return to Spring 2023 MATH 4321 webpage
| Recommended textbook (required): |
A First Course in Abstract Algebra, 8th Ed, by J. B. Fraleigh & N. E. Brand, Pearson, 2021. |
- You should make sure you are viewing the most current version of this page (i.e., the first table below) and not the version in your browser’s cache; reload the page from source or clear the cache and reload.
- 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 assignments below are essentially the assignments found here from Spring 2022, but we are using the 8th edition of the textbook, so the page numbers and section numbers do not match those at that website.
- Recall that our test dates are: Feb 2-8 (online), Feb 9, Mar 9, April 13, May 9.
- LAST REVISION: 4/27/23.
| Jan 17 | Check your Canvas notifications to check you can receive Canvas announcements. Attendance will be noted, 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. Review the course’s Canvas portal. Read these study techniques and read https://www.jeffreybennett.com/pdf/How_to_Succeed_general.pdf for ideas on how to study most effectively. Read your lecture notes (meaning the notes you should have taken during lecture) and do Sec 22 pg 191: 1, 3, 5, 7, 9, 11. |
| Jan 19 | Read your lecture notes and Section 22, & do Sec 22 pgs 192-3: 33, 40, 48 (hint: think binomial theorem from Math 1302; or see here), 22, 27, 23. (order of questions is not random; recall remark above) |
| Jan 24 | Read your lecture notes and Section 22 and do Sec 22 pgs 192-3: 14, 16, 19, 20, 42, 39. 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 so that the results of the theorems become known to you, though perhaps with different wording or using pictures. |
| Jan 26 | Read your lecture notes & Sec 23 & do Sec 23 pgs 198-200: 20, 29, 30, 34, 5-11, 14-18, 33, 35. Watch the video “Section 24” in Canvas Modules and read Sec 24 through pg 202 & do Sec 24 pgs 204-5: 1-3, 24, 5, 23a-h (justify answers). Optional: I also suggest that y’all skim Section 25 to see how Fermat’s Little Theorem is used in cryptology. If we have time at the end of the semester, we will briefly discuss Section 25. The Quiz will open 1 week from today; see Canvas for an information sheet. |
| Jan 31 | Read your lecture notes & Sec 26 & do Sec 26 pgs 216-217: 1, 2, 7, 8,, 12, 14. The Quiz will open on Thursday; see Canvas for an information sheet. |
| Feb 02 | Read your lecture notes & Sec 27 & do Sec 27 pgs 225-227: 1-6, 22, 25,, 7, 8, 14, 20. The Quiz opens today; see Canvas for an information sheet. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Test 1 will be 1 week from today; see Canvas for an information sheet. |
| Feb 07 | Read your lecture notes & Sec 28 & do Sec 28 pgs 235-237: 2, 4, 35, 36, 9, 10, 6. Look over the quiz and its solutions on Canvas to study for Test 1; use password “math4321” to open the file. (If you have trouble opening the pdf file, send an email to Dr. Vancliff about it.) Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Test 1 will be on Thursday; see Canvas for an information sheet. |
| Feb 09 | Test 1 today; see Canvas for an information sheet. Read your lecture notes & Sec 28 & do Sec 28 pgs 235-237: 34, 14, 16. |
| Feb 14 | Read your lecture notes & Sec 28 & do Sec 28 pgs 235-237: 18, 27, 28. Look over the solutions to Test 1 on Canvas; use password “math4321” to open the file. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. |
| Feb 16 | Read your lecture notes & do Sec 32 pg 264: 14, 5, 4, 6, 10. |
| Feb 21 | Read your lecture notes & Sec 30 & do Sec 30 pgs 248-250: 17, 37, 29, 18,, 26, 31, 30, 34,, 4, 12-14, 24 (hint: see #18), 25, 32. |
| Feb 23 | Read your lecture notes & pgs 250-252 & do Sec 31 pgs 256-8: 25, 40, 36, 37, 39. |
| Feb 28 | Read your lecture notes & Section 31 & learn the 3 facts on page 253 (just prior to Prime Fields). Do Sec 31 pgs 256-8: 1, 2, 26, 14(a)(b)(f), 33. |
| Mar 02 | Read your lecture notes & Section 31. Do Sec 31 pgs 256-8: 5, 6, 32. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Test 2 will be 1 week from today; see Canvas for an information sheet. |
| Mar 07 | Read your lecture notes & Section 33. Do Sec 33 pgs 273-5: 15(a)-(d) (justify), 25 (note: “linear transformation” is defined in #24), 1-6, 9, 19. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Test 2 will be on Thursday; see Canvas for an information sheet. |
| Mar 09 | Test 2 today; see Canvas for an information sheet. |
| Mar 14 & Mar 16 |
SPRING BREAK Go over the Quiz & any tests and their solutions on Canvas & read over all lecture notes & get caught up on watching any lecture recordings/videos. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Get caught up on all homework!! Watch this fun TED talk on symmetry and algebra. |
| Mar 21 | Read your lecture notes and Sec 39. Look over the solutions to Test 2 on Canvas; use password “math4321” to open the file. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. |
| Mar 23 | Read your lecture notes & Sec 39 and do Sec 39, pgs 317-319: 1, 2, 4, 11, 12, 14, 6 (hint: E. Criterion), 21, 27, 13, 15. |
| Mar 28 | Read your lecture notes & Sec 39 and do Sec 39, pgs 317-319: 18, 30, 31. |
