01/17/17

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
read    https://www.jeffreybennett.com/pdf/How_to_Succeed_general.pdf  for ideas on how to study most effectively.

Read lecture notes & do Sec 18 pgs 174/5: 1, 3, 5, 7, 9, 11.

01/19/17

Read lecture notes, pages 167-174 & do Sec 18 pgs 175/6: 14, 16, 19, 20, 31, 38,
46 (hint: think binomial theorem from Math 1302; or see here), 22, 27, 23, 40.

01/24/17

Read lecture notes & Sec 19 & do Sec 19 pgs 182/3: 14, 23, 24, 28, 5-12, 27, 29.
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.

01/26/17

Read lecture notes & Sec 20 up to pg 187.5 & do Sec 20 pgs 189/90: 1-3, 5, 24, 23a-h (justify answers).

01/31/17

Read lecture notes & Sec 21 & do Sec 21 pgs 196-7: 1, 2, 7, 8, 12, 14.

02/02/17

To finish Section 22, notice that the kernel of the evaluation map Φα consists of those polynomials that 
evaluate to zero on α. So if, e.g., the field F = ℚ and the field  E = ℝ, then  x2 + x - 6  belongs to the kernel
of Φ2, since x2 + x - 6 evaluated at α = 2 is zero.
Moreover, also notice that it is possible for a polynomial f ϵ F[x] to have no zero at all in the field F; 
e.g., f =  x2 - 2 ϵ ℚ[x]  has no zero in ℚ.
This finishes Section 22; we will start off Tuesday's lecture with Section 23.
Read lecture notes & Sec 22 & do Sec 22 pgs 207-8: 1-6, 22, 25, 7, 8, 14, 20.

The  Quiz  will be one week from today & will cover Sections 18-22; see the information sheet.

02/07/17

Read lecture notes & pgs 209-213 & do Sec 23 pgs 218-220: 2, 4, 35, 36, 9, 10.
Quiz  on Thursday;  see Feb 2 above for details.

02/09/17

Quiz  today; see Feb 2 above for details.
Read lecture notes & pgs 209-213 & do Sec 23 pgs 218-220: 34, 14, 16, 18, 6, 27, 28.

Test 1  will be one week from today; it will cover Sections 18-23; see the information sheet.
Look over quiz and its solutions to study for Test 1; use password  "math4321" to open the file.

02/14/17

Read lecture notes & pgs 224.5-226 & do Sec 24 pgs 226-7: 14, 5, 4, 6, 10.  
Test 1  on Thursday;  see Feb 9 above for details.

02/16/17

Test 1  today; see Feb 9 above for details. 
Read lecture notes & Sec 26 & do Sec 26 pgs 243-5: 2, 17, 18, 29, 37, 38(a)(b), 4, 12-14, 24 (hint: see #18).

02/21/17

Look over Test 1 and its solutions; use password  "math4321" to open the file.
Read lecture notes & Sec 26 & do Sec 26 pgs 243-5:  22(a)(c), 25, 26, 32.

02/23/17

Read pgs 245-7 & lecture notes & do Sec 27 pgs 252-4: 1 (max ideals only), 2 (max ideals only), 34, 35, 37.

02/28/17

Learn box on pg 248. Read lecture notes & Sec 27 & do 
Sec 27 Pgs 252-4: 1, 2, 24, 14(a)(b)(f), 31, 5, 6, 30.

03/02/17

Read lecture notes & pgs 265-9 & do Sec 29 pgs 272-4: 1, 2, 4, 6 (Hint: E. Criterion), 
11, 12, 14, 21, 27.

03/07/17

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

03/09/17

To address Darshan's question today about linear dependence: finitely many vectors, v1, v2, …, vn, are
linearly dependent means that there exist scalars, a1, a2, …, an, not all zero,  such that  a1 v1 + a2 v2 +···+an vn = 0.
Infinitely many vectors, u1, u2, …, are linearly dependent means that finitely many of them ( ui₁, ui₂, …, where
ij ≠ ik for all j ≠ k) are  linearly dependent. 

Read lecture notes & Sec 30 & do Sec 30 pgs 280-2: 15(a)-(d) (justify), 
25 (note: "transformation" = "map"), 1, 2, 4, 6, 7, 19.
Test 2  will be 2 weeks from today; see Mar 14-16 for details.

03/14/17 
and
03/16/17

SPRING BREAK
Go over the Quiz and Test 1 and read over all lecture notes from start of semester until now.   
Watch this TED talk on symmetry and algebra.
Test 2 is on Thurs Mar 23; it will cover through Sec 30 inclusive – see the information sheet.

03/21/17

Read lecture notes & pgs 283-286 & do 
Sec 31 pgs 291-3: 1-3, 5, 7, 9, 11, 13, 19(a)-(c), 22, 28, 29.
Test 2 is on Thurs; see Mar 14-16 above for details.

03/23/17

Test 2 today; see Mar 14-16 above for details.
Read lecture notes & pgs 286-289.
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.

03/28/17

Read lecture notes & pgs 286-289 & do 
Sec 31 pg 293: 35 (hint: show that the squaring function is not one-to-one nor onto).
Read lecture notes & Sec 33 & do Sec 33 pgs 304-5: 8(a),(g)(justify), 11.
Look over Test 2 and its solutions; use password  "math4321" to open the file.

03/30/17

Read lecture notes & Sec 33 & do Sec 33 pgs 304-5: 1, 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 on Tuesday in class with the example
drawn from Sec 29 #18.)

04/04/17

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

04/06/17

Read lecture notes & Sec 48 & do Sec 48 pgs 422-4: 26, 15-21, 36(a),(b).
Test 3  will be one week from today; it will cover through Sec 48; see the information sheet.

04/11/17

Read lecture notes & Sec 49 & do Sec 49 pgs 430-1: 1-3, 7, 8(b)(d)(e) (justify), 13.
Test 3 is on Thurs; see April 6 above for details.

04/13/17

Test 3  today; see April 6 above for details.

04/18/17

Look over Test 3 and its solutions; use password  "math4321" to open the file. 
Read lecture notes & Sec 50 & do Sec 50 pgs 434-6: 1-5, 14(a)-(e),(j) (justify), 18, 21.

04/20/17

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

04/25/17

Read lecture notes & Sec 53 & do Sec 53 pgs 454-6: 1, 2, 11(a)(b), 13. 
Look over today's handout.

04/27/17

Look over Tuesday's handout.
Read lecture notes & Sec 53 & do Sec 53 pgs 454-6: 3, 4, 8, 11, 15(a)-(c),(e),(g) (justify).
Read Sec 56.

05/02/17

We will spend today's lecture finishing up loose ends, reviewing the course material and doing a practice test (written by class); no new homework. 
Complete online the student feedback survey by 11 pm on Fri May 5 -- check your mymav e-mail for the link.
I appreciate the feedback (e.g., projector vs whiteboard? quality of website? examples provided in lecture?); thank you!

05/04/17

No new homework; today's lecture will be a chance for you to ask questions and/or doing a practice test (written by class).
Complete online the student feedback survey by 11 pm on Fri May 5 -- check your mymav e-mail for the link.
I appreciate the feedback (e.g., projector vs whiteboard? quality of website? examples provided in lecture?); thank you!

05/08/17
3:15 PM

Office hour today from 4:45 pm until 6:30 pm in PKH 462.
This is time Dr V is planning to be in her office for students to drop by to ask questions.

05/09/17

FINAL TEST  today, starting at 2:00 pm; see the information sheet.