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Homework assignments
(MATH 1165-001, Spring 2010)

Last update: Wednesday, April 28, 2010

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.

Notation: 23.1/(4)a means exercise 1, part (4)a, in section 23.

No.	Date due:	Problems:
7	Mo May 3	22.1/bc, 22.2/bcjm; 23.1/beg, 23.2; 24.2; 26.1cd.
6	We Apr 21	19.1 bc, 19.2, 19.4c, 19.5; 20.2, 20.3, 20.4, 20.6; 21.3 bd, 21.4c. Bonus: Let a₁, a₂, ... be the sequence given by a₁=3, a₂=3 and by the recursion formula a_n+1=4a_n-4a_n-1. Prove by induction that a_n=9/4 2ⁿ-3/4* n* 2ⁿ*.
5	Mo Mar 29	16.7, 16.10, 16.15, 17.3, 17.10 abc; 18.1, 18.3, 18.4. Our second test is on Wednesday March 31. You may download the Study Guide I will distribute in class on Monday March 29.
4	Mo Mar 15	10.1 cdf, 10.2 cdf, 10.4 bcde, 10.5 bce ; 11.1 adf, 11.3, 11.5, 11.7, 11.9, 11.16 acf; 16.3, 16.4ac. Bonus questions: Find a formula expressing the maximum numbers of regions created by drawing n circles in the plane. Let n be a positive integer and p be a prime number. Use the base p representation of n to express the highest exponent m for which p^m divides n. (Hint: involve the sum of the digits and the summation formula for a geometric sequence.)
3	Mo Feb 22	7.3, 7.6, 7.9bd, 7.12; 8.3, 8.4, 8.8; 9.3, 9.5, 9.6. Bonus: Show how the answer we found to 2.7 may be justified using the law of cosines; solve 8.8; show that the power set of an infinite set A has more elements than the set A itself (only need to complete the proof presented in class). Our first test is on Wednesday February 10. You may download the Study Guide I distributed in class on Monday February 8.
2	Mo Feb 8	5.3, 5.7, 5.8; 6.11bf, 6.12b, 6.15ab.
1	Mo Jan 25	2.7, 2.9 a; 3.1bd, 3.2, 3.4, 3.8; 4.2, 4.11, 4.13, 4.15. Bonus: 2.9 b (write pseudocode); find the answer to 2.9a in St. Augustine's book "The City of God".