**(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.**(11/09 - 2:20pm)**The last day to drop the course with a WP/WF is**this coming Wednesday (11/13)**. Remember that both WP/WF withdraw you from the course, which may drop you below the required number of hours to maintain full-time status. This may have serious consequences if you have a scholarship. So, I strongly suggest that you check with financial aid before filing the form.**(11/09 - 2:00pm)**As we've discussed in class Wednesday, we will have a makeup exam. Here is some extra information:- If G1 is your grade for Midterm II and G2 is the grade for your
makeup exam, then your
*official grade for the Midterm II*(which counts as 20% of your grade) will beMax(G1,(1.5*Max(G1,G2)+Min(G1,G2))/2.5) i.e., the best between G1 and the weighted average of your two exams with weight 1.5 for your best grade. - The material covered in the same as for the Midterm II and it should have the same level of difficulty. (But don't expect a copy of it with ``numbers changed''.)
- You have an option of taking it home or doing it in 50 minutes.
If you take it home:
- It goes without saying that
*you cannot discuss it with*. (You will get a zero and I**anyone***will*report you if I find out you did.) You cannot even say things like ``number 3 is hard'', ``I finished the exam in 30 minutes'', etc. I really mean**nothing**should be said about the exam to**anyone**(even people not associated with the university). - Of course, I won't discuss the exam with you. (Except if you did
not understand what a question is asking.) I will not give you any
definitions or discuss anything at all (not even problems not related
to the exam, like new HW problems) until you turn in the exam. I will
not clarify any solutions posted, nor things from lectures or from the
book either. So,
**if you have any questions, you should ask me before you take the exam home**! Remember that, if you want to take it home on Friday. - You can use your book.
- I will be much more exacting when grading your solutions than I usually am when grading exams taken in class. For instance, you will get no partial credit for citing things straight from the book (like definitions and theorems).
- Your solutions will have to be neatly written. I won't be forgiving about messy solutions. You will have plenty of time to work on a scratch and to organize your thoughts before writing down your solution.
- I will give you the exam in class either Friday (11/10) or Monday
(11/13). You have to return it in the
**beginning**of (or before) class on Monday (11/13), if you took it on Friday, or Wednesday (11/15), if you took it on Monday. (You cannot turn it in on Wednesday if you took it on Friday!) - You will still not be allowed to talk about the exam to anyone until the solution is posted here in this site.

- You will have to take it in a different time than our usually class time.
- You will not be allowed to use book, notes or anything. (If you want to use them, take the exam home.)
- All students that choose to take it in 50 minutes will have to
agree to the
**same time**on either Friday (11/10), Monday (11/13) or Tuesday (11/14). (Things can be more flexible, depending on the number of students who choose to take it in 50 minutes.)**The preliminary time is Monday at 4pm!** - You are not allowed to talk to
**anyone**about**anything**on the exam until I post solutions in this page!! (Just like people that take the exam home. See above.) - You should e-mail me
**ASAP**to let me know you choose to do it in 50 minutes, so that I can make the necessary arrangements. - I might give you more than 50 minutes...

- It goes without saying that

- If G1 is your grade for Midterm II and G2 is the grade for your
makeup exam, then your
**(11/08 - 5:45pm)**I've posted the solution to our second midterm. Check the section Midterm II below.**(11/06 - 3:10pm)**The second midterm has been graded and will be returned in class on Wednesday (11/08). Check Midterm II for more information. The results were very bad and we will need to figure out a way to mend the situation. Please check your e-mails (I will be writing you soon) and come to class on Wednesday to discuss it.**(11/01 - 6:10pm)****Updates on the exam:**After talking to a few people, I've made a few changes in the exam. It now has four questions: three from chapter 2 and one from chapter 5. Two are more computational (adding to 20+25=45 points) and two are more theoretical (adding to 25+30=55 points).**(11/01 - 1:05pm)**We will have a review Thursday (11/02) 5:30pm at Ayres 209A.**(10/31 - 9:00pm)**I've finished a preliminary version of our second midterm. (I want to show it to other professors before making it final.) Here is some info:- It is this coming Monday (11/06) in class (from 10:10am to 11:00am in our usual room.)
- I recommend you start studying early, so you can ask me questions and have time to think about and learn from the answers.
- It will
*focus*on sections 2.6 to 2.8, 2.10, 5.5 and 5.6. (I will not ask you questions about 2.9.) On the other hand, you*do*have to know the previous material! (I won't ask question about the previous sections, but to talk about a quotient group you have to know what a normal subgroup is, and so on...) - (
**UPDATED on 11/01 - 6:10pm**): The exam has four questions: three from chapter 2 and one from chapter 5. Two are more computational (adding to 20+25=45 points) and two are more theoretical (adding to 25+30=55 points). - You will
**not**be allowed to use your book, notes, index cards, calculators, PDAs, etc. in your exam. (The goal is not to make you memorize. -- Believe me, I am not sadistic. -- The idea is that if you do enough exercises, and if you**understand**the concepts, remembering the definitions and theorems should not be difficult. It seems to me that when you let students use other resources, they think that they do not have to study as much, which usually leads to disastrous consequences.) - The problems in the exam are quite similar to the HW problems,
maybe even a bit easier. But, please,
*do not expect to be exactly the same problems*. What I mean is that they compare in difficulty, length, and necessary background requirements to your*average*homework problem. (We had a couple of hard (or long) problems in the HWs. You should not expect, of course, something like those...) - Please, remember to check the exam before you start and do the easier questions first. Don't spend too much time on a single question.
- 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, I recommend:
- 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.
- Look at all examples and solved problems. (Some proofs of Propositions are just like a solved problem!)
- Review your old HWs. Redo all problems that you've 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??) - 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.
- 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 five problems to work on as if you were in the exam: no notes, allow only 50 minutes, etc. This might give you an idea if you are prepared.

