Math 330 (Shipley, Fall 2008) Homework assignments.

Email: bshipley@math.uic.edu

OFFICE HOURS:

in SEO 508: TBA
Also available at the Math Learning Center, SEO 4th Floor east, 8am-6pm Monday through Friday.

You are encouraged to work together on all of these assignments, but write the solutions on your own to reflect your own understanding of the problem.
Homework due in class Friday (or in Shipley mailbox in SEO 304 by 9:30am) No late homework accepted (several lowest grades will be dropped). Only legible writing will be graded.
See http://www.math.uic.edu/~bshipley/math330.html (the syllabus) for other comments on grading, academic honesty and the importance of doing as many extra problems as you can (even more than those listed here).

Reading assignments are implicit in the problem assignments. You should read the text before it is covered in lectures and read the text again while working on the problem set. See http://www.math.uic.edu/~bshipley/math330.html (or the bottom of this page) for the pages for which you are responsible in each chapter.
  1. Problem Set 1: Due : Friday, August 29 Chap. 0: 2, 9, 11, 14, 16
    (extra, odd problems, not to hand in: 3, 5, 19, 25 and as many others as possible.)




    2. Since the bookstore is out of books I'll write the problems here. I won't do this next week though, ask someone in class to see their book for a bit...

    # 2: Determine gcd(2^4 . 3^2 . 5 . 7^2 , 2 . 3^3 . 7 . 11) and lcm(2^3 . 3^2 . 5, 2 . 3^3 . 7 . 11).
    #9 and #11 were written down in class slightly differently than in the book. Here's what is actually in the book.
    #9: If a and b are integers and n is a positive integer, prove that a mod n = b mod n if and only if n divides a - b.
    #11: Let n be a fixed positive integer greater than 1. If a mod n = a' and b mod n = b', prove that (a + b) mod n = (a' + b') mod n and (ab) mod n = (a'b') mod n.
    #14: Show that 5n +3 and 7n + 4 are relatively prime for all n.
    #16: Use the Euclidean algorithm to find gcd(34, 126) and write it as a linear combination of 34 and 126.





  2. Pages to be covered (may be updated as we go):

    Chapters 0-4, all pages; Ch. 5, p.94-105; Ch 6, p.120-128; Ch 7, p.137-142; Chapter 8, p.153-157; Ch 9, p.177-184; Ch 10, p.199-207; Ch. 11, 217; Chapters 12-15, all pages: Ch 16, p.291-294; Ch 17, p.303-313;

    See also http://www.math.uic.edu/~radford/ for more practice final exams and solutions from 2003 and 2004 (under link for "Teaching 2004").