Josh Laison
Math 251: Foundations of Advanced Mathematics


                               Section 2: Radu, Mark, Hanna, Michael, Jenna, Zach, Reid, Katy, Estella, Jose, Heather

                               Section 3: Taylor, Nick, Ross, Kara, Arlin, Aaron, Allison, Brian, Phil, Alyssa, Stephanie, Stephanie, Matt, Patrick
Course Procedures

LaTex Resources:
To install LaTeX on Windows, first download MikTex (the "small MikTex installer" should be fine), and then download WinEdt.
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

Links:
The Mathematics Subject Classification
The MathSciNet article database
Hilbert's Problems
The Clay Millennium Problems
The Erdös Number Project
The Mathematics Genealogy Project and Grapher
The On-Line Encyclopedia of Integer Sequences

Course calendar:
Monday Wednesday Friday
Week 1 Jan 19: First day of class. Jan 21: Reading: Sections 1.1, 1.2
Section 1.2 Exercises 3.6, 4.3, 11.1, 11.2
Oral: Mathematical statements handout		 Jan 23: No class, MLK day!
Week 2 Jan 26: LaTeX day, meet in Collins 407 Jan 28: Reading: Section 1.3, Exercises 5.1, 5.3, 8.5, 11.2, 11.4 Jan 30: Reading: Sections 1.4 and 1.5,
Section 1.5 exercises 2.1, 5.2, 5.5, 6.4, 6.6
Week 3 Feb 2: Reading: Section 2.1 (no exercises)
Written #1: For Fact 1.3.2, prove parts 6, 12, and 14, and then explain why they make sense intuitively.		 Feb 4: Reading: Section 2.2 and 2.3.
Section 2.2 exercises 1(2), 1(3),
Section 2.3 exercises 1(2), 1(3).
Oral: Negate the statements from class on Monday.		 Feb 6: Reading: Section 2.4 and 2.5.
Section 2.4 exercises 1(2), 1(3),
Section 2.5 exercises 3(2), 3(3)
Week 4 Feb 9: No assignments. Feb 11: No reading.
Oral problems: Proof techniques handout
Individual Problems #1 due. 		Feb 13: Reading: Section 2.6.
Section 2.6 exercises 1(4), 1(6), 1(7).
Week 5 Feb 16: Reading: Sections 3.1, 3.2.
Section 3.2 exercises 2, 3(1), 3(2).
Written #1 rewrites due today.		 Feb 18: Reading: Section 3.3.
Section 3.3 exercise 1.		 Feb 20: No reading.
Written Problems #2 due.
Week 6 Feb 23: Oral problems: Set identities handout. Feb 25: Oral problems: Set identities handout. Feb 27: Reading: Section 3.4.
Section 3.4 exercises 1(1), 1(2), 2(1).
Individual Problems #2 due.
Week 7 March 2: Reading: Section 6.3.
No reading problems.
Oral problems: Theorem 3.4.3 parts 4, 5, 6. 		March 4: No assignments. March 6: No assignments.
Week 8 March 9: Oral problems: Induction handout.
Written Problems #3 due. 		March 11: Reading: Sections 4.1 and 4.2.
Section 4.1 exercises 2(2), 2(4),
Section 4.2 exercises 1(3), 1(5), 2(5).		 March 13: Reading: page 152.
Section 4.3 exercise 3.
Week 9 March 16: Reading: Section 4.4
Section 4.4 exercise 2.
Oral problems: Theorem 4.2.3 (excluding v and vi) 		March 18: Individual Problems #3 due. March 20: No assignments.
Week 10 March 30: Reading: Section 5.1
Section 5.1 exercises 3(1), 3(2), 3(3), 4(1), 4(5). 		April 1: Reading: Section 5.2
Section 5.2 exercise 1. 		April 3: No assignments.
Week 11 April 6: Oral problems: Mod arithmetic handout.
Reading: 5.3 ex. 1(1), 1(3), 1(6), 10(1), 10(2), 10(3).
Written Problems #4 due. 		April 8: Reading: Section 7.1
exercises 2(1), 2(3), 2(5). 		April 10: Reading: Section 7.2 exercise 2.
Week 12 April 13: No assignments. April 15: SSRD, no class today. April 17: Oral problems: Groups handout.
Week 13 April 20: Reading: Class handout exercise 5.5.14.
Individual Problems #4 due. 		April 22: Reading: Class handout exercise 8.5.4. April 24: No assignments.
Week 14 April 27: Reading: Section 7.6 exercises 1, 2, 4. April 29: Reading: 7.7 exercises 11(1), 11(2), 11(3).
Written Problems #5 due. 		May 1: No assignments.
Week 15 May 4: Last day of class! May 8: Individual Problems #5 and all old assignments due.