| Mar 30 | Read your lecture notes & Sec 40, especially the Tower Theorem. Watch the video “A Few Results from Section 40” in Canvas Modules. Do Sec 40 pgs 327-8: 1, 7, 2, 3, 5, 9, 11, 13, 19(a)-(c), 22, 28, 29, 35 (hint: show that the squaring function is neither one-to-one nor onto). Optional exercise: compare Zorn’s Lemma on page 325 with the “version’’ of Zorn’s Lemma in the episode of The Simpsons that aired on Sunday April 5, 2015 (S26,E11); are there any mistakes in the “version’’ in that episode? Warning: it is very important that you keep up with the homework at this point; there will be a lot of new concepts and you will need fluency with the terminology and notation. |
| Apr 04 | Read your lecture notes & Sec 42. Watch the video “A Few Results from Section 42” in Canvas Modules. Do Sec 42 pgs 339-340: 8(g)(justify), 1, 9 (hint: see pg 336), 8(a)(justify), 11, 8(c)(justify), 4 (hint: there are many ways to do this question: (i) you could read the statement of Thm 42.10 and either use Euler’s φ function (why?), or (ii) you could write down a generic field with 9 elements using an element α 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 α (we did something like this 2nd method in class with the example drawn from Sec 39 #18)), 15(a)-(f). |
| Apr 06 | Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Test 3 will be 1 week from today; see Canvas for an information sheet. |
| Apr 11 | Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. Test 3 will be on Thursday; see Canvas for an information sheet. |
| Apr 13 | Test 3 today; see Canvas for an information sheet. |
| Apr 18 | Read your lecture notes & Sec 43 and watch the video “One Result from Section 43” in Canvas Modules. Do Sec 43 pgs 347-349: 1-3, 7, 8, 9-13, 25, 16-21, 38(a)(b). Look over the solutions to Test 3 on Canvas; use password “math4321” to open the file. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. |
| Apr 20 | Note that if ψ : F ⟶ F′ is a field homomorphism, and if φ : E ⟶ E′ is another field homomorphism, where F ≤ E and F′ ≤ E′, such that φ|F = ψ, we say that ψ extends to E and that φ is an extension of ψ to E. Read your lecture notes & Sec 44 and watch the videos on Sec 44 that should appear in Canvas Modules by the end of Friday April 21. Do Sec 44 pgs 355-357: 1-6, 10, 20(c)-(f),(j) (justify), 24, 26, 11-13, 17, 22 (see the last 2 videos), 30 (see the last video). |
| Apr 25 | Read your lecture notes & Sec 45 and do Sec 45 pgs 363-364: 7, 8(a)-(c),(i) (justify), 9, 12, 13, 1-4. |
| Apr 27 | Look over today’s handout; this handout can also be found in Canvas under Modules > Relevant Links, and is called “April 27 handout”. Read your lecture notes & Sec 46 and do Sec 46 pgs 369-371: 1, 2, 11(a)-(c), 13,, 3, 4, 8, 11, 15(a)-(c),(e),(g) (justify). Please remember to complete online the student feedback survey by 11 pm on May 2 — check your mymav e-mail for the link. I appreciate the feedback (e.g., use of website, the use of Canvas, the choice of homework questions from the book and/or any questions not from the book, the information sheets and/or the solution sheets for the tests, the examples provided in class, use of any videos, corniness of jokes …??). Thank you! |
| May 02 | We will spend today’s lecture discussing Section 49 & reviewing the course material & discussing any questions from students. Read your lecture notes & Sec 49. No new homework. Please remember to complete online the student feedback survey by 11 pm today — check your mymav e-mail for the link. I appreciate the feedback (e.g., use of website, the use of Canvas, the choice of homework questions from the book and/or any questions not from the book, the information sheets and/or the solution sheets for the tests, the examples provided in class, use of any videos, corniness of jokes …??). Thank you! The Final Test will be on Tuesday May 9; see Canvas for an information sheet. Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. I will have my usual office hours through today inclusive; after today, I will have office hours as noted below. |
| May 03 2:00 PM |
Office hour today 2:00-3:00 pm on Teams only – see Canvas announcements for the Teams link. This is time the instructor is planning to be on Teams for students to “drop by” to ask questions. |
| May 04 2:00 PM |
Review Session with Chris in PKH 485 today 2:00-3:30 pm. |
| May 05 12:45 PM |
Office hour today 12:45-1:45 pm in-person in PKH 462 and on Teams – see Canvas announcements for the Teams link. This is time the instructor is planning to be in PKH 462 and on Teams for students to “drop by” to ask questions. |
| May 06 3:00 PM |
Office hour today 3:00-4:00 pm on Teams only – see Canvas announcements for the Teams link. This is time the instructor is planning to be on Teams for students to “drop by” to ask questions. |
| May 08 11:00 AM |
Office hour today 11:00-11:59 am on Teams only – see Canvas announcements for the Teams link. This is time the instructor is planning to be on Teams for students to “drop by” to ask questions. |
| May 09 1:00 PM |
Office hour today 1:00-1:30 pm in-person in PKH 462 and on Teams – see Canvas announcements for the Teams link. This is time the instructor is planning to be in PKH 462 and on Teams for students to “drop by” to ask questions. |
| May 09 2:00 PM |
FINAL TEST today, starting at 2:00 PM; see Canvas for an information sheet. Remember to look over Tests 1-3 and the Quiz and their solutions posted on Canvas when you study for this test. (Pay attention to how the solutions on the solution sheets are written; e.g., the level of detail provided in each solution.) Read through the suggestions of study techniques from Jan 17 above and see which one(s) might work for you. |
Recall that the assignments from Spring 2022 can be viewed here .