).**Sep 27:**Reading: Sections 3.2, 3.3

Section 3.2 Exercises 3(1), 3(2), 3(3), Section 3.3 Exercises 2(2), 2(4).

Homework #1 revisions due today.**Week 6****Sep 30:**No assignments.**Oct 2:**Presentations: Sets handout.**Oct 4:**Reading: Section 3.4 Exercises 1(1), 1(2), 2(1).

Homework #2 due today.**Week 7****Oct 7:**Class cancelled!**Oct 9:**Quiz #2 today.**Oct 11:**Reading: Section 6.3.

No reading problems.**Week 8****Oct 14:**No assignments.**Oct 16:**No assignments.**Oct 18:**Mid-semester break today, no class!**Week 9****Oct 21:**Presentations: Induction handout.**Oct 23:**Reading: Sections 4.1 and 4.2.

Section 4.1 exercises 1, 3, Section 4.2 exercises 1(1), 2(5).**Oct 25:**Reading: The first page of Section 4.3.

Section 4.3 Exercise 3.**Week 10****Oct 28:**Reading: Section 4.4.

Section 4.4 exercise 2.

Homework #2 revisions due today.**Oct 30:**No assignments.**Nov 1:**No reading assignments.

Homework #3 due today.**Week 11****Nov 4:**No assignments.**Nov 6:**Reading: Section 5.1.

Section 5.1 exercises 3(5), 4(1), 4(3), 4(5), 4(6).**Nov 8:**Quiz #3 today.**Week 12****Nov 11:**No assignments.**Nov 13:**Reading: Section 5.2. Section 5.2 exercise 1.**Nov 15:**Reading: Section 5.3.

Section 5.3 exercises 1(1), 1(3), 1(6), 8(1), 8(2), 8(3).

Note: #8 is #10 in the first edition.**Week 13****Nov 18:**Homework #4 due today.**Nov 20:**Homework #3 revisions due today.**Nov 22:**Section 7.1 exercises 2(1), 2(3), 2(5), 3(1), 3(2).**Week 14****Nov 25:**Reading: Section 7.2. No reading problems.**Nov 27:****Nov 29:**Thanksgiving!**Week 15****Dec 2:**Reading: Section 7.8 (only in 2nd edition). No reading problems.**Dec 4:**Assignment #5 due today.**Dec 6:**Last day of class!**Week 16****Sat. Dec 14:**All work due by 5:00 PM.

Last day to schedule final exams.- Hilbert's Problems