• Important Notes (Last updated: 12/13 - 5:35pm)
• Homeworks (Last updated: 12/04 - 2:00pm)
• Latest Homework Assigned
• Solutions to Selected HW Problems (Last updated: 12/04 - 2:00pm)
• Instructor Contact and General Information
• Course Information
• Legal Issues
• NEW! Final Grades
• Exams :
  • Midterm I
  • Midterm II
  • Makeup Midterm II
  • NEW! Final
• Important dates
• Links
• Handouts
• On-line Feedback Form

• (12/13 - 5:35pm) I've just posted some info about the final resutls. Check Final Grades below. Your grades haves also been submitted to the Registrar Office (check them at Circle Park Online) and posted at Blackboard.

the solutions for the finals. Check the section Final below.

• (12/12 - 7:00pm) I've just posted the solutions for the finals. Check the section Final below.

• (12/11 - 3:00pm) I've just posted some info about the results of the Final: check the section Final below. (All your grades, except the letter grade for the course, have been posted at Blackboard.) Information about the grades for the course should come tomorrow.

• (12/05 - 2:00pm) Here is the Take-Home Final. Remember that it is due on Friday (12/08) at 10:15am, i.e., before the In-Class Final.

• (12/04 - 2:00pm) Section 10.3 will not be in the exam.

• (12/01 - 6:50pm) I've finished a preliminary version of our final(s). I want to show it to other professors and see how far we will go on Monday before making it final. Here is some info:

  • It has two parts:
    • Take-home: I will give this part to you after the review. I will also post it here sometime on Tuesday afternoon for those who can't come to the review. (Or you can pick it up with me in my office.) It will have 5 questions, with total worth 60 points.
      You can use your book, notes, posted solutions, and other books. But you cannot communicate with anyone about anything from the exam, until the Friday (12/08) after the in-class exam.
    • In-class: You will take this exam in our scheduled final time, i.e., Friday (12/08) from 10:15am to 12:15am, in our usual classroom. (You should be able to finish in less than one hour, though.) This part contains 6 (easier) problems, and it is worth 40 points. At least 3 of these should be immediate. To get a C in the course, you need at least 20 points (out of 40) in this part. (Of course, getting 20 points does not guarantee you a C in the course.)
      In this part, you are not allowed to use your book, notes, calculators, etc.
  • I recommend you start studying early (this weekend!!), so you can ask me questions and have time to think about (and learn from) the answers.
  • The final is comprehensive (except for Chapter 1). It includes sections 2.1-2.10, 5.3 (dihedral group only -- use your notes), 5.6, 5.7, 6.1, 6.3, 6.4, 6.6, 6.7.
  • About half of the exam will be regarding the new material (Sylow Theorems, dihedral group, generators and relations, and rings), but as you probably know, to work on those you will have to know the previous material.
  • The problems in the exam are quite similar to the HW problems. The ones to be done in class, are easier than the average HW problem, while the ones you will take home are about average.
  • You can use any fact you learned in Math 300, Calculus, Linear Algebra (or Matrix Algebra) without justifications: just state clearly what you are using. You cannot use facts you've learned from another abstract algebra course. (Or you can, but you will get only partial credit, which could be very little.) You can also use any result stated and proved in class and any result you proved in HW (again, just state it clearly, but do not prove it), unless I say otherwise in the question.
  • Try to be as relaxed as possible during the exam. Being anxious can only make things harder. Even if you think the exam is way too hard (which I am pretty sure it will not be), relax: there can be a curve...
  • To study for the in-class part:
    • Make sure you understand the concepts and definitions, and you that you can work out concrete examples. (Remember the 1st problem of the second midterm?)
    • Make sure you know the theorems and propositions, especially those that can solve a problem easily, and the ones which were used many times in the course.
    • Keep in mind that the problems will be short and not difficult. You can rework HW problems like that.
    • Working on your take-home will help you review and study, but remember that there can be topics in the in-class that were not covered in the take-home.
    • Look at all examples and solved problems. (Some proofs of Propositions are just like a solved problem!) Especially the easy ones that can be done quickly.
    • Look in solutions for ideas that can make a solution shorter or simpler. Even if you got it right, there might be an easier way.
    • Review your old HWs. Look for problems with very short solutions or purely computational, especially the ones you missed! (You should always learn from your mistakes!) Always look for exactly what went wrong! (Did I not understand the definition? Was I missing an idea? If so, which??) Try to find the ideas, theorems, and tricks that made the problem short!
    • Quickly review your notes and read the book. The most important parts is to review the definitions and Theorems/Propositions. If necessary, write those in a different sheet of paper so that you don't have to browse your book every time you need to refresh your memory.
    • Do as many problems as possible from the book and the other references.
    • When you first start studying, you can look at the definitions and propositions, but by the end, you should be able to do problems without looking.
    • Try to choose six problems to work on as if you were in the exam: no notes, allow 2 hours, etc. This might give you an idea if you are prepared.

