Math 3110 Section 101 Homepage
News & Announcements
11/18 Final Exam!
For a weird end to a weird semester, I offer two options:
*) Take the final early (next Tuesday, November 24th 9:30am to noon-ish) face-to-face.
==> I think we can use our regular classroom WA 105, but haven't gotten a confirmation yet.
*) Take the final as scheduled (Friday, December 4th 11:00am to 1:30pm) via Zoom.
Either way, the final exam will be cumulative. I will allow one page of
notes. Make it count. Fill out theorems, examples, etc. that might be
helpful.
I have some old final exams posted here.
They should give you an idea of the kinds of things I might ask.
11/13 Homework #9 [Source: (.tex)] is due Friday, November 20th.
11/06 Test #3 graded. Test #3 and its answer key posted here.
11/04 Handouts:
Ring Definitions [Source: (.tex)]
Ring Examples [Source: (.tex)]
Homework #8 [Source: (.tex)] is due Friday, November 13th.
10/28 Test #3 is Monday (November 2nd). We'll spend most (or all) of class
Friday reviewing for the test.
Test #3 will cover chapters 7-11. This includes cosets, normal subgroups,
quotient groups, homomorphisms, the first isomorphism theorem, direct
products of groups, and the classification of finite abelian groups.
Old tests can be found here.
Relevant or somewhat relevant tests/questions...
Fall 2015 Test 3: all of it
Final Exam: 1a, 2a, 6a, 8, 9, 10
Spring 2015 Test 3: all of it
Final Exam: 1abc (just addition table in (b), 5b, 7, 8ab, 9c
Fall 2011 Test 2: 5
Test 3: all of it
Spring 2010 Test 2: 4cd, 5bc
Test 3: 2, 3
Fall 2009 Test 3: 2, 3, 5, 6
Final Exam: 2a, 5ab, 7, 8a
Spring 2009 Test 3: 2, 4, 5
Final Exam: 2, 4bc, 8
10/21 Homework #7 [Source: (.tex)] is due Wednesday, October 28th.
10/14 Homework #6 [Source: (.tex)] is due Wednesday, October 21st.
10/05 Relations Review (background for Chapter 7): Equivalence Relations and Partial Orders (.pdf) [Source: (.tex)]
Companion video: Equivalence Relations, Partition, and Partial Orders (75 mins)
10/02 Test #2 is next Friday (October 9th). It will cover Chapters 4, 5, & 6.
Old tests can be found here.
Relevant or somewhat relevant tests/questions...
Fall 2015 Test #2: All of it.
Final Exam: 2bc,4a,10
Spring 2015 Test #2: All of it.
Final Exam: 2,4a
Fall 2013 Midterm: 2-5,7c,9,10
Fall 2011 Test #2: 1-4.
Spring 2010 Test #2: 1,3,4b,5b
Fall 2009 Test #2: 3cd,4b,5,6
Final Exam: 1,3d,8bc
Spring 2009 Test #2: 3a,4,5
Final Exam: 2a,5,8a (ignore the kernel question)
09/29 Homework #5 [Source: (.tex)] is due Wednesday, October 7th.
09/23 Homework #4 [Source: (.tex)] is due Wednesday, September 30th.
Even vs. Odd & More [Source: (.tex)]
09/11 Test #1 is Wednesday. It will cover Chapters 0, 1, 2, 3, & part of Chapter 4.
We have covered the bulk of what is in Chapter 0, but I don't plan on asking questions
directly about this material. The one specific tool you need from this chapter is the
Extended Euclidean Algorithm.
All of Chapters 1, 2, and 3 are relevant.
We have not covered much of Chapter 4. The one specific thing I do want you to know from
this chapter is how to draw the subgroup lattice for Z mod n (under addition mod n).
[We did Z mod 12's lattice today at the end of class.]
Overall, I plan to write a test very similar in style to Fall 2015 and
Spring 2015's Test #1 as well as Fall 2013's Big Quiz #1.
Old homework, suggested homework, notes, and the textbook are all good things
to consider, but looking at old tests is probably the best way to study for
Wednesday's test.
Old tests can be found here.
Relevant or somewhat relevant tests/questions...
Fall 2015 Test #1: all of it.
Spring 2015 Test #1: all of it.
Fall 2013 Big Quiz #1: all of it.
Fall 2011 Test #1: all of it.
Test #2: 1a
Spring 2010 Test #1: all but 4a.
Test #2: 1(ignore the last line with S4),2,4a,5a
Fall 2009 Test #1: all but 5.
Test #2: 1-3,4a,5
Spring 2009 Test #1: all of it.
Test #2: 1-4
Final Exam: 6
09/02 Homework #3 [Source: (.tex)] is due Friday, September 11th Monday, September 14th.
?Fun? Function Facts [Sourece: (.tex)]
08/26 Homework #2 [Source: (.tex)] is due Wednesday, September 2nd.
08/24 I will be missing class today to attend my father's funeral. Instead of a lecture,
we'll have a video. Please watch the part 2 video below. It covers the Euclidean
algorithm. It's about 56 minutes long.
We will discuss some of what appears in part 3 later (probably on Wednesday). I was
intending on finishing up our D4 example, but that will have to wait until Wednesday.
I plan to hand out copies of the following related handout:
The Euclidean Algorithm and Basic Number Theory (.pdf) [Source: (.tex)]
Also, I wrote a couple of SageMath interactive webpages to automate the Extended
Euclidean Algorithm. They can be found here.
NOTE: While you are welcome to watch all three videos. I only intend you to
watch part 2. If you want to see a proof of the division algorithm, this appears
around 20 minutes into part 1 (right as the camera gets back into focus).
Video: Divisbility and the Extended Euclidean Algorithm (part 1 of 3) (33 mins)
[On part 1: SORRY! The camera went out of focus for a few minutes.
You can follow along by looking at the proof in the handout.]
WATCH --> Divisbility and the Extended Euclidean Algorithm (part 2 of 3) (56 mins)
Divisbility and the Extended Euclidean Algorithm (part 3 of 3) (55 mins)
Part 1 covers the Well Ordering Principle and how it relates to Math Induction.
Then the Division Algorithm is proven.
Part 2 covers some basic number theory, definitions of gcd/lcm, the extended Euclidean algorithm,
and some results about facotoring into primes.
Part 3 covers "basics" about modular arithmetic and some examples of computing multiplicative
inverse mod n. Bonus: how to rationalize a denominator using the Euclidean algorithm.
08/19 Homework #1 [Source: (.tex)] is due Wednesday, August 26th Friday, August 28th.
Handout:
Examples of Groups Handout [Source: (.tex)]
08/17 I do intend to record each class. I just emailed a link to today's
video but unfortunately stupid Zoom mirrored it. Hopefully, that
won't be a problem in the future.
Also, as mentioned in class, I will make a few minor fixes to our syllabus very soon.
08/06 Course Data
MAT 3110 Section 101
INTROD TO MOD ALG
MWF 12:00pm-12:50pm
WA 108 105
Any questions about this class?
Send me an email at cookwj@appstate.edu
Course Title & Description:
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Topics covered include equivalence relations, groups, subgroups,
homomorphisms, isomorphisms, and a survey of other algebraic
structures such as rings, integral domains, and fields.
Prerequisites: MAT 2110 or MAT 2510, and R C 2001 or its equivalent.
Corequisite: MAT 2240.
-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
Any questions about this class?
Send me an email at cookwj@appstate.edu
In case you've never watched it...
A Finite Simple Group of Order 2
by the Klein Four Group.
Stuff for LATER and MUCH LATER...
[?Check for updated versions from 2110 honors?]
Equivalence Relations and Partial Orders (.pdf) [Source: (.tex)]
The Euclidean Algorithm and Basic Number Theory (.pdf) [Source: (.tex)]
Even and Odd Permutations (.pdf)
Alternating Groups (.pdf)
[I will distribute pages 3-4 from the above handout. They cover the alternating A4's
subgroups and quotients (as an extended example). That handout was created for a
more advanced class and contains some extra information which isn't directly
relevant to us.]
Ring Definitions
Ring Examples