# which problems do you recommend it to me to solve it? [closed]

i study abstract algebra from dummit and foote .

i started to solve some problems in section 3 in chapter 4

there is 36 problems

i study the subject myself , so there is no proffesor to recommend or instructor !

so , i hope that you help me to recommnd some of therse exercises because solving all of them will require lot's of time !!

so , i wait your suggestions !

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## closed as too localized by Austin Mohr, Robert Mastragostino, 5PM, rschwieb, Brett FrankelFeb 4 '13 at 1:39

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I think this question should be closed as too localized - it's not going to be relevant to anyone but you. And if there's no professor, why not at least try every problem? What's the hurry? The more problems you think about, the more you'll learn... –  Zev Chonoles Feb 4 '13 at 1:15
I just go through the problems and do the ones that either look interesting, or focus on what I consider the trickier parts of the chapter. This also might mean going back to the problem set later if the text does more with a subject than you've practiced for. Essentially all the problems in there are good, so exactly which ones you do should be based on what you personally find interesting and/or difficult. –  Robert Mastragostino Feb 4 '13 at 1:20
@ZevChonoles Isn't this question potentially useful to anyone studying this particular section of Dummit & Foote? A great deal of people study Dummit & Foote to learn abstract algebra, so potentially many people could benefit from a list of good problems from this section. –  JSchlather Feb 4 '13 at 1:34
@Jacob: I don't think it is useful - are any of these 36 problems so terrible / hard / uninteresting that they should be explicitly disrecommended to people? –  Zev Chonoles Feb 4 '13 at 1:57
@ZevChonoles I don't think that by recommending certain problems over other problems, you're saying these problems are without merit, simply that other problems have more merit. I've frequently found that certain problems can be much more illuminating than other exercises. Particularly in cases where Dummit & Foote put an important example or theorem as a series of exercises. For instance I recall Dummit & Foote asking you to show that the Prufer $p$-group has no maximal subgroups in an exercise. Surely this is a better exercise than counting the number of conjugacy classes of $A_4$? –  JSchlather Feb 4 '13 at 2:13

Usually textbooks list problems/exercises in the order in which they progress from easier to solve to greater and greater levels of difficulty. So your best bet, if you don't want to solve them all!, is to pick a few earlier problems, to get warmed up, then some middles problems, and build up to selecting some of the problems from the last third.

A good approach would be to do all even problems, or all odd problems, or, if you aren't struggling to much with a particular section of the text, perhaps every third problem. That way you are following a progression from starting with easier exercises, and progressing to more difficult ones.