MATH 5331 HOMEWORK (Spring 2016)

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Book = Abstract Algebra, by D. S. Dummit & R. M. Foote, 3rd Ed., Wiley
A list of known errata for this book is posted here.
Note that there might be more than one correct answer/solution for any given question.

LAST REVISION: 5/04/16

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!


01/19/16

Attendance will be recorded, starting today.
Read course syllabus carefully. Make a note of the test dates in your calendar. Review course website and
repeat frequently during the semester. Read https://vancliff.utasites.cloud/T/S09/1426study.pdf and
https://www.jeffreybennett.com/pdf/How_to_Succeed_general.pdf for ideas on how to study most effectively.
Read pgs 1-3 & do pg 4: 1, 5.
Read pgs 4-7 & do pgs 7-8: 1(a), 7.
Read pgs 8-11 & do pgs 11-12: 3, 9, 15(a).
Read lecture notes & pgs 16-21 & do pgs 21-23: 6(a)-(c), 8, 9, 12, 22, 25-27, 29, 30.
Do H1.

01/21/16

Read lecture notes & pgs 23-27 & do pg 28: 14, 16.
Read lecture notes & pgs 29-32 & do pgs 32-33: 1, 4(a).
Read lecture notes & pg 34 & do pg 35: 2, 3, 10, 11(a)(b).
Read pg 36 & do pg 36: 1.
Read lecture notes & pgs 36-39 & do pgs 39-41: 1, 13, 14, 15, 18, 20, 26.

01/26/16

Read lecture notes & pgs 41-44 & do pgs 44-45: 2, 4, 6, 16, 17.
By this time, you have seen quite a few theorems. It is best NOT to memorize the theorems,
but to do enough of the homework that the results of the theorems become known to you,
though perhaps with different wording or using pictures.

01/28/16

Read lecture notes & pgs 46-48 & do pgs 48-49: 1(a)(e), 2(d), 10, 11(a)(c), 15, & do H2.
Read pgs 51-52 & do pgs 52-53: 2, 3, 10, 11, 12(a)-(c).

02/02/16

Read lecture notes & 2nd half of pg 59 & do pgs 60-61: 2, 3, 11, 12, 13(a), 16.
Read pg 64 & pgs 908-909 & do pgs 65-66: 1, 5, 6, 14(a)(b), 17.

02/04/16

Read Section 2.5 (pgs 66-71) & pgs 75-85 & do pgs 85-89: 6, 7, 10, 4, 3, 20, 22(a)   & H3 &
pgs 85-89: 33, 36, 37, 40, 41.
Test 1 is a week from today; see the information sheet for the test.

02/09/16

Read pgs 89-95 & do pgs 95-96: 1, 6, 5, 4, 12 (hint: consider gh ↦ ? ), 16 (hint: see Corollary 9 in book).
Test 1 on Thursday; see link to information sheet on Feb 4 above.

02/11/16

Test 1 today; see link to information sheet on Feb 4 above.
Read pgs 100, 103, 105 & do pg 106: 1, 7.

02/16/16

Read pgs 106-111 & do H4 & do pg 111: 2, 10.
Go over the solutions to Test 1; use password ``math5331'' to access the file.

02/18/16

Read pgs 223-228 & do pgs 230-233: 1, 11, 14(c), 28, 29, 30(a), 5(c), 6(c), 7, 9.

02/23/16

Read pgs 233-237 & do pgs 237-239: 1, 3(b)(c), & do H5 & pg 239: 9-12. Optional: do pg 238: 4.

02/25/16

Read pgs 239-244 & pgs 246-247 & do pgs 247-251: 6, 7, 16, 32, 10(a)(b)(f), 18, 22, 34(a)(b) ( for the last question,
note the definitions on pg 247 – in particular, IJ = { ∑ i
kjk : where the sum is a finite sum & ik ∊ I & jk ∊ J ∀ k } );
also do H6.