• (12/01 - 5:45pm) We will have a review on Monday (12/04) at 4:30pm. The room is Ayres 309A.

• (11/27 - 4:40pm) If you have any grade corrections to be made in homeworks or exam, please bring it to me ASAP. I will not change a grade (of old HW or midterm) after I figure out the curve for the course!

• (11/27 - 4:15pm) I've started thinking about your final. My first idea is to give it in two parts. I will give you the first part as take-home (worth about 60 points) in the last class day (12/05), and you would turn it back on our final scheduled time (Friday 12/08 at 10:15am). Then, at that time you would take the second part, the in-class part (worth about 40 points), from 10:15am to 12:15pm.
  This second part (in-class) would be straight forward (you should be able to do it without having to think much about it!), and I'd expect you to be able to finish in about one hour (or less), but you would have 2 hours for it. The first part (take-home) would contain the harder problems, but I would expect a well prepared student to do it in about one hour and a half (or less).
  On the other hand, there will be limits (do be determined later) on how many points you have to get in the in-class part, like, ``to get a C or more, you need at least 25 out of 40'', ``to get an A you need at least 35 out of 40'', etc.
  This is my first idea, and I will start working on the final with that in mind. If you have any comments or suggestions, e-mail me or use the On-line Feedback Form ASAP.

• (11/23 - 11:00am) I posted the classification of groups of order 18 in the section Handouts below.

• (11/17 - 11:45am) I posted the solution to the Extra credit problem in the section Handouts below.

• (11/15 - 2:40pm) I've posted the results of the Makeup Midterm II.

• (11/09 - 5:30pm) I strongly recommend that you check all your HWs and exams to see if your points were added correctly. In HWs, you should also make sure that the totals add up to the total of the assignment. (If not, I might have skipped one of your questions.) Bring me your assignment if you find any mistake.
  Please, do not leave this to the last minute!!!! The longer you wait, the harder it is to change your grade.

• (09/15 - 12:35pm) I will start now using Blackboard for posting grades only!! This way you can keep track of your scores and let me know if there are any discrepancies between your actual grade and your recorded grade. You are probably familiar with Blackboard, but in any case, to check your grades go to http://online.utk.edu/, log in and choose ``Abstract Algebra I''. Then, click on ``Tools'' and then on ``My Grades'' (or click on ``Course Information'' and ``View Grades''). But note that this site will have all other info! (Blackboard is only for grades.)

• (08/23 - 4:00pm) Please, check this section often. I will put announcements and important info here.

• (08/23 - 9:45am) Please, hit the ``Refresh'' or ``Reload'' button on your web browser every time you visit this page, so that you can see the most recent updates.

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The total grades for the course were computed. The average for the total grades was 65, the median 64.14.

Here is how the grades were assigned and the number of people in each range:

You can round your average to the closest integer: 77.2 is a 77, 77.5 is a 78.

This is as nice as I can be! I've talked to a few professors, and this is the best I can do. As some of you might notice, I dropped the "you need at least a 20 in your In Class Final to get a C" requirement.

If you want to see your final or check your average, make an appointment.

I have already submitted the grades to the registrar office. I suppoese that you can already check it at Circle Park Online. I also posted them at Blackboard.

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e-mail: lfinotti@utk.edu

Office Hours: MWF 9:00am-10:00am or by appointment (subject to change!!)

Textbook: M. Artin. ``Algebra'', 1st Edition. Prentice Hall, 1991.

Prerequisite: Math 300 and Math 251 or 257.

Class: MWF 10:10-11:00 at Ayres Hall 214. (Section 1.)

Exams: Midterms: 09/29 (Fri) and 11/06 (Mon), in regular classroom and time; Final: 12/08 (Fri) from 10:15am to 12:15pm, also in our regular classroom.

Grade: 20% for HW + 20% for each Midterm + 40% for the Final. Note the weight of the HWs!

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Here is the Midterm I and the Midterm I with solutions.

The exams were graded and will be returned in class on Monday (10/02). If you are not in class that day, you have to come by my office to pick up yours. (I will not take them to class anymore.) The average was 70.36 and the median was 74.5, which seems OK. The highest grade was 92.

Here is how I would curve the grades for this exam and the number of people with each grade:

Note: This curve is just to give you an idea of how I curve. In the end I will not even look at this curve, I will just curve all the final averages.

