Book =

A First Course in Abstract Algebra, 7th Ed, by J. B. Fraleigh, Addison-Wesley.
(Note: not the new 8th edition!!)
See our course's Canvas portal for options.

Jan 18

Attendance will be noted, starting today.
Check your Canvas notifications to check you can receive Canvas announcements and Canvas notification of BBB 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 these study techniques 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 18 on Canvas BBB page (1 or 2 minutes were added at the end to comment on required reading).
This video can also be found on the Canvas Modules page.

Required reading: read “chit-chat”, theorem statements, examples and definitions in Section 34 (proofs not needed in this section).

Jan 20

Watch (or possibly rewatch) the video for Jan 20 on Canvas BBB page; this video can also be found on the Canvas Modules page (it runs about 10-15 minutes beyond where the lecture terminated).
Read your lecture notes & Sec 18 & do Sec 18 pgs 174-6: 1, 3, 5, 7, 9, 11.
Read the required reading assigned Jan 18 (if not done so yet).

Jan 25

Watch (or possibly rewatch) the video for Jan 25 on Canvas BBB page; this video can also be found on the Canvas Modules page.
Read your lecture notes & Sec 18 & do Sec 18 pgs 174-6: 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).
Read the required reading assigned Jan 18 (if not done so yet).

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 27

Watch (or possibly rewatch) the video for Jan 27 on Canvas BBB page; this video can also be found on the Canvas Modules page.
Read your lecture notes & Sec 19 &
do Sec 19 pgs 182/3: 14, 23, 24, 28, 5-12, 27, 29.
Watch the video “Section 20” in Canvas Modules and read Sec 20 up to pg 187.5 &
do Sec 20 pgs 189/90: 1-3, 24, 5, 23a-h (justify answers).
The Quiz will open 1 week from today; see Canvas for an information sheet.

Feb 01

Watch (or possibly rewatch) the video for Feb 1 on Canvas BBB page; this video can also be found on the Canvas Modules page.
Read your lecture notes & Sec 21 &
do Sec 21 pgs 196-7: 1, 2, 7, 8,, 12, 14.
The Quiz will open on Thursday; see Canvas for an information sheet.

Feb 03

LECTURE CANCELLED BY ORDER OF UTA (inclement weather).
(See e-mail sent Feb 2.)
Lectures resume on Tuesday, on campus, in PKH 109.

The Quiz opens today; see Canvas for an information sheet.
Test 1 will be 1 week from today; see Canvas for an information sheet.

Feb 08

Read your lecture notes & Sec 22 &
do Sec 22 pgs 207-8: 1-6, 22, 25.

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 18 above and see which one(s) might work for you.
Test 1 will be on Thursday; see Canvas for an information sheet.

Feb 10

Test 1 today; see Canvas for an information sheet.

Read your lecture notes & Sec 22 & do Sec 22 pgs 207-8: 7, 8, 14, 20.

Feb 15

Read your lecture notes & pgs 209-212.
Do Sec 23 pgs 218-220: 2, 4, 35, 36, 9, 10, 6.

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 18 above and see which one(s) might work for you.

Feb 17

Read your lecture notes & Sec 23.
Do Sec 23 pgs 218-220: 34, 14, 16.

Feb 22

Read your lecture notes & Sec 23 & pgs 224.5-226. Also watch the video re Section 24 in "After-Class Videos” in Canvas Modules.
Do Sec 23 pgs 218-220: 18, 27, 28  &
Sec 24 pgs 226-7: 14, 5, 4, 6, 10.

Feb 24

LECTURE CANCELLED BY ORDER OF UTA (inclement weather).
Lectures resume on Tuesday, on campus, in PKH 109.

Mar 01

Read your lecture notes & Sec 26. Also watch the video re Section 26 in "After-Class Videos” in Canvas Modules.
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.

Mar 03

Read your lecture notes & pgs 245-7 & learn box on pg 248. Also watch the video re Section 27 in "After-Class Videos” in Canvas Modules.
Do Sec 27 pgs 252-4: 34, 35, 37,, 1, 2, 24,, 14(a)(b)(f).

Test 2 will be 1 week from today; see Canvas for an information sheet.
Look over the Quiz and Test 1 and their solutions on Canvas to study for Test 2; use password "math4321" to open the solution files.
(If you have trouble opening the pdf files, send an email to Dr. Vancliff about it.)

Mar 08

Read your lecture notes & pgs 245-7 & learn box on pg 248.

Theorem
Let p denote an irreducible polynomial in F[x], where F is a field. If p|gh, where g, h ∊ F[x], then p|g or p|h.
(We saw this theorem without a proof in Section 23, in order to illustrate that irreducible polynomials are the polynomial analog of prime numbers.)
Proof
Suppose p|gh, where g, h ∊ F[x]. It follows that gh ∊ <p>, which is a maximal ideal by the last theorem we proved in lecture today (Mar 8).
Since maximal ideals are prime ideals (by a theorem from lecture on March 3), we have g ∊ <p> or h ∊ <p>.
In the first case, p|g while, in the second case, p|h.          

Do Sec 27 pgs 252-4: 31, 5, 6, 30.

