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:
- Read CPZ Chapter 8.
- CPZ, Chapter 8: 16, 22, 30, 36, 53, 58, 59.
- HW6, due Tuesday, October 27:
- Read CPZ Chapter 6.
- 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:
- Read CPZ Chapter 5.
- CPZ, Chapter 5: 6, 22, 27, 33, 44, 47, 62.
- Programming Assignment 1, due Tuesday, October 6:
- HW4, not collected (preparation for Exam 1):
- Read CPZ Chapter 4.
- CPZ, Chapter 4: 11, 13, 14, 16, 32, 33, 46, 51, 70.
- HW3, due Thursday, Sept 24:
- HW2, due Thursday, Sept 17:
- Read CPZ Chapter 2.
- CPZ, Chapter 1: 38, 45, 46, 52, 60, 63 (will not be collected/be part of quiz);
- CPZ, Chapter 2: 1, 7, 13, 14, 16, 22, 25, 26, 27, 30, 34, 49, 51, 55, 59, 69, 78, 79, 81, 83 (for the in-class quiz).
- HW1, due Thursday, Sept 3:
- Read CPZ Chapters 0 and 1.
- CPZ: Chapter 1: 5, 6, 7, 9, 11, 19, 20, 22, 27, 31, 33, 35.
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