**(10/27 - 5:00pm)**Here is an extra credit problem**due in class Monday (10/30)**.*You are not allowed to discuss this problem with***anyone**!**(10/25 - 1:40pm)**I've updated the ``Course Structure'' in Course Information and in the Syllabus again.**(10/19 - 2:40pm)**We will have class as usual on Friday (10/20).**(10/16 - 12:40pm)**I've decided (a little while ago) to go slower when covering the material in class to make things a bit easier and more understandable. To do so, I had to change the structure of the course a little, leaving somethings out that I previously intended to cover. Thus, I've just updated the ``Course Structure'' in Course Information with the necessary changes. I also updated the Syllabus. (The original is still available in the section Handouts below.)*You should note that this in no way will make us cover less than we were suppose to.*What I'm leaving out is just the particular cases of symmetries and linear groups, which although are quite important and interesting, are not necessary for a good course in group theory.**(10/02 - 10:05am)**I have just posted the solution to the first midterm. Check Midterm I below.**(09/29 - 4:10pm)**The exams were graded. For more information check Midterm I below.*Note that the last day to drop the course with a "W" is this coming Tuesday (10/03).*Your grades will be posted at the Blackboard site soon and the exams will be returned in class Monday.
If you feel like you need to discuss your situation, feel
free to make an appointment.
**(09/25 - 5:00pm)**The review for the exam will be Wednesday (09/27) at 6pm.**UPDATE:**The review will be at Ayres Hall 101,*not*in our usual classroom. (Feel free to bring something to eat.)**(09/25 - 2:10pm)**Here is some info about your first midterm:- It is this coming Friday (09/29) in class (from 10:10am to 11:00am in our usual room.)
- I recommend you start studying early, so you can ask me questions and have time to think about and learn from the answers.
- It will cover sections 1.1 to 1.4 and 2.1 to 2.5. From section
2.5 you only need to know (for this exam) Proposition 5.13 and
Corollary 5.16. (I will finish the material for the exam in the
beginning of class Monday (09/25).) Although Chapter 1 is part of the
exam, much more emphasis will be on Chapter 2. If you are familiar
with matrices (product, determinants, etc.), then the most important
part of Chapter 1 is
*permutation matrices*(section 1.4). - It has only 4 questions (25 points each): one from chapter 1, one from 2.1, one from 2.2, one from 2.3-2.5.
- You will
**not**be allowed to use your book, notes, index cards, calculators, PDAs, etc. in your exam. (The goal is not to make you memorize. -- Believe me, I am not sadistic. -- The idea is that if you do enough exercises, and if you**understand**the concepts, remembering the definitions and theorems should not be difficult. It seems to me that when you let students use other resources, they think that they do not have to study as much, which usually leads to disastrous consequences.) - The problems in the exam are quite similar to the HW problems.
But, please,
*do not expect to be exactly the same problems*. What I mean is that they compare in difficulty, length, and necessary background requirements to your*average*homework problem. - Please, remember to check the exam before you start and do the easier questions first. Don't spend too much time on a single question.
- 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, I recommend:
- 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.
- Look at all examples and solved problems. (Some proofs of Propositions are just like a solved problem!)
- Review your old HWs. Redo all problems that you've 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??) - 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 four problems to work on as if you were in the exam: no notes, allow only 50 minutes, etc. This might give you an idea if you are prepared.

**(09/18 - 2:10pm)**Due to popular demand, HWs are now due on**Wednesdays**. The assignments will still only cover material from Monday until Friday of the previous week, though. Since I'm catching up with the assignments, it is likely that I will be able again to assign HWs after every class (not only on Friday, like the last couple of times). So you should have more time to work on your HW. (Do not leave things for the weekend only! You should learn much better if you do a little every day!)**(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.)**(09/08 - 12:30pm)**Since I spent too much time going over the HW in class today, I did not cover all I had planed. Although you can do most of the assigned problems of HW3, I decided to postpone it until Wednesday (09/13) anyway, so that I can talk about*cyclic groups*in class. The problems I think could cause some difficulty are 13 and 16(a). The rest should be reasonable. (So, maybe you should do all but those before Monday to make sure you will have enough time to do all the problems by Wednesday.) You might need the following definition:**Definition:**The*order*of an element*x*is the*smallest positive*integer, say*n*, such that*x*to the*n*-th power is 1. If no such*n*exists (i.e., if no positive power of*x*gives 1), then*x*has*infinite order*.**(09/07 - 4:45pm)**I have just posted solutions to HW1 and HW2. I will*try*to post detailed solutions to all problems. I*strongly*recommend you go over the solutions very carefully to learn how to write proper proofs and see what were your mistakes (if any).**(09/01 - 5:00pm)**I've contacted the Library and Fraleigh's book in on reserve now. Herstein and Gallian should be there soon too.**(09/01 - 4:50pm)**I sent yesterday an e-mail to all students enrolled in the course. If you did not get it (its subject line was ``[Math 455] e-mail verification and drop deadline''), please write me an e-mail ASAP! In that e-mail I reminded all that today is (or was) the last day to drop a course without a ``W''.**(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.