Week 1

Tuesday (6/27/06)

• Course Orientation. Axioms of Arithmetic.
• Worksheet #1

Wednesday (6/28/06)

• The Integers (I). The Principle of Mathematical Induction and the Principle of Well-Ordering.
• References
  • Notes on the Integers
  • Sections 4.5 and 5.2 in Proof, Logic, and Conjecture: The Mathematician’s Toolbox
  • Appendix C in Chapter 1 Notes.
• Worksheet #2

Thursday (6/29/06)

• The Integers (II). The Division Algorithm. References
  • Notes on the Integers
  • Section 8.2 in Proof, Logic, and Conjecture: The Mathematician’s Toolbox
• Worksheet #2

Week 2

Tuesday (7/4/06)

• Independence Day (no class)

Wednesday (7/5/06)

• The Integers (III). The Fundamental Theorem of Arithmetic. References
  • Notes on the Integers
  • Section 8.2 in Proof, Logic, and Conjecture: The Mathematician’s Toolbox
• Worksheet #3

Thursday (7/6/06)

• Logic.
• References
  • Read Chapter 2 in Proof, Logic, and Conjecture: The Mathematician’s Toolbox before class.
  • Section 1.6 and Appendix A in Chapter 1 Notes.
• Worksheet #4

Week 3

Tuesday (7/11/06)

• Sets (I): Set Operations and Maps.
• References
  • Notes on Sets and Maps
  • Chapters 5 and 7 in Proof, Logic, and Conjecture: The Mathematician’s Toolbox
  • Appendix B in Chapter 1 Notes.
• Worksheet #5

Wednesday (7/12/06)

• Sets (II): Partitions and Equivalence Relations.
• References
  • Notes on Sets and Maps
  • Chapter 6 in Proof, Logic, and Conjecture: The Mathematician’s Toolbox
  • Section 3.1 in Chapter 3 Notes.
• Worksheet #6

Thursday (7/13/06)

• Topological Spaces
• References
  • Chapter 1 in Chapter 1 Notes.
• Worksheet #7

Week 4

Tuesday (7/18/06)

• Midterm I (In Class)
  Solutions to Midterm I

Wednesday (7/19/06)

• Closed Sets
• References
  • Chapter 2 in Chapter 2 Notes.
• Worksheet #8

Thursday (7/20/06)

• Closed Sets and the Cantor Set
• References
  • Chapter 2 in Chapter 2 Notes.

Week 5

Tuesday (7/25/06)

• The Euclidean Closure Operator
• References
  • Chapter 3 in Chapter 3 Notes.
• Worksheet #9

Wednesday (7/26/06)

• Connected Sets
• References
  • Chapter 4 in Chapters 4, 5, and 6 Notes.
• Worksheet #10

Thursday (7/27/06)

• The Rationals are Not Connected
• References
  • Chapters 5 and 6 in Chapters 4, 5, and 6 Notes.

Week 6

Tuesday (8/1/06)

• Midterm II Due (Take Home)
  Solutions to Midterm II
• Completeness of the Real Numbers
• References
  • Chapter 6 in Chapters 4, 5, and 6 Notes.
• Worksheet #11

Wednesday (8/2/06)

• Continuous Functions
• References
  • Chapter 8 in Chapters 8 and 9 Notes.
• Worksheet #12

Thursday (8/3/06)

• Limits and Continuity in Rⁿ
• References
  • Chapter 9 in Chapters 8 and 9 Notes.
• Worksheet #13

Week 7

Tuesday (8/8/06)

• The Brouwer Theorem in One Dimension
• References
  • Chapter 10 in Chapters 10 and 11 Notes.
• Worksheet #14

Wednesday (8/9/06)

• Topological Equivalence
• References
  • Chapter 11 in Chapters 10 and 11 Notes.
• Worksheet #15

Thursday (8/10/06)

• The Brouwer Fixed Point Theorem
• References
  • Chapter 12 in Chapter 12 Notes.
• Worksheet #16

Week 8 (Final Exams)

Tuesday (8/15/06)

• The final examination for MATH S-101 is scheduled for 1:30 pm, Tuesday, August 15 in Science Center, Hall E.
• Final Exam
• Solutions to Final Exam

• Assignment 1 - Due on July 5, 2006.
  You can find an example of how to right up a proof at InductProof.pdf.
  Solutions to Assignment 1
• Assignment 2 - Due on July 11, 2006.
  Solutions to Assignment 2
• Assignment 3 - Due on July 20, 2006
  Solutions to Assignment 3
• Assignment 4 - Due on July 27, 2006
  Solutions to Assignment 4
• Assignment 5 - Due on August 3, 2006
  Solutions to Assignment 5
• Assignment 6 - Due on August 10, 2006
  Solutions to Assignment 6

Grading of Homework Assignments

One of the goals of this course is for you to learn to think and communicate mathematically. This means that homework assignments should be written with justification and explanations of your steps in English. See the course textbook and notes for examples of well-written solutions. Since many of the exam problems ask for justification, this will be good practice. In general, each problem or part of a multi-part problem will be worth three points. We grade homework according to the following rubric.

• 3 Points. Work is completely accurate and essenttially perfect. Work is thoroughly developed, neat, and easy to read. Complete sentences are used.
• 2 Points. Work is good, but incompletely developed, hard to read, unexplained, or jumbled. Answers that are not explained may received 2 points even if correct. The work contains the right idea but is flawed.
• 1 Points. Work is sketchy. There is some correct work, but most of the work is incorrect.
• 0 Points. Work is minimal or non-existant. Solution is completely incorrect.