University of Connecticut College of Liberal Arts and Sciences
Department of Mathematics
Tom Roby's Math 3230 Home Page (Fall 2014)
Abstract Algebra I

Questions or Comments?

Class Information

COORDINATES: Classes meet Tuesdays and Thursdays 12:30–1:45 in MSB 303. The registrar calls this Section 001.

PREREQUISITES: MATH 2710 or MATH 2142. I will assume you have some ability to read and write proofs, particularly proofs by mathematical induction. You should also have familiarity with equivalence relations, modular arithmetic, and functions being 1-1/onto. This is all covered in Chapter 0 of the text, which you can review on your own as necessary (for a quiz on Tuesday of Week 2).

TEXT: Joe Gallian: Contemporary Abstract Algebra, 8th Edition. (This website has supplements as well as basic bibliographic information).

WEBPAGE: The homepage for this course is Some others web resources are listed below.

SOFTWARE: While doing some computations by hand is generally essential for learning, having software that can do bigger computations or check your work is very useful. One free source on the web is WolframAlpha. For a full-fledged programming environment, check out the free open-source computer algebra system called Sage, which has a number of commands useful for abstract algebra. See the tutorial Group Theory and Sage by Rob Beezer. We may also try out SageMathCloud.

GRADING: Your grade will be based on one midterm exam, one final exam, weekly quizzes and homework.

The breakdown of points is:

HW Quizzes Midterm Final
10% 20% 30% 40%

MIDTERM EXAM: Will cover all the material up to that point in the term. It is currently scheduled for THURSDAY 21 OCTOBER 2014 during our usual class meeting. Please let me know immediately if you have a conflict with that date. There are no makeup exams.

QUIZZES: Quizzes will be given roughly once per week on TUESDAYS, covering the material from the HW handed in the previous THURSDAY. The best way to prepare for them is to do more exercises than I've assigned. The first quiz will be Tuesday 2 September, covering prerequisite material from Chapter 0.

HOMEWORK: Homework will be assigned most weeks, and should be attempted by the following TUESDAY, when I will be happy to answer questions or provide hints. It will generally be due Thursdays at the start of class. Since I may discuss the homework problems in class the day they are due, late assignments will be accepted only under the most extreme circumstances. (Please let me know as soon as possible if you find yourself with a situation that might qualify.) The lowest written homework score will be dropped in any event.

The book has many exercises for each chapter, and I recommend you also attempt a number of the odd-numbered exercises, whose answers are in the back. If you get stuck on one, feel free to ask!

You may find some homework problems to be challenging, even frustrating, leading you to spend lots of time and effort working on them. This is a natural part of doing mathematics, faced by everyone from school children to top researchers. I encourage you to work with other people in person or electronically. It's OK to get significant help from any resource, but in the end, please write your own solution in your own words. Copying someone else's work without credit is plagiarism and will be dealt with according to university policy. It also is a poor learning strategy.

ACADEMIC INTEGRITY: Please make sure you are familiar with and abide by The Student Code governing Academic Integrity in Undergraduate Education and Research. For quizzes and exams you may not discuss the material with anyone other than the instructor or offical proctor, and no calculators, phones, slide rules or other devices designed to aid communication or computation may be used.

ACKNOWLEDGEMENTS: Many people have influenced my approach to this material, particularly Arnold Ross & Keith Conrad. Some of the links on this page were gleaned from one of the latter's earlier homepages for this course.

CONTENT: Abstract Algebra is a core subject within the undergraduate math major. The basic objects of study are groups, rings and fields, specific examples of which abound in all kinds of mathematics. From very small sets of axioms one builds mathematical theories of great richness and wide applicability. See the web resources below for more information.

This semester we plan to cover at least the main chapters on group theory (chapters 1–11 and 24). We may do more as time permits. The second semester in this sequence, Math 3121, covers rings, fields, and Galois Theory, which is fundamental material for anyone planning to continue on to graduate work in mathematics.

ACCESSIBILITY & DISABILITY ISSUES: Please contact me and UConn's Center for Students with Disabilities as soon as possible if you have any accessibility issues, have a (documented) disability and wish to discuss academic accommodations, or if you would need assistance in the event of an emergency.

LEARNING: The only way to learn mathematics is by doing it! Complete each assignment to the best of your ability, and get help when you are confused. Come to class prepared with questions. Don't hesitate to seek help from other students. Sometimes the point of view of someone who has just figured something out can be the most helpful.

Especially for learning this subject, it is important to do lots of problems—many more than I could reasonably assign you to hand in. The text has a number of problems ("Exercises") with solutions for you to try to test your understanding.

READING INCENTIVE: When you prepare for class, you may fill up to one side of an 8.5 x 11-inch sheet of paper with any handwritten notes from the assigned reading you wish. I will collect these, and return them to you to use on the midterms or final as crib sheets. Make sure you put your name on these! Since this is an incentive for you to come to class prepared, I will only accept notes on previously covered sections if you had an excused absence.

CLASSTIME: We will sometimes spend classtime doing activities in groups (as well as on groups!), presenting mathematics to one another, or having interactive discussions. There will not be time to "cover" all material in a lecture format so you will need to read and learn some topics on your own from handouts, web sources, or otherwise.

SCHEDULE: The following is the start of a tentative schedule that I will update throughout the semester. If you have a religious observance that conflicts with your participation in the course, please meet with me within the first two weeks of the term to discuss any appropriate accommodations.

Date Chapter Topics HW, etc.
8/26 T Ch. 1 Introduction to Groups HW1: Ch. 1: #2, 3, 6, 12, 24.
8/28 R Ch. 2 Groups: Axioms & Examples HW1: Ch. 2: #14, 18, 22, 28, 30, 36, 38, 44, 48, 54.
9/2 T Ch. 3 Finite Groups; Subgroups HW2: Ch. 3: #2, 4, 10, 12, 26, 28, 32, 34;
9/4 R Ch. 3 Subgroups HW2: Ch. 3: #37, 41, 52, 60, 66, 68, 72.
9/9 T Ch. 3 Centers & Centralizers
9/11 R Ch. 4 Cyclic Groups HW3: Ch. 4: #2, 8, 14, 16, 20, 28, 30, 32, 38, 46, 48, 52, 66, 74, 78.
9/16 T Ch. 1–4 Catchup & Review HW4: Supp. Ch. 1–4: #2, 4, 6, 12, 36, 48.
9/18 R Ch. 5 Permutation Groups HW4: Ch. 5: #1, 2, 4, 6, 14, 22, 28, 32, 36.
9/23 T Ch. 5 Applications of Perm. Groups HW5: 10, 12, 16, 20, 35, 40, 46, 54, 62, 70, 72, 78, 81, 82, 83.
9/25 R Ch. 6 Catchup Day
9/30 T Ch. 6 Isomorphisms HW6: Ch. 6: #2, 4, 6, 10, 20, 24, 30, 32, 34, 38, 42, 48, 52, 54
10/2 R Ch. 6 Isomorphisms
10/7 T Ch. 7 Cosets & Lagrange's Thm. HW7: Ch. 7: #2, 6, 14, 16, 18, 20, 22, 26, 32, 36, 42, 46, 50, 60, 62bd;
10/9 R Ch. 7 Orbit-Stabilizer Thm.
10/14 T Ch. 8 External Direct Products
10/16 R Ch. 1–8 Catchup & Review Day Do Practice Midterm by today!
10/23 R Ch. 8 External Direct Products HW8: Ch. 8: 8, 10, 12, 14, 32, 36, 38, 44, 56, 64, 72, 80, 84, 86;
10/28 T Ch. 9 Normal Subgroups Reading Incentive due;
10/30 R Ch. 9 Quotient (Factor) Groups HW9: Ch. 9: #4, 6, 10, 16, 22, 24, 28, 29, 38, 40, 42, 44, 56, 70
11/4 T Ch. 9–10 Applications & Group Homomorphisms Quiz #8 on Ch. 7–8; Midterm rewrites due.
11/6 R Ch. 10 Group Homomorphisms HW10: Ch. 10: #6, 8, 9, 16, 18, 20, 22, 24, 34, 42, 44, 50, 56, 62
11/11 T Ch. 24 Sylow Theorems Quiz #9 on Ch. 9; Reading Incentive for Ch. 24;
11/13 R Ch. 24 Sylow Theorems HW11: Ch. 9: #30, 32, 48, 50; Ch. 24: #2, 4, 18, 20, 22, 34, 36, 44, 48, 54.
11/18 T Ch. 1–10, 24 Catchup Day Quiz #10 on homomorphisms.
11/20 R Ch. 11 Fund. Thm. of Finite Abelian Groups HW12: Ch. 11: #4, 8, 10, 12, 14, 18, 28, 30, 38; Supp. Ch. 9–11: #6, 16, 20, 28, 40.
12/2 T Ch. 11 Fund. Thm. of Finite Abelian Groups Quiz #11 on Sylow Theorems
12/4 R Ch. 1–11, 24 Catchup & Review Day
THURSDAY 11 DECEMBER 2014 12:30–2:30 REVIEW SESSION IN MSB 303 or 203

Web Resources

Anonymous Feedback (Now disabled)

Use this form to send me anonymous feedback or to answer the question: How can I improve your learning in this class?  I will respond to any constructive suggestions or comments in the space below the form. 

Feedback & Responses

  1. [Date] This is a test.

    This is only a test.

  2. [27 Aug 2014] I was reading over the website and had a question about the "Reading Incentive" that I was hoping you could clarify [see above]. Does this mean that every class period I could turn in one page of hand written notes on the chapter? If yes, then potentially I could have 14 note sheets to use on the midterm assuming that I did this for every class? If no, then can you explain in more detail as to how the reading incentive works? Also it says "to use on the midterm or final." Is 'or' in this context inclusive or exclusive? By that I mean if we wanted could we use them on both the midterm and the final or must we choose one? Thanks for clarifying this matter..

    Yes. And yes you can use those same notes for each in-class midterm and final, but not for the weekly quizzes. Thanks for reading the syllabus carefully!

  3. [9 Oct 2014] I have noticed I've been having difficulty reading the board when you use the pink chalk. Is there any way you could limit your use of the pink chalk because it's quite difficult to view on the green board. Thank you =).

    Thanks for letting me know. I'll try to remember, but if others who read this notice me using the pink, please remind me!

  4. [20 Oct 2014] Is there any way you can include the Table 2.1 on the hand out for midterm? It will just make our life easier when considering what the inverses are and looking for examples on the midterm./i>

    I don't think it would help much. The midterm isn't about your ability to to use complicated formulae for the inverses. The rest of it you should know or be able- p to rederive with no sweat. But it was worth thinking about.

  5. [4 Nov 2014] Can you collect the midterm rewrites in a way so that other students will not see our grades?.

    Thanks for the suggestion; I think we managed this OK.

  6. [23 Nov 2014] Please post a practice final sooner rather than later. Given my original exam grade, I would like to get a feel for the final as early as possible. Please make the practice final more indicative of the true difficulty of the final. In the case of the midterm, the practice exam was far easier.

    OK, it's posted now [24 Nov.], and I emailed it to the class. I always try to put the longer, more involved problems on the practice one, and am a bit surprised that the actual midterm seemed much harder. Did you take the practice midterm under exam conditions? That can make a big difference. In any case, please don't assume that all the problems on the final will be similar to the ones that ended up on practice final. It's just as important to go over all the problems on homework, quizzes, the midterm and practice midterm.

  7. [10 Dec 2014] Would it be possible to please post the solutions to the practice final before the review session?



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