Principles of Analysis

Homework Assignment #1

Due Wednesday, September 11, START of Class

Homework should be turned in at the BEGINNING OF CLASS. All problem numbers refer to Bilodeau and Thie's book, the required text for the course. You should write up solutions neatly to all problems, paying particular attention to your arguments and proofs. A nonempty subset will be graded. You are strongly encouraged to work on these problems with other classmates, although the solutions you turn in should be YOUR OWN WORK.

Section 1.1
Problems:   1, 2c, 3, 6 (all parts)

Hint: For problem #3b, try proving your statement by using certain items from Theorem 1.1.1.

Section 1.2
Problems:   7 (all parts), 8 (all parts), 9, 11

Hint: For problem #11, investigate the equation f(f(x)) = x. Which values of a and b make this equation true for all x?

Additional Problem
State and prove the Pythagorean Theorem. You may use any references you like (textbook, paper, internet site) but please cite any source you use other than yourself (title, author, publisher, etc.) Anyone who finds a proof I've never seen gets extra credit.