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You can check the Midterm II and the Midterm II with solutions.

The exams were graded and will be returned in the class Wednesday (11/08). The average and median were around 39, which is, of course, just horrible. The highest score was 77.

I will not give a curve to this exam here, since I can't make myself give a C to someone with 39. This means that we need to figure something out to settle this situation. We will discuss it in class on Wednesday.

Here is a little about the distribution of the grades.

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You can check the Makeup Midterm II and the Makeup Midterm II with solutions.

The exams were graded and were be returned in the class today, Wednesday 11/15. The average was 77.6 and the median 85. The highest score was 99. The results were good, but it was a simple exam, very similar to the Midterm II itself.

I will not give a curve to this exam, since I will curve only your ``official grade''. (See below.) But here is a little about the distribution of the grades.

Your ``Official Midterm II Grade'', which will count as 20% of your grade, replacing your actual ``Midterm II Grade'', was computed as

The average of these grades was 59 and median was 64.4. The highest score is a 88.4.

Here is how I would curve these grades and the number of people with each grade:

Note: This curve is just to give you an idea of how I curve. In the end I will not even look at this curve, I will just curve all the final averages.

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Here are the finals: Take Home Final, Take Home Final Solution, In Class Final, In Class Final Solution.

The finals were graded. We had:

The results of the Take Home part were reasonable, but the results of the In Class were pretty bad. Given the level of diffculty of the exam, and the amount of time given to you for the In Class, I find that pretty disturbing. We had 5 people below 20, and, as stated in class, those should not get a C in the course. (I will think about it and discuss it with others though.)

Here is the grade distribution for the Final (Total):

Note that the finals will not be returned, since they have to be kept on file. If you want to see your final or check your average, make an appointment.

There is no point in giving a curve for this grades, since I will curve your averages directly.

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Content

In this course (and in its sequel, Math 456) you will be introduced to algebraic structures such as groups, rings, and fields. It is very important that you already have some practice with writing proofs (which was covered in Math 300) and familiarity with matrices and vector spaces (which was covered in Math 251 or 257). You will have to write many proofs in this course, and many of the examples we will look into will be related to matrices. Therefore, I will assume you have the proper background from both Math 300 and Math 251/257. If you had difficulty in those courses, you might need to review the material. (I would gladly try to help you with that if you come to my office hours.)

Homeworks

Homeworks will be assigned after every class and will be posted at this page. (See Homeworks below.) No paper copy of the HW assignments will be distributed in class. It is your responsibility to check this page often!

The HWs will be collected on Mondays (except on Labor's Day week, when it will be due on Wednesday). (EDIT: HWs are now due on Wednesdays.) Each HW will have problems from the previous week (Monday, Wednesday and Friday lectures). The problems to be turned in, as well as due dates, will be clearly posted at the Homework section below. Note that not all of the problems turned in will be graded, but you won't know which until you get them back.

No late HWs will be accepted, except in extraordinary circumstances which are properly documented.

It is your responsibility to keep all your graded HWs and Midterms! It is very important to have them in case there is any problem with your grade.

I will do my best to post solutions. Please check the Important Notes section soon.

In my opinion, doing the HW is one of the most important parts of the learning process, so the weight for them is equal to the weight of a single midterm, and I will assume that you will work very hard on them.

Also, you should try to come to my office hours if you are having difficulties with the course. I will do my best to help you. Please try to come during my scheduled office hours, but feel free to make an appointment if that would be impossible.

E-Mails

You will have to check your e-mail at least once a week, preferably daily. I will use your e-mail (given to me by the registrar's office) to make announcements. If that is not your preferred address, write me an e-mail letting me know ASAP. I will assume that any message that I sent via e-mail will be read in a week or less, and it will be considered an official communication.

Due to privacy issues, I cannot send grades via e-mail, unless you sign a document saying that you are aware that e-mails are not secure and not necessarily private. If you want to sign such document, please let me know. (I will post a form at this page soon. Please check the Important Notes section soon.)

Feedback

I have an Online Feedback Form where you can anonymously send me your comments and suggestions. I will consider your comments and try to do whatever I can to resolve possible problems before it is too late. So, please, feel free to use it whenever you have any constructive comment or suggestion. (In fact, I would greatly appreciate it.) If you don't want you comments to be anonymous, just send me an e-mail or come by my office and we can discuss the problem.

Course Structure -- UPDATED 12/04

We will likely cover the following portions from the text:

• Quick overview of Chapter 1. (You should have seen this material in Math 251 or 257.)
• Chapter 2: all sections.
• Chapter 5: Sections 5-7 and part of section 3 (dihedral groups) towards the end.
• Chapter 6: Sections 1, 3, 4, 7, 8.
• Chapter 10: as much as time allows. (Section 10.1 and 10.3.)

