Math 103, Fall 2007

Assignment for November 22-26

 

1. Read Pages 108-114 of the textbook.

2. Make a (hand-written) list of all definitions given in pages 108-114. You must turn this (Definitions) list in along with your solutions to Homework 7 problems.

3. Make a (hand-written) list of all theorems (including lemmas, propositions, corollaries) given in pages 108-114 without proof. You must turn this (Theorems) list in along with your solutions to Homework 7 problems.

4. Read the entries in your Theorems List try to reproduce the definition of each technical term appearing in these theorems without referring to your Definitions List. If you fail to remember a definition look it up and then start over from the top of your Theorems List. Continue until you could remember the definition of all the technical terms appearing in your Theorems List.

 

5. Try to prove Propositions 6.5.4 and 6.5.5 using induction on your own. If you cannot succeed in producing a proof, read the proofs given in the textbook trying to understand every single step. Try to reproduce these proofs on your own after you finish studying them.

 

6. Give a proof of every entry in your Theorems List (Except Propositions 6.5.4 and 6.5.5) starting from the top of your list and without referring to the book or your lecture notes. If you fail to prove a theorem look it up in the book and then start over proving the theorems in your list. After a few trials you should be able to produce the proofs of all the theorems in your Theorems List.

 

Homework 7 (Due on Tuesday, November 27, 9:30 am):

1 (10 points): Make a (hand-written) list of all definitions given in pages 108-114. 

2 (15 points): Make a (hand-written) list of all theorems, lemmas, propositions, corollaries given in pages 108-114.

3 (75 points): Solve problems 6.16,  6.18, 6.19, 6.20, and 6.21 on page 122 of the textbook.

Note: The minimum of your grade in this homework set and in Quiz 7 will contribute about 4.5 points out of 100 to your total numerical grade in this course.

Policy for Homeworks: Homeworks will be collected in class. The assistants will not accept late homeworks nor will they return them directly to the students. If a student fails to turn in his (her) homework by the deadline, his (her) grade for that homework set will be reduced by 10 points (out of 100) for each day passed the deadline.