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Homework assignments
(MATH 3166-001, Spring 2011)

Last update: Tuesday, April 26, 2011

Disclaimer: The information below comes with no warranty. If, due to typographical error, there is a discrepancy between the exercises announced in class and the ones below, or this page is not completely up to date, the required homework consists of those exercises which were announced in class. Check for the time of last update above. If, by my mistake, a wrong exercise shows up below, I will allow you extra time to hand in the exercise that was announced in class. If, however, exercises are missing because this page is not up to date, it is your responsibility to contact me before the due date. (No extra time will be allowed in that case.) This page is up to date if the last update happened after the last class before the next due date.

The deadlines do not apply to the Bonus questions, which expire only once we solve them in class, or on April 28 at latest.

Notation: 1.4/16a means exercise 16, part a, in chapter 1, section 4.

No.	Date due:	Problems:
13	We Apr 27	4.3/6,7 8.1/1,3 (prove it!); 8.5/3,4 (show work!)
12	We Apr 20	Redo 4.1/13. Express your answer using Catalan numbers. 4.3/1, 4cd (use ab), 8, 9, 12, 13.
11	We Apr 13	4.1/4, 8 (finish argument given in the back of the book), 10; 4.2/1a, 6b. Bonus questions: Write a generating function equation for the Catalan numbers, solve it and deduce the explicit formula for the Catalan numbers. (Similar to the argument given in the book for the triangulations, but you have to shift all indices by two.) Translate finding the Catalan number C_n into finding all circular arrangements of n+1 gas stations with one unit of fuel and n road segments, consuming one unit of fuel by proving that there is a unique gas station where you can start and drive around without ever having less than one unit of fuel in your tank.
10	We Apr 6	4.1/2a, 5, 6, 13.
9	Mo Apr 4	3.5/1be, 3ab; 3.6/2bd. Bonus (2pts): Show how to improve the 1.9ⁿ bound in 3.2/10. Our second test is on Monday March 28. You may download the Sample Test 2 I will be distributing in class on Wednesday March 23. You may also want to have a look at the document Fibonacci-type sequences (easy approach).
8	We Mar 23	3.3/3be, 4, 8; 3.4/2,5,10. Bonus: 3.4/12, 13.
7	We Mar 16	3.2/1bc, 3, 4a, 9, 10, 11. Bonus question: 3.2/14.
6	We Mar 2	2.3/7, 2.4/8,10,12 (hint: use the answer to 11 from the back of the book); 3.1/2,4. Bonus question: 2.3/16.
5	We Feb 23	2.3/4,6,9,11.
4	We Feb 16	2.1/3,4d; 2.2/4ac. Bonus: Extend Vandermonde's formula (formula (2.5) in section 2.1) to the case when m and n are not integers. Our first test will be on Monday February 14. You may download the Sample Test 1 I distributed on Wednesday February 9.
3	We Feb 9	1.4/2,6,10.
2	We Feb 2	1.2/4,6,8,10 1.3/4,12.
1	We Jan 26	1.1/6,8,10,16. Bonus question: 1.1/12. Note: The book does not make it clear, but my understanding is that sets in a Venn diagram are represented by circles, not arbitrary (even concave) shapes. This reading of the question makes it hard, and that's why I consider it bonus.