03/01/16

Read pgs 251-256 & do H7 & pgs 256-260: 8, 16(b), 4, 6 (hint: be sure to show that any inverse is both a left inverse & a right inverse),
32(a), 37, 38 (hint: use #37), 5, 9, & H8 & H9.
Test 2 is a week from today; see the information sheet for the test.

03/03/16

Read pgs 260-264 (note the error on pg 263 in the Definition – see errata) & do pgs 264-265: 4  & H10.
Test 2 on Tuesday; see link to information sheet on Mar 1 above.

03/08/16

Test 2 today; see link to information sheet on Mar 1 above.
Do H11, H12 (optional) & H13 (optional).
Read remark on pg 279.
  Do pg 282: 3   &   pg 292: 1, 6(a).

03/10/16

Go over the solutions to Test 2; use password ``math5331'' to access the file.
Read pgs 295-298 & Theorem 3 on pg 299 (Division Algorithm for F[x], where F is a field).
Do pgs 298-299: 1(a)(b), 2(a)(b), 6, 15   &   pg 301: 6(a)(b)(c)   &   pg 306: 4(d)   &   pgs 311-312: 7, 11.
Hint: although some of these questions are in sections not covered in class, they can be done using the material covered in class.

03/15/16 &

03/17/16

SPRING BREAK

03/22/16

Read pgs 337, 339, 342-343.   Do pg 343: 1   & do H14-H17 & pgs 343-4: 3, 5-7, 9,   & H18 & pgs 344-345: 10, 20, 18.
Optional: 13 & 22 on pgs 344-345.

03/24/16

Read pgs 345-349.   Do pg 350: 1, 7   & do H19, H20 & read pgs 351-355 & do pg 356: 4, 8, 11 & H21 & H22.

03/29/16

No new homework.

03/31/16

No new homework.

04/05/16

Read pgs 112, 114-115 & do pgs 116-117: 1, 6(a).
Read pgs 118-120 & do pgs  121-122: 1(a), 14, 8 (hint: do not assume |G| finite, but consider G acting on the left cosets of H in G).

04/07/16

Read pgs 122-125.   Do pgs 130-132: 25, 10(a), 6, 13.
Test 3 is a week from today; see the information sheet for the test.

04/12/16

Do pgs 137-138: 2, 7, 15.
Test 3 on Thursday; see link to information sheet on April 7 above.

04/14/16

Test 3 today; see link to information sheet on April 7 above.
Read pgs 152-154.

04/19/16

Go over the solutions to Test 3; use password ``math5331'' to access the file.
Read pgs 142-146  
& do pgs 146-147: 13-16, 18, 19, 30.   Optional: 17 on pg 147.
Read pgs 152-154 if not already done so (needed before next lecture).

04/21/16

Read pgs 152-154 if not already done so & pg 158.

04/26/16

Read pgs 158-165   & do pgs 165-166: 1(a)-(c), 2(a)-(d), 3(a)-(d), 4(a),(b), & do   H23, H24   &   do pg 198: 8.

04/28/16

No new homework.
Complete the student feedback survey by 11 pm Friday May 6 – check your mymav email for the link;
they are anonymous and instructors don't get to read them until after the grades are submitted.

05/03/16

Read pgs 193-195 & Theorem 11 on pg 196   &   do   H25, H26.
Complete the
student feedback survey by 11 pm Friday May 6 – check your mymav email for the link;
they are anonymous and instructors don't get to read them until after the grades are submitted.

05/05/16

No new homework.

Complete the student feedback survey by 11 pm Friday May 6 – check your mymav email for the link;
they are anonymous and instructors don't get to read them until after the grades are submitted.

05/07/16
Approx 3:30-5:00 pm:  office hours in PKH 462.
05/09/16
Approx 3:30-5:00 pm:  office hours in PKH 462.
05/10/16
Approx 3:00-4:15 pm:  office hours in PKH 462.
FINAL TEST  today, starting at 5:30 pm; see the information sheet.
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