Chapters 2, (parts of) 5, and 6 give an introduction to basic concepts of ``Group Theory''. (Chapter 5 also deals with the particular case of ``Groups of Symmetries'' in details.) We will likely start Chapter 10, which deals with ``rings'', but we might have to finish it in Math 456.

Additional Bibliography

• J. Fraleigh ``A First Course in Abstract Algebra'', 7th Ed., 2002. Addison Wesley.
• J. Gallian, ``Contemporary Abstract Algebra'', 6th Ed., 2005. Houghton Mifflin Co.
• I. Herstein, ``Topics in Algebra'', 2nd Ed., 1975. Wiley.

The first two books are considered ``easier'' books, and although they also have a somewhat different approach, they have most of the topics we will cover and may be of good help if you have difficulty reading Artin's book.

The last one is a ``standard'' text for a first course in abstract algebra, but might have a higher level of difficulty. (It's been used for the honors section of this course.) Nevertheless, it is a very good reference.  

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You should also be familiar with the ``Classroom Behavior Expectations''.

Disabilities

Students with disabilities that need special accommodations should contact the ``Office of Disability Services'' and bring me the appropriate letter/forms.

Sexual Harassment and Discrimination

For Sexual Harassment and Discrimination information, please visit the ``Office of Equity and Diversity''.  

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Wednesday, August 23 - Classes begin.

Friday, September 01 - Last day to add, change grade options, or drop a full semester course without a "W".

Monday, September 04 - Labor Day Holiday. (No class.)

Friday, September 29 - Midterm I.

Tuesday, October 03 - Last day to drop a full term course with a "W".

Thursday-Friday, October 12-13 - Fall Break. (No class.)

Monday, November 06 - Midterm II.

Tuesday, November 14 - Last day to drop with a WP/WF.

Thursday-Friday, November 23-24 - Thanksgiving. (No class.)

Tuesday, December 05 - Last Class Day.

Friday, December 08 - Final.

More dates.

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• UT Knoxville Home
• UTK's Math Department.
• Blackboard -- Check your grades for this course.
• On-line Feedback Form - here you can give me some feedback for the course. It's confidential and might help fix problems before the quarter is over.
• Services for Current Students and Circle Park Online (registration, view your grades, etc.).
• Office of the Registrar
• Important Dates for Fall 2006 (add, drops, etc.) and 2006/2007 Academic Calendar.
• UT Code of Conduct, Academic Integrity, and Classroom Behavior Expectations.
• Office of Disability Services
• Office of Equity and Diversity (includes sexual harassment and discrimination).
• Course Listings (courses offered).
• Undergraduate Catalog (2006/2007) and Course Descriptions.
• Student Success Center.
• Academic Guide 2006/2007.
• My homepage

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• Syllabus (original handed in class).
• Quadratic Equations: a very simple handout with the deduction of the quadratic formula. (High School algebra material, really.)
• Syllabus (UPDATED 12/04).
• Extra credit problem and its solution.
• Classification of Groups of Order 18.
• Take-Home Final.

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Please read: I will try to post here a few solutions. The new solutions will be added to this same file. They might come with no explanation, just the ``answer''. If yours do not match mine, you can try to figure out again. (Also, read the disclaimer below!) You can come to office hours if you want explanations for the answers. Be careful that just because our ``answers'' were the same, it doesn't mean that you solved the problem correctly (it might have been a ``fortunate'' coincidence), and in the exams what matters is the solution itself. I will do my best to post somewhat detailed solutions, though.

Disclaimer: I will have to put these solutions together rather quickly, so they are subject to typos and conceptual mistakes. (I expect you to be a lot more careful when doing your HW than I when preparing these.) You can contact me if you think that there is something wrong and I will fix the file if you are correct.

Solutions to Selected HW Problems (Click on ``Refresh'' or ``Reload'' if you don't see the changes!)

CHANGE LOG:

• (12/01 -- 5:40pm) Added solutions of the extra credit problems from HW14 and for a few problems from HW15.
  UPDATE: Since 10.3 is not in the exam, this update was the final one!
• (11/29 -- 3:30pm) Added solutions of HW14.
• (11/23 -- 10:05am) Added solutions of HW13.
• (11/17 -- 11:40am) Added solutions of HW12 (and fixed some typos in the previous HWs).
• (11/09 -- 1:45pm) Added solutions of HW11.
• (11/02 -- 11:20am) Added solutions of HW10.
• (10/27 -- 4:45pm) Added solutions of HW9.
• (10/18 -- 11:30am) Added solutions of HW8.
• (10/16 -- 11:45am) Added solutions of HW7.
• (10/06 -- 11:30am) Added solutions of HW6.
• (09/27 -- 2:30pm) Added solutions of HW5.
• (09/22 -- 9:30am) Added solutions of HW4.
• (09/14 -- 7:00pm) Added solutions of HW3.
• (09/07 -- 4:35pm) Posted solutions of HW1 and HW2.

