Updated: 11/6/07, 7am
What is new: Homework 07 (which I emailed to you last week, with additional comments).

Office

• Location: Goldsmith 305
• Hours: MWR 10-11, MW 1-2.
• Phone 3062.
• email: igusa(at)brandeis(dot)edu

Teaching assistants
These are the people who grade your homework. The three of us also rotate in running the problem sessions. Brian and Jim can answer questions and give you hints about how to do the homework.

• Brian Drake, Room 103, Office hour: Tuesday 1-2.
• Jim Tseng, Room 104, Office hour: Monday 4-5.

Announcements

• I decided to use both a webpage and Latte. However, when Latte is fully operational, I am planning to close this webpage or at least move it into Latte.
• Here is the syllabus.
• See Latte for the revised calendar.
• We have weekly problem sessions Tuesdays 5-6pm in room 101.

Quizzes
There will be two quizzes (each counting 10% of your grade) and a final exam (30% of grade). Your homework counts for 50%.

• Quiz 1 on Wednesday, Oct 3. Induction will not be on this quiz. Quiz 1 covers everything before induction. Below are two practice quizzes that I handed out in class with answers.
  • Practice Quiz 1a with answers
  • Practice Quiz 1b with answers
  • Answers to Quiz 1
  • Quiz 1 results: The median grade was 24/30.
  
  
• Quiz 2 on Thursday, Nov 15.

Notes
These are notes on how to write proofs. They are designed to help you with your writing assignments.

• Notes 01 Proof by contradiction
• Notes 02 Counterexamples
• Notes 03 Proof vs derivation
• Notes 04 Induction and strong induction
• Notes 05 The coin problem

Homework
Every homework will be handed in and graded twice except for HW10 which will only be graded once. For HW2-9, the first version will count 1/3 of the grade and the final version will count 2/3. On HW1, the final grade replaces your grade for the first draft. On HW10, the first grade is your final grade. Your Homework will be graded for mathematical correctness and for competence in proof-writing.

• Chapter 1a: Homework 01 first version due Wednesday, Sept. 12 (extended to Friday, Sept 14 in my mailbox on the second floor of the math building). Final version now due Monday, Oct 1.
• Chapter 1b: Homework 02 is due Sept 19 with revised version due Oct 8.
• Chapter 2: Homework 03 is due Sept 26 with final version due Oct 15.
• Chapter 3: Homework 04 and Homework 05 are due Oct 18 with final version due Oct 31.
• Chapter 4: Homework 06 is due Oct 25 with final version due Nov 8.
• Chapter 11: Homework 07 is due Nov 8 with final version due Nov 29.

Topics
Here is list of some of the topics that we will cover.

• Equality of sets (Chap 1)
• Inequalities (Chap 1)
• Methods of proof:
  • By contradiction (Chap 1)
  • Case by case (Chap 1)
  • By induction (Chap 3)
  • By reduction to a known case
• Functions (Chap 1)
• Logic (Chap 2)
• Quantifiers (Chap 2)
• Cardinality (Chap 4)
• Graphs (Chap 11)
• Recurrence (Chap 12)
• Real numbers (Chap 13)
• Sequences and series (Chap 14)