Math 308 Homework Assignments, Fall 2015:

The problems will be taken from the textbooks CPZ: Mathematical Proofs, 3rd edition, by Chartrand, Polimeni, and Zhang, and Ross: Elementary Analysis, 2nd edition, by Ross.
• HW8, due Thursday, December 3 (not to be collected):
• Read CPZ Chapter 9 and 10.
• CPZ, Chapter 10: 16, 19, 30, 32, 36, 37.
• HW7, due Thursday, November 13:
• CPZ, Chapter 8: 16, 22, 30, 36, 53, 58, 59.
• HW6, due Tuesday, October 27:
• CPZ, Chapter 6: 1, 13, 20, 22, 24, 35, 40, 46.
• Show the equivalence of the Principle of Math Induction and the Strong Principle of Math Induction.
• Find the mistake in the following "proof" that all horses are black. We want to prove the following statement: if n is a natural number, then in any collection with n horses, if one is black, then all are black. We proceed by induction: the statement is clear for n=1, so all we need to show is the induction step. Consider a collection with k horses, where one is black. Now, remove any black horse from the set. Now, this collection contains k-1 horses, and since at least one is black, then all must be black. Adding the other black horse you previously removed, we then have that this collection of k horses only contains black horses.
• HW5, due Thursday, October 15:
• CPZ, Chapter 5: 6, 22, 27, 33, 44, 47, 62.
• Programming Assignment 1, due Tuesday, October 6:
• HW4, not collected (preparation for Exam 1):