MATH 4321 HOMEWORK (Spring 2012)

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Book = A First Course in Abstract Algebra, 7th Ed, by J. B. Fraleigh, Addison-Wesley.
Note that there might be more than one correct answer for any given question.

You should make sure you are viewing the most current version of this page and not the version in your browser's cache; reload the page from source. Dates indicate homework assigned in lecture that day. Dates for future assignments are tentative, and subject to change.
Skimming through the main ideas in a section shortly before that section is covered in class should help you understand the lecture -- try it!

1/17 Read lecture notes & do Sec 18 pgs 174/5: 1, 3, 5, 7, 9, 11.  
1/19 Read lecture notes, pages 167-174 & do Sec 18 pgs 175/6:  14, 16, 19, 
     20, 31, 38, 46 (hint: think binomial theorem from Math 1302), 22, 27, 
     23, 40.  
1/24 Read lecture notes & finish previous assignments.
1/26 Read lecture notes & Sec 19 & do 
     Sec 19 pgs 182/3: 14, 23, 24, 28, 5-12, 27, 29.
1/31 Read lecture notes & Sec 20 up to pg 187.5 & do 
     Sec 20 pgs 189/90: 1-3, 5, 24, 23a-h (justify answers).
2/02 Test 1 today. See information sheet.
     Read lecture notes & Sec 21 & do Sec 21 pgs 196-7: 1, 2, 7, 8, 12, 14.
2/07 Read lecture notes & Sec 22 & do 
     Sec 22 pgs 207-8: 1-4, 5-8, 14, 20, 22, 25. 
2/09 Read lecture notes & pgs 209-214 in Sec 23 & do  
     Sec 23 pgs 218-220: 2, 4, 6, 35, 36. 
2/14 Read lecture notes & pgs 215-8 in Sec 23 & do 
     Sec 23 pgs 218-220: 9, 10, 27, 28, 34, 14, 16, 18.
2/16 Read lecture notes & pgs 224.5-226 & do 
     Sec 24 pgs 226-7: 14, 5, 4, 6, 10. 
     Look over Test 1 and its solutions.
2/21 Read lecture notes & Sec 26 & do Sec 26 pgs 243-5: 29, 2, 17, 37, 4. 
     Look over Test 1 and its solutions.
2/23 Test 2 today. See information sheet.
     Read lecture notes & Sec 26 & do Sec 26 pgs 243-5: 12-14, 18, 
       22(a)(c), 24-26, 32, 38(a)(b).
2/28 Read pgs 245-7 & lecture notes & do Sec 27 
       pgs 252-4: 1 (max ideals only), 2 (max ideals only), 34, 35, 37.
3/01 Learn box on pg 248. Read Sec 27 & lecture notes & do 
       Sec 27 pgs 252-4: 1, 2, 24, 14(a)(b)(f), 31, 5, 6, 30.  
3/06 Read lecture notes & pgs 265-9 & do 
     Sec 29 pgs 272-4: 1, 2, 4, 6(Hint: E. Criterion), 11, 12, 14, 21, 27.
3/08 Read lecture notes & Sec 29 & do Sec 29 pg 272: 13, 15, 18. 
     Go over Tests 1 and 2 during Spring Break and read over all lecture
     notes from start of semester!!  Next test on Mar 22.
3/13 SPRING BREAK
3/15 SPRING BREAK
3/20 Read Theorem 29.18 & Example 29.19. Do Sec 29 pg 273: 30, 31.  
     Read lecture notes & Sec 30 & do 
     Sec 30 pgs 280-2: 15(a)-(d) (justify), 25 (note: "transformation" = 
     "map"), 1, 2, 4, 6, 7, 19.
     Look over Tests 1 & 2 and their solutions.
3/22 Test 3 today. See information sheet.
     Finish previous assignments. 
3/27 Finish previous assignments & thoroughly understand solutions to 
     Test 3. 
3/29 Read lecture notes & pgs 283-289 & do
     Sec 31 pgs 291-2: 1-3, 5, 7, 9, 11, 13, 19(a)-(c), 22, 28, 29.
4/03 Sec 31 pg 293: 35 (hint: show that the squaring function is not
     one-to-one nor onto).  Read lecture notes & Sec 33 & do 
     Sec 33 pgs 304-5: 8(a),(g)(justify).
4/05 Sec 33 pgs 304-5: 11, 1, 8(c)(justify), 4.
     (Hint for #4: there are many ways to do this question. You could 
     read the statement of Thm 33.10 and either use Euler's phi 
     function (why?), or you could write down a generic field with 
     9 elements using an element alpha for the generator of the cyclic 
     group of nonzero elements in the field and work with the nonzero 
     elements of the field as powers of alpha (we did something like 
     this 2nd method today in class with the example drawn from 
     Sec 29 #18.)   
     Watch the short film at 
     https://www.ted.com/talks/marcus_du_sautoy_symmetry_reality_s_riddle.html
     if you have not done so already.
4/10 Read lecture notes & Sec 48 & do Sec 48 pgs 422-4: 1-3, 7-11,13,25. 
4/12 Read lecture notes & Sec 48 & do
     Sec 48 pgs 422-4: 26, 15-21, 36(a),(b).  
     Read lecture notes & Sec 49 & do
     Sec 49 pgs 430-1: 1-3, 7, 8(b)(d)(e) (justify).
4/17 Sec 49 pg 431: 13.  
     Read lecture notes & Sec 50 & do
     Sec 50 pgs 434-6: 1-5, 14(a)-(e),(j) (justify), 18,21.
     Next test on April 26.
4/19 Read lecture notes & Sec 51 & do
     Sec 51 pgs 442-4: 7, 15, 8(a)-(g)(justify). 
     Go through Tests 1-3 and their solution sheets.
4/24 Read lecture notes & Sec 51 & do
     Sec 51 pgs 442-4: 1-4, 9 (hint: use E = F(alpha, beta), 13. 
     Go through Tests 1-3 and their solution sheets.
4/26 Test 4 today. See information sheet.
     Read lecture notes & Secs 53 & do
     Sec 53 pgs 454-6: 1, 2, 11(a)(b), 13.
5/01 Read lecture notes & Secs 53 & 56 & do
     Sec 53 pgs 454-6: 3, 4, 8, 11, 15(a)-(c),(e),(g) (justify).
     Complete online the student feedback survey by 11 pm on 
     Fri May 4 -- check your mymav e-mail for the link. Thanks!
5/03 Go through Tests 1-4 and their solution sheets.
     Complete online the student feedback survey by 11 pm on 
     Fri May 4 -- check your mymav e-mail for the link. Thanks!
5/08 Final exam at 5:30 pm.
     See information sheet.