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HW1 - Due on Monday 08/28:

Review matrices and vector spaces (from Math 251/257).

Section 1.1 (pg. 31): 1, 2, 4, 11.

Section 1.2: 2, 12, 14.

Section 1.3: 1(b), (c), (d), 2 (Hint: row operations).

HW2 - Due on Wednesday 09/06:

Section 1.4: 1, 4.

Section 2.1 (pg. 69): 1(b), 3, 4, 7, 11. (Note: I did not do in class anything very similar to number 4, but just remember that every element of a group has an inverse. It is almost like you can ``divide'' both sides by something, but in fact you multiply both sides by an inverse to get rid of a term. But be careful: the group might not be Abelian!

HW3 - POSTPONED!!! (See Important Notes above.) Due on Wednesday 09/13:

Section 2.2: 2, 3, 4, 11, 13, 16(a), 17. Note: I excluded number 10 (from my previous list here)!

HW4 - POSTPONED!!! (See Important Notes above.) Due on Wednesday 09/20:

Section 2.3: 1, 4, 5, 9, 12.

Note: For 12 you need to know what an automorphism is: an automorphism is just an isomorphism from a group G onto itself.

HW5 - Due on Wednesday 09/27:

Section 2.4: 4, 8(b), 9, 13(a), 14, 17, 22.

HW6 - Due on Wednesday 10/04:

Section 2.5: 2, 5, 6. (Maybe you should also review a little about equivalence relations from Math 300.)

HW7 - Due on Wednesday 10/11:

Section 2.6: 1, 3, 5, 10(a). (Hint for 10(a): use Proposition 6.18)

Section 2.7: 1, 3.

HW8 - Due on Wednesday 10/18:

Section 2.8: 2, 3, 4(a), 4(b), 5, 6.

HW9 - Due on Wednesday 10/25:

Section 2.9: 1, 2, 5.

Section 2.10: 1(a), (b), (d), 3, 9, 10. (The last one was supposed to be 11.)

HW10 - Due on Wednesday 11/01:

Section 5.5 (pg. 192): 1(b), (c), 3, 8 (hint for 8(a)), 11(a).

Section 5.6: 1.

You can also try the Extra Credit Problem, but it is due in class Monday (10/30), NOT Wednesday!!! You are not allowed to discuss this problem with anyone!

HW11 - Due on Wednesday 11/08:

Section 5.6: 2, 6, 7.

Section 5.7: 6. (Hints: For (a) use problem 5: you can assume its statement is true without proving it. For (b), don't make it complicated. Look at some of our ``most used'' groups.)

HW12 - Due on Wednesday 11/15:

Section 6.1 (pg. 229): 1, 2, 4, 6, 10(a), (e), 12.

Section 6.3: 4, 5, 7, 13.

HW13 - Due on Wednesday 11/22:

Section 6.4: 1, 2, 3, 13, 15.

HW14 - Due on Wednesday 11/29:

Section 5.3 (pg. 189): 1, 2, 4. (These are about the dihedral group. Note that the text uses D_n for what we use D_2n.) Hint for 4(c): The answer is yes and to prove it you just need to show that the product group has two generators that satisfy the same properties as the two generators of the dihedral group.

Section 6.7 (pg. 233): 1.

Section 6.8: 1 (to show this, you basically need to show that you can get a and b from the two elements given in the problem), 6 (there is a typo in the statement: it should read ``N and G/N cyclic'' instead of ``G and G/N cyclic''), 16.

Extra Credit: Prove that if a group has order 24, then it is not simple. Alternatively, prove the same for order 36. (You can do either one.) These might be difficult... (Or, maybe I just did not see the easy way...) You are not allowed to discuss this problem with anyone! You should not look for the solved problem in other references either!

HW15 - not to turn in (just to study for the final):

Section 10.1 (pg. 379): 6 (you can replace the complex numbers with real numbers in this problem), 8(a), (c), 9(a), (c), 11(a), (b), 13.

If it is already Friday afternoon and there still is a ``More to come'' after the HW assignment due on the coming Monday, write me an e-mail at lfinotti@utk.edu, and I'll update it and let you know.

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