Test 2 will be on Thursday; see Canvas for an information sheet.
Look over Test 1 and its solutions on Canvas to study for Test 2; use password "math4321" to open the file.
(If you have trouble opening the pdf file, send an email to Dr. Vancliff about it.)

Mar 10

Test 2 today; see Canvas for an information sheet.

Watch the video re Section 29 in "After-Class Videos” in Canvas Modules.  Read pgs 265-7.

Mar 15

&

Mar 17

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 18 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 22

Read your lecture notes & pgs 265-9.
Do Sec 29 pgs 272-4: 1, 2, 4, 11, 12, 14, 6 (Hint: E. Criterion), 21.

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 18 above and see which one(s) might work for you.

Mar 24

Continuing from where we left off today with Section 19….

Case 2: suppose the element α is transcendental over the field F.
In this case, we had a result in the last lecture that tells us that the evaluation homomorphism ϕ_α is injective, and so ϕ_α(F[x]) is a subdomain of E.
The field of quotients of ϕ_α(F[x]) is the smallest field that contains ϕ_α(F[x]) (by Corollaries 21.8 and 21.9), so the field of quotients of ϕ_α(F[x]) is a subfield of E. (Similar to Case 1, we have that F is contained in ϕ_α(F[x]) and α = ϕ_α(x) ∊ ϕ_α(F[x]).)
We denote the field of quotients of ϕ_α(F[x]) by F(α), and it is the smallest field that contains F and α (which is analogous to what happens in Case 1, where α was algebraic over F).

Definition
Suppose F ≤ E are fields. If E = F(α), for some α ∊ E, then we call E a simple extension of F.

Read your lecture notes & pgs 265-9 and do Sec 29 pgs 272-4: 27, 13, 15, 18, 30, 31.

Watch the video re Section 30 in "After-Class Videos” in Canvas Modules.
Recall: if F ≤ E are fields, and if α ∊ E is algebraic over F and n = deg (α, F) , then our work in lecture and in the video implies that {1, α , α², …., α^n-1 } is a basis for F(α) over F.
Read your lecture notes & Sec 30.
Do Sec 30 pgs 280-2: 15(a)-(d) (justify), 25 (note: "transformation" = "map"), 1, 2, 4, 6, 7, 19.

If you found the TED talk linked above led to a broken link, retry it; it should (in theory) work now.

Mar 29

Read your lecture notes & pgs 283-286, especially the (First) Tower Theorem.
Do Sec 31 pgs 291-3: 1, 7, 2, 3, 5, 9, 11, 13, 19(a)-(c), 22, 28, 29.

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.

Mar 31

Read your lecture notes & pgs 286-289.
Do Sec 31 pg 293: 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 (S26,E11); are there any mistakes in the ``version’’ in that episode?

Apr 05

Read your lecture notes & Sec 33 and this file.
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 07

Read your lecture notes & Sec 48.
Do Sec 48 pgs 422-4: 1-3, 7-11, 13, 25.

Test 3 will be 1 week from today; see Canvas for an information sheet.
Look over the Quiz and Tests 1 & 2 and their solutions on Canvas to study for Test 3; use password "math4321" to open the solution files.
(If you have trouble opening the pdf files, send an email to Dr. Vancliff about it.)

Apr 12

Read your lecture notes & Sec 48.
Do Sec 48 pgs 422-4: 26, 15-21, 36(a),(b).

Test 3 will be on Thursday; see Canvas for an information sheet.
Look over the Quiz and Tests 1 & 2 and their solutions on Canvas to study for Test 3; use password "math4321" to open the solution files.
(If you have trouble opening the pdf files, send an email to Dr. Vancliff about it.)

Apr 14

Test 3 today; see Canvas for an information sheet.
No new homework today.

Apr 19

Read your lecture notes & Sec 49.
Do Sec 49 pgs 430-1: 1-3, 7, 8(b)(d)(e) (justify), 13.

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 18 above and see which one(s) might work for you.

Apr 21

Read your lecture notes & Sec 50.
Do Sec 50 pgs 434-6: 1-5, 14(a)-(e),(j) (justify), 18, 21.

Apr 26

Read your lecture notes & Sec 51.
Do Sec 51 pgs 442-4: 7, 15, 1-4, 9 ( hint: use E = F(α, β) ), 13,, 8(a)-(g)(justify).

Apr 28

Look over today's handout; this handout can also be found in Canvas under Modules and is called “ April 28 "handout" “.
Read your lecture notes & Sec 53.
Do Sec 53 pgs 454-6: 1, 2, 11(a)(b), 13,, 3, 4, 8, 11, 15(a)-(c),(e),(g) (justify).

Remember to complete online the student feedback survey by 11 pm Tuesday May 3 -- 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 online lectures in 1^st 3 weeks of semester, use of ipad for lectures, use of 2 video feeds for online lectures, use of Canvas, tests’ solutions, quality of corny jokes,…..); thank you!

May 03

We will spend today's lecture discussing Section 56 & reviewing the course material & discussing any questions from students.
Read your lecture notes & Sec 56. No new homework.

Remember to complete online the student feedback survey by 11 pm Tuesday May 3 -- 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 online lectures in 1^st 3 weeks of semester, use of ipad for lectures, use of 2 video feeds for online 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 10

FINAL TEST today, starting at 2:00 pm in PKH 109; see Canvas for an information sheet after April 29.