MATH 4321 HOMEWORK (Spring 2011)

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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.

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1/18 Read lecture notes & do Sec 18 pgs 174/5: 1, 3, 5, 7, 9, 11.  
     Submit Jan 27.
1/20 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.  Submit Jan 27.  
1/25 Read lecture notes & pgs 177-9 including Def 19.6 & do 
     Sec 19 pgs 182/3: 14, 23, 24, 28.  Submit Jan 27.
1/27 Read lecture notes & Sec 19 & do Sec 19 pgs 182/3: 5-12, 27, 29. 
     Read lecture notes & Sec 20 & do Sec 20 pgs 189/90: 1, 2, 3, 5, 
     24, 23(justify answers to 23 (e.g., pg reference or theorem or 
     counterexample)), 11, 13.
     Submit Feb 8.   
2/01 UTA closed owing to bad weather & icy roads.
2/03 UTA closed owing to bad weather & icy roads.
2/08 Test 1 today.  Test 1 on Secs 18, 19, 20. See information sheet.
     Read lecture notes & Sec 21.  
2/10 Read lecture notes & Sec 21 & do Sec 21 pgs 196-7: 1, 2, 7, 8, 12, 14.
     Read lecture notes & Sec 22 & do Sec 22 pgs 207-8: 1-4.
     Submit Feb 17.  
2/15 Read lecture notes & Sec 22 & do  Sec 22 pgs 207-8: 5-8, 14, 20, 22, 25.   
     Read lecture notes & pgs 209-214 in Sec 23 & do  
     Sec 23 pgs 218-220: 2, 4, 6, 35, 36. 
     Submit Feb 17.  
2/17 Read lecture notes & pgs 215-8 in Sec 23 & do 
     Sec 23 pgs 218-220: 9, 10, 27, 28, 34, 14, 16, 18.
     Submit Feb 24. 
2/22 Read lecture notes & pgs 224.5-226 & do 
     Sec 24 pgs 226-7: 14, 5, 4, 6, 10. 
     Read lecture notes & Sec 26 & do Sec 26 pgs 243-5: 29, 2, 17, 37.
     Submit Feb 24.    
2/24 Read lecture notes & Sec 26 & do 
     Sec 26 pgs 243-5: 4, 12-14, 18, 22(a)(c), 24-26. 
     Submit Mar 3.   
3/01 Learn box on pg 248. Read pgs 245-8. 
     Read lecture notes & do Sec 27 pgs 252-4: 1, 2, 24, 34, 35, 37. 
     Look over Test 1 and its solutions.
     Submit Mar 3.     
3/03 Test 2 today.  See information sheet.
     Read Sec 27 & lecture notes & do 
     Sec 27 pgs 252-4: 14(a)(b)(f) (justify), 31.  Submit Mar 10.   
3/08 Sec 27 pgs 252-4: 5, 6, 30.  
     Read last 2 paragraphs on pg 251 and read pg 252.  Submit Mar 10.   
3/10 Read lecture notes & Sec 29 & do 
     Sec 29 pgs 272-4: 1, 2, 4, 6(Hint: E. Criterion), 11-15, 21, 27.
     Submit Mar 24.   
     Go over Tests 1 and 2 during Spring Break and read over all lecture
     notes from start of semester!!
3/15 SPRING BREAK
3/17 SPRING BREAK
3/22 Read lecture notes & Sec 29 & do 
     Sec 29 pgs 272-4: 18, 30, 31.   Submit Mar 24.   
3/24 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.    Submit Mar 31.
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.
     Submit April 5.  
3/31 Test 3 today; material through Sec 29 inclusive;
     see information sheet.
     Finish homework from 3/29 due April 5.
4/05 Go over solutions to Test 3. 
4/07 Read lecture notes & Sec 33 & do 
     Sec 33 pgs 304-5: 8(a),(g)(justify), 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.)   Submit April 14.
4/12 Read lecture notes & Sec 48 & do Sec 48 pgs 422-4: 1-3, 7-11,13,25. 
     Submit April 14.         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.
4/14 Read lecture notes & Sec 48 & do
     Sec 48 pgs 422-4: 26, 15-21, 36(a),(b).  Submit April 21.  
4/19 Read lecture notes & Sec 49 & do
     Sec 49 pgs 430-1: 1-3, 7, 8(b)(d)(e) (justify), 13.  Submit April 21.  
     Read lecture notes & Sec 50 & do
     Sec 50 pgs 434-6: 1-5, 14(a)-(e),(j) (justify), 18,21. Submit April 26.
4/21 Read lecture notes & Sec 51 & do
     Sec 51 pgs 442-4: 1, 4, 7, 8(a)-(g)(justify), 
                       9 (hint: use E = F(alpha, beta), 13, 15.
     Submit April 28.
4/26 Study for test.
4/28 Test 4 today; material through Sec 51 inclusive;
     see information sheet.
5/03 Read lecture notes & Secs 53 & 56 & do
     Sec 53 pgs 454-6: 1-4, 8, 11, 13, 15(a)-(c),(e),(g) (justify).
     Submit May 5.