Math 3110 Section 101 Homepage
News & Announcements
04/30 Final grades have been sent out. I hope to type up and post an answer key for the
final exam sometime soon.
If you ever have any questions about this class, other math classes, or whatever, my door
is open. Stop by anytime - even just to say "Hi"!
I hope you all have a great summer!
04/16 Homework #10 [Source: (.tex)] is due Friday, April 23rd.
04/14 Test #3 and is answer key are now posted here.
04/09 Homework #9 [Source: (.tex)] is due Friday, April 16th.
03/31 Handouts (for after Test 3)...
Ring Definitions [Source: (.tex)]
Ring Examples [Source: (.tex)]
03/29 Test #3 is Wednesday, April 7th. We'll spend Monday's class
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 2020 Test 3: all of it
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
03/24 I messed up an example in class today. So here's a detailed correction:
Direct Product Quotient Example [Source: (.tex)]
03/22 Homework #8 [Source: (.tex)] is due Monday, March 29th.
03/19 Test 2 was returned. It and its answer key are posted with the old exams: Exam Archive
03/15 Homework #7 [Source: (.tex)] is due Monday, March 22nd.
03/08 Relations Review (background for Chapter 7): Equivalence Relations and Partial Orders (.pdf) [Source: (.tex)]
Companion video: Equivalence Relations, Partition, and Partial Orders (75 mins)
03/05 Test #2 is next Friday (March 12th). It will cover Chapters 4, 5, & 6.
Old tests can be found here.
Relevant or somewhat relevant tests/questions...
Fall 2020 Test #2: All of it.
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)
03/03 Homework #6 [Source: (.tex)] is due Wednesday, March 10th.
02/26 Homework #5 [Source: (.tex)] is due Friday, March 5th.
02/24 Even vs. Odd & More [Source: (.tex)]
Test #1 and its answer key are posted here.
02/19 Homework #4 [Source: (.tex)] is due Friday, February 26th.
02/10 Don't forget that Homework #3 [Source: (.tex)] is due Friday, February 12th.
Test #1 is Wednesday (2/17). 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).
[I plan to discuss this on Friday.]
Overall, I plan to write a test very similar in style to Fall 2020, 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 2020 Test #1: all of it.
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
02/05 Homework #3 [Source: (.tex)] is due Friday, February 12th.
Don't forget that we have class online on Monday. I will be around
Tuesday morning to answer questions.
Monday = Watch videos "Generators and Relations (lightly)" and "Subgroups Introduction"
NOTE: Skip to minute 25 in the Generators and Relations video to pick up
where today's class left off.
02/03 I plan to record each class going forward. Links will be sent out via email
through AsULearn's "Announcement" feature. If you go to AsULearn and look at our
course under "Announcements", you should find previous announcements with video
links.
I referenced this "handout" in class today:
?Fun? Function Facts [Sourece: (.tex)]
Friday = Homework #2 due.
Monday = Sadly, we will be online. I will post video(s) to watch. Sorry! This one's my fault.
01/29 Homework #2 [Source: (.tex)] is due Friday, February 5th.
01/27 I have a couple of announcements/reminders/notes...
Unless something changes, we are slated to MEET IN PERSON MONDAY
(sorry to yell). So hopefully I will see you on Monday at 10am in
Howard Street Hall (HSH 103). I understand that some of you may
have move in time conflicts, etc. I plan on recording class and
sending out a link later that morning.
Homework #1 is due Friday (1/29/2021). Please scan/email me your
beautifully written up solutions. I plan to post Homework #2
(due the following Friday) by the end of this week.
01/25 Weekly Schedule & Suggested Videos:
Monday = "Order of an element and D4 geometrically"
Wednesday = "Divisbility and the Extended Euclidean Algorithm (part 2 of 3)"
[The other parts (i.e., parts 1 & 3) are optional.]
These videos correspond to the following 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.
Friday = "Z mod n and Units mod n"
[part of] "Groups from matrices"
Homework #1 [Source: (.tex)] is due.
Notes about the "number theory" video(s)...
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I have 3 videos covering some "basic number theory". The second video is most
relevant. It covers the Euclidean algorithm and is about 56 minutes long.
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).
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.
01/20 Homework #1 [Source: (.tex)] is due Friday, January 29th.
Videos for the week:
Today = [Optional] What is Abstract or Modern Algebra? (59 mins)
Group Axioms (43 mins)
Friday = Z mod n and Latin Square (36 mins)
Handout:
Examples of Groups Handout [Source: (.tex)]
01/18 In case you've never watched it...
A Finite Simple Group of Order 2
by the Klein Four Group.
01/11 Per the chancellor's announcement, class will meet online until
at least the beginning of February. I will send out more information
regarding meeting plans soon. For now, we should plan to meet via Zoom.
Course Data
MAT 3110 Section 101
INTROD TO MOD ALG
MWF 10:00am-10:50am
HSH 103 [if we ever start face-to-face]
Final Exam:
Friday, April 30th 8-10:30am
Any questions about this class?
Send me an email at cookwj@appstate.edu
Course Title & Description:
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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.
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Any questions about this class?
Send me an email at cookwj@appstate.edu