return to Spring 2025 MATH 4321 webpage
| Recommended textbook (required): |
A First Course in Abstract Algebra, 8th Ed., by J. B. Fraleigh & N. E. Brand, Pearson, 2021. |
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- Homework will not be collected.
- There might be more than one correct answer for any given question.
- Dates indicate homework assigned in lecture on that date. Dates for future assignments are tentative and subject to change.
- If you notice some questions are in a nonincreasing order, then it means that the order is recommended by your instructor and is usually chosen to match the order in which the material was presented in class.
- Any optional exercises are for those students who wish to explore some of the ideas in more depth – those questions are NOT game for the tests.
- Skimming through the main ideas in a section shortly before that section is covered in class should help you understand the lecture – try it!
- The homework from Spring 2023 can be viewed here; in particular, it will give you a rough outline of what material will be presented and how many lectures will be spent on each item.
- Recall that our test dates are: Feb 1-5 (online), Feb 6, Mar 6, April 10 and May 6.
- LAST REVISION: 4/17/25.
Read this guide for ideas on how to study most effectively.
| Jan 16 |
Read your lecture notes and Section 22, & do Sec 22 pgs 191-3: 1, 3, 5, 7, 9, 11, 33, 40, 48 (binomial theorem), 27. |
| Jan 21 |
Definition A subring of a ring R is a subset S of R that is itself a ring. A subfield of a field F is a subset S of F that is itself a field. Example: 2ℤ ≤ ℤ. Nonexample: {odd integers} is not a subring of ℤ. To prove S is a subring: show 0 ∈ S, a − b ∈ S, ab ∈ S. Do Sec 22 pgs 192-3: 22, 23, 14, 16, 19, 20, 42, 39. |
| Jan 23 |
Read your lecture notes & Sec 23 & do Sec 23 pgs 198-200: 20, 29, 30, 34, 11, 14-16. Quiz will open in 1 week; see Canvas for info. |
| Jan 28 |
Read your lecture notes & Sec 23 & do Sec 23 pgs 198-200: 5-10, 17-18, 33, 35. Watch “Section 24” video and read Sec 24, then do Sec 24 pgs 204-5: 1-3, 24, 5, 23a-h. Optional: skim Sec 25 (Fermat’s Little Theorem). Quiz will open on Friday. |
| Jan 30 |
Read your lecture notes & Sec 26 & do Sec 26 pgs 216-217: 1, 2, 7, 8, 12, 14. Quiz opens tomorrow. Tip: Don’t memorize theorems — practice until they become familiar. Test 1 will be 1 week from today. |
| Feb 04 |
Read your lecture notes & Sec 27 & Sec 28. Do Sec 27 pgs 225-227: 1-6, 22, 25, 7, 8, 14, 20 and Sec 28 pgs 235-237: 2, 4, 35, 36. Quiz is due tomorrow. Test 1 will be on Thursday. |
| Feb 06 |
Test 1 today. Read your lecture notes & Sec 28 & do Sec 28 pgs 235-237: 9, 10. |
| Feb 11 |
Read your lecture notes & Sec 28. Do Sec 28 pgs 235-237: 6, 34, 14, 27, 28. Review Test 1 solutions on Canvas. |
| Feb 13 | Read lecture notes and Sec 28 & do pgs 235-237: 16, 18. |
| Feb 18 | Read lecture notes & do Sec 32 pg 264: 14, 5, 4, 6, 10. |
| Feb 20 | Read lecture notes & Sec 30 & do Sec 30 pgs 248-250: 17, 37, 29, 18, 26, 31, 30, 34, 4, 12-14, 24, 25, 32. |
| Feb 25 | Read lecture notes & pgs 250-252 & do Sec 31 pgs 256-8: 25, 40, 36, 37, 39. |
| Feb 27 |
Read lecture notes & Sec 31. Do Sec 31 pgs 256-8: 1, 2, 26, 14(a)(b)(f), 15-19, 33, 5, 6, 32. Test 2 will be 1 week from today. |
| Mar 04 |
Read lecture notes & Sec 31 & Sec 33. Test 2 will be on Thursday. |
| Mar 06 |
Test 2 today. Read lecture notes & Sec 33. Do Sec 33 pgs 273-5: 15(a)-(d), 25, 1-6, 9, 19. |
| Mar 11 & Mar 13 |
SPRING BREAK Review quizzes & tests. Watch TED Talk on symmetry. |
| Mar 18 | Review Test 2 solutions. Review study techniques. |
| Mar 20 | Read lecture notes & Sec 39. Do Sec 39 pgs 317-319: 1, 2, 4, 11, 12, 14, 6, 21, 27, 13, 15. |
| Mar 25 | Read lecture notes & Sec 39. Do Sec 39 pgs 317-319: 18, 30, 31. |
| Mar 27 |
Read lecture notes & Sec 40. Do Sec 40 pgs 327-8: 1, 7, 2, 3, 5, 9, 11, 13, 19, 22, 28, 29, 35. Warning: Keep up with homework. |
| Apr 01 | Read lecture notes & Sec 42. Do Sec 42 pgs 339-340: 1, 9, 8(a)(c)(g), 11, 4, 15(a)-(f). |
| Apr 03 |
Read lecture notes & Sec 43. Do Sec 43 pgs 347-349: 1-3, 7, 8, 9-13, 25, 16-21, 38(a)(b). Test 3 will be 1 week from today. |
| Apr 08 |
Read lecture notes & Sec 44. Do Sec 44 pgs 355-357: 1-6, 10, 20(c)-(f)(j), 24, 26. Test 3 will be on Thursday. |
| Apr 10 | Test 3 today. |
| Apr 15 |
Read lecture notes & Sec 44. Do Sec 44 pgs 355-357: 11-13, 17, 22, 30. Review Test 3 solutions. |
| Apr 17 | Read lecture notes & Sec 45. Do Sec 45 pgs 363-364: 7, 8(a)-(c), 9, 12, 13. |
| Apr 22 | Read lecture notes & Sec 45. Do Sec 45 pgs 363-364: 8(i), 1-4. |
| Apr 24 |
Read lecture notes & Sec 46 & Sec 49. Do Sec 46 pgs 369-371: 1, 2, 11, 13, 3, 4, 8, 15. Complete student feedback survey by Apr 29. |
| Apr 29 |
Review session. Student feedback survey due today. Final Test on Tuesday May 6. |
| Apr 30 | Office hour today 4–6 pm in PKH 462. |
| May 01 | Office hour today 2–4 pm in PKH 462. |
| May 05 | Office hour today 1–2 pm online (Teams). |
| May 06 – 2:00 PM |
FINAL TEST today at 2 PM. Review all prior quizzes & tests. |
The homework from Spring 2023 can be viewed in its entirety here.