MATH 4321 HOMEWORK (Spring 2021)

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Book = A First Course in Abstract Algebra, 7th Ed, by J. B. Fraleigh, Addison-Wesley.
(Note: not the new 8th edition!!)

Jan 19

Attendance will be recorded, starting today.
Check your Canvas notifications to check you can receive Canvas announcements and Canvas notification of conference initiation.
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 Canvas course website.
Read https://vancliff.utasites.cloud/T/study.pdf and read https://www.jeffreybennett.com/pdf/How_to_Succeed_general.pdf for ideas on how to study most effectively.

Watch (or possibly rewatch) the video for Jan 19 on Canvas Conference page.

Jan 21

Read lecture notes & also watch (or possibly rewatch) the video for Jan 21 on Canvas Conference page.
Note that there are 2 recordings in Canvas conference for Jan 21; the shorter one covers material we did not have time to cover in lecture and students should watch that video too.

Do Sec 18 pgs 174/5: 1, 3, 5, 7, 9, 11.

Jan 26

Read lecture notes & Sec 18 & also watch (or possibly rewatch) the video for Jan 26 on Canvas Conference page.
Do Sec 18 pgs 175/6: 31, 38, 46 (hint: think binomial theorem from Math 1302; or see here), 22, 27, 23, 14, 16, 19, 20, 40
(order of questions is not random; recall remark above).

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 28

Read lecture notes & Sec 19 & also watch (or possibly rewatch) the video for Jan 28 on Canvas Conference page.
The end of the lecture recording has a small amount from Section 19 that we did not have time to cover in lecture.
Do Sec 19 pgs 182/3: 14, 23, 24, 28, 5-12, 27, 29.

Watch the video “Section 20” under Modules in Canvas and read Sec 20 up to pg 187.5 &
do Sec 20 pgs 189/90: 1-3, 24, 5, 23a-h (justify answers).

Feb 02

Read lecture notes & Sec 21 & also watch (or possibly rewatch) the video for Feb 2 on Canvas Conference page.
Do Sec 21 pgs 196-7: 1, 2, 7, 8,, 12, 14.
The Quiz will open 1 week from today; see Canvas for an information sheet.

Feb 04

Read lecture notes & Sec 22 & also watch (or possibly rewatch) the video for Feb 4 on Canvas Conference page.
The end of the lecture recording has a small amount from Section 22
that we did not have time to cover in lecture.
Do Sec 22 pgs 207-8: 1-6, 22, 25,, 7, 8, 14, 20.
The Quiz will open on Tuesday; see Canvas for an information sheet.

Feb 09

Read lecture notes & pgs 209-213 & also watch (or possibly rewatch) the video for Feb 9 on Canvas Conference page.
The end of the lecture recording has a small amount (8 minutes) from Section 23
that we did not have time to cover in lecture.
Do Sec 23 pgs 218-220: 2, 4, 35, 36, 9,
10, 6.

The Quiz opens today.

Test 1 will be 1 week from today Feb 23; see Canvas for an information sheet.

Feb 11

Read lecture notes & Sec 23 & also watch (or possibly rewatch) the video for Feb 11 on Canvas Conference page.
The end of the lecture recording has a small amount (15
minutes) from Section 23 that we did not have time to cover in lecture.
Do Sec 23 pgs 218-220: 34, 14, 16,, 18, 27, 28.

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 19 above and see which one(s) might work for you.
Test 1 will be on Tuesday Feb 23; see Canvas for an information sheet.

Feb 16

Owing to weather etc, Test 1 moved to Feb 25.
No lecture today per UTA instructions (to help conserve electricity).

Test 1 will be on Tuesday Feb 25; see Canvas for an information sheet.

Feb 18

No lecture today per UTA instructions (to help conserve electricity).

Test 1 will be on Thursday; see Canvas for an information sheet.

Feb 23

No lecture today – instructor ill.
Test 1 will be on Thursday; see Canvas for an information sheet.

Feb 25

Test 1 today online during lecture time – due 3:20 pm; see Canvas for an information sheet.
No new homework today.

Mar 02

Read lecture notes & pgs 224.5-226 & also watch (or possibly rewatch) the video for Mar 2 on Canvas Conference page.
Do Sec 24 pgs 226-7: 14, 5, 4, 6, 10.

Look over the solutions to Test 1 on Canvas; 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 19 above and see which one(s) might work for you.

Mar 04

Read lecture notes & Sec 26 & also watch (or possibly rewatch) the video for Mar 4 on Canvas Conference page.
The end of the lecture recording has a small amount (20 minutes) from Section 26 that we did not have time to cover in lecture.
Do Sec 26 pgs 243-5: 2, 17, 18, 29, 37, 38(a)(b), 4,, 12-14, 24 (hint: see #18),, 22(a)(c), 25, 26, 32.

Test 2 will be 1 week from today; see Canvas for an information sheet.

Mar 09

Read lecture notes & pgs 245-7 & learn box on pg 248. Watch (or possibly rewatch) the video for Mar 9 on Canvas Conference page.
The end of the lecture recording has 50 minutes extra from Section 27 that we did not have time to cover in lecture.
Do Sec 27 pgs 252-4: 34, 35, 37,, 1, 2, 24,, 14(a)(b)(f), 31, 5, 6, 30.

Test 2 will be on Thursday in PKH 105; see Canvas for an information sheet.

Mar 11

Test 2 today in PKH 105; see Canvas for an information sheet.
No new homework today.

Mar 16
&
Mar 18

SPRING BREAK
Go over the
Quiz & Tests 1 & 2 and their solutions on Canvas & read over all lecture notes & get caught up on watching the lecture recordings. Read through the suggestions of study techniques from Jan 19 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 23

Read lecture notes & pgs 265-9 & watch (or possibly rewatch) the video for Mar 23 on Canvas Conference page.
The end of the lecture recording has 45 minutes extra from Section 29 that we did not have time to cover in lecture.
Do Sec 29 pgs 272-4: 1, 2, 4, 11, 12, 14, 6 (Hint: E. Criterion), 21, 27,, 13, 15, 18, 30, 31.

Look over the solutions to Test 2 on Canvas; 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 19 above and see which one(s) might work for you.

Mar 25

Recall: if F ≤ E are fields, and if α ∊ E is algebraic over F and n = deg (α, F) , then our work in class today implies that {1, α , α2, …., αn-1 } is a basis for F(α) over F.
Read lecture notes & Sec 30 & also watch (or possibly rewatch) the video for Mar 25 on Canvas Conference page.
Do
Sec 30 pgs 280-2: 15(a)-(d) (justify), 25 (note: "transformation" = "map"), 1, 2, 4, 6, 7, 19.

Mar 30

Read lecture notes & pgs 283-289, especially the Tower Theorem, & also watch (or possibly rewatch) the video for Mar 30 on Canvas Conference page.
The end of the lecture recording has about 30 minutes extra from Section 31 that we did not have time to cover in lecture.
D
o Sec 31 pgs 291-3: 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 289 with the ``version’’ of Zorn's Lemma in the episode of The Simpsons that aired on Sunday April 5, 2015; 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 01

Read lecture notes & Sec 33 & also watch (or possibly rewatch) the video for April 1 on Canvas Conference page.
The end of the lecture recording has about 29 minutes extra from Section 33 that we did not have time to cover in lecture.
Do
Sec 33 pgs 304-5: 8(g)(justify), 1, 8(a)(justify), 11, 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 φ function (why?), or 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 29 #18).)

Apr 06

Read lecture notes & Sec 48 & also watch (or possibly rewatch) the video for April 6 on Canvas Conference page.
The end of the lecture recording has about 25-30 minutes extra from Section 48 that we did not have time to cover in lecture.
Do Sec 48 pgs 422-4: 1-3, 7-11, 13, 25,, 26, 15-21, 36(a),(b).

Test 3 will be next week on Tuesday and Thursday; see Canvas for an information sheet.

Apr 08

Read lecture notes & Sec 49 & also watch (or possibly rewatch) the video for April 8 on Canvas Conference page.
Do Sec 49 pgs 430-1: 1-3, 7, 8(b)(d)(e) (justify), 13.

Test 3 will be next week on Tuesday and Thursday; see Canvas for an information sheet.

Apr 13

Test 3 (part 1) today in PKH 105; see Canvas for an information sheet.
No new homework today.

Apr 15

Test 3 (part 2) today in PKH 105; see Canvas for an information sheet.
No new homework today.

Apr 20

Read lecture notes & Sec 50 & also watch (or possibly rewatch) the video for April 20 on Canvas Conference page.
Do Sec 50 pgs 434-6: 1-5, 14(a)-(e),(j) (justify), 18, 21.

Look over the solutions to Test 3 on Canvas; 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 19 above and see which one(s) might work for you.

Apr 22

Read lecture notes & Sec 51 & also watch (or possibly rewatch) the video for April 22 on Canvas Conference page.
Do
Sec 51 pgs 442-4: 7, 15, 1-4, 9 ( hint: use E = F(α, β) ), 13,, 8(a)-(g)(justify).

Apr 27

Look over today's handout; this handout can also be found in Canvas under Modules and is called “ April 27 "handout" “.
Read lecture notes & Sec 53 & also watch (or possibly rewatch) the video for April 27 on Canvas Conference page.
Do Sec 53 pgs 454-6: 1, 2, 11(a)(b), 13,, 3, 4, 8, 11, 15(a)-(c),(e),(g) (justify).

Apr 29

Read lecture notes & Sec 56 & also watch (or possibly rewatch) the video for April 29 on Canvas Conference page.
Look over the solution sheets for Tests 1-3.

Remember to complete online the student feedback survey by 11 pm Tuesday May 4 -- check your mymav e-mail for the link.
I appreciate the feedback (e.g., quality of website, quality of information sheets, quality of videos, quality of conference lectures, use of ipad for lectures, use of 2 video feeds for lectures, use of Canvas, tests’ solutions,
quality of corny jokes,…..); thank you!

May 04

We will spend today's lecture reviewing the course material & discussing any questions from students; no new homework.

Remember to complete online the student feedback survey by 11 pm today (Tuesday May 4) -- check your mymav e-mail for the link.
I appreciate the feedback (e.g., quality of website, quality of information sheets, quality of videos, quality of conference lectures, use of ipad for lectures, use of 2 video feeds for lectures, use of Canvas, tests’ solutions,
quality of corny jokes,…..); thank you!

Regular office hour times do not apply after today. See announcements in Canvas for times of office hours after today.

May 11

FINAL TEST today, starting at 2:00 pm in PKH 105; see Canvas for an information sheet after April 28.

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