Homework assignments
(MATH 3163-003, Fall 2012)

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Instructor: Gábor Hetyei Last update: Friday, November 30, 2012

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: In the table below, 1.1/1a means exercise 1, part a, in section 1.1. There is also a single PDF file containing all additional homework problems that are not to be found in the book.

No. Date due: Problems:
There will be no more homework assigned in this class. Our final exam will be on Tuesday, December 11, 5:00 - 7:30 pm. You may download the current version of the Sample Final Exam Questions that I will distribute on Tuesday December 4.
12 Tue Nov 20 6.1/2,4,8,12a, 12b.
11 Th Nov 15 5.2/2,6,8,10;   5.3/8, 9a.
Bonus question:
  1. 5.3/9b.
10 Th Nov 8 5.1/2,4,6,10,12.
9 Th Nov 1 4.4/12, 14a, 14b, 19a;   4.6/2a, 2b.
Our second test will be on Tuesday, October 30, 2012. You may download the current version of the Sample Test 2 that I distributed on Thursday October 25.
8 Th Oct 25 4.3/2,4,6,8;   4.4/2b,2d,4a,4b.
7 Th Oct 18 4.1/10,16,18,20;   4.2/2,10.
6 Th Oct 11 3.3/2, 10a, 10b, 22b, 24;   4.1/2, 4a, 4b, 6a, 6c, 6d, 6e.
5 Tu Oct 2 3.2/2b, 2c, 6, 12a, 14, 16a, 18.
Bonus question:
  1. 3.2/36a
4 Th Sep 20 3.1/4a, 6, 10, 18, 14, 30, 32.
Our first test will be on Thursday, September 20, 2012. You may download the current version of the Sample Test 1 I will distribute on Tuesday September 18. Note that the draft you find online is still subject to minor corrections and updates.
3 Th Sep 13 2.2/6, 10ad;   2.3/2ab, 5b, 9b, 10a.
Bonus questions:
  1. 2.2/11
  2. Prove that the square root of a positive integer is either a positive integer, or it is an irrational number.
2 Tu Sep 4 1.3/4, 12ab, 14, 16, 22ab;   2.1/14 (hint: think of the parity of c+d), 16ab, 22.
Bonus question:
  1. We say that a and b are associates if a divides b and b divides a. We say that u is a unit if u divides 1. Prove that a and b are associates if and only if a equals u times b for some unit u. (Use only the above terms in your proof, which should be applicable to integers, as well as to Gaussian integers.)
    Note added on Thursday, October 11, 2012: The answer to this question is due Tuesday October 16. You may want to phrase your statement as follows: In an integral domain, a and b are associates if and only if a equals u times b for some unit u.
1 Tu Aug 28 1.1/4,6;   1.2/2, 4b,8.
Bonus questions:
  1. 1.1/8.
  2. Prove, by induction on k, that each remainder rk that appears in the Euclidean algorithm finding the greatest common divisor of a and b, is an integer linear combination of a and b.