Math 3110 Section 101 Homepage
News & Announcements
04/XX Our Final Exam is Monday, May 2nd from 8am until 10:30am in our regular classroom WA 314.
This exam will be cumulative. I will allow one page of notes (one side of one sheet
of standard sized paper). 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.
Sadly, I won't be there! But you should!! [I am doing final judging for a contest
and won't be able to get back from Texas for our exam.] However, Sherry Nikbakht
has graciously offered to proctor for me. I hope to get back Monday afternoon/evening
and get exams graded with grades turned in the next day.
04/06 Homework #10 [Source: (.tex)] is due Friday, April 22nd.
04/06 Homework #9 [Source: (.tex)] is due Wednesday, April 13th.
Handouts...
Ring Definitions [Source: (.tex)]
Ring Examples [Source: (.tex)]
03/29 Test #3 is Monday, April 4th. We'll spend Friday'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...
Spring 2021 Test 3: all of it
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
03/21 Homework #8 [Source: (.tex)] is due Monday, March 28th.
Handout:
Direct Product Quotient Example [Source: (.tex)]
03/14 Homework #7 [Source: (.tex)] is due Monday, March 21st.
02/25 Test #2 is next Friday (March 4th). It will cover Chapters 4, 5, & 6.
[Roughly: Cyclic groups, permutation groups, & Isomorphisms]
Old tests can be found here.
Relevant or somewhat relevant tests/questions...
Spring 2021 Test #2: All of it.
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)
02/21 Reminder -- Homework #6 [Source: (.tex)] is due Wednesday, March 2nd.
02/18 Homework #5 [Source: (.tex)] is due Friday, February 25th.
Also, breaking with tradition, Homework #6 will be due the following Wednesday:
Homework #6 [Source: (.tex)] is due Wednesday, March 2nd.
However, Homework #5 is short and I'm posting Homework #6 early so you can
get a jump start on it (if you want).
02/14 Even vs. Odd & More [Source: (.tex)]
02/11 Homework #4 [Source: (.tex)] is due Friday, February 18th.
02/10 Test #1 is Wednesday (2/9). 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).
Overall, I plan to write a test very similar in style to Spring 2021, 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...
Spring 2021 Test #1: all of it.
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
01/28 Handout from today: ?Fun? Function Facts [Source: (.tex)]
Homework #3 [Source: (.tex)] is due Friday, February 4th.
01/21 Homework #2 [Source: (.tex)] is due Friday, January 28th.
Handout (for today):
The Euclidean Algorithm and Basic Number Theory (.pdf) [Source: (.tex)]
I have some old videos posted here.
The ones entitled "Divisbility and the Extended Euclidean Algorithm" (3 parts)
cover this entire handout. However, we'll be focusing on pieces of it - not the
whole thing.
Also, I wrote a couple of SageMath interactive webpages to automate the Extended
Euclidean Algorithm. They can be found here.
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 to our class. It covers the Euclidean algorithm and is about 56 minutes long.
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.
01/12 Homework #1 [Source: (.tex)] is due Friday, January 21st.
01/10 In case you've never watched it...
A Finite Simple Group of Order 2
by the Klein Four Group.
Handout (to use in a future class):
Examples of Groups Handout [Source: (.tex)]
01/05 Syllabus, Schedule, & Suggested Homework posted.
Suggested Homework [Source (.zip)]
10/11 Course Data
MAT 3110 Section 101
INTROD TO MOD ALG
MWF 09:00am-09:50am
WA 314
Final Exam:
TBD
Course Title & Description:
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Introduction to Modern Algebra
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 and RC 2001 (or equivalents).
Corequisite: MAT 2240.
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Any questions about this class?
Send me an email at cookwj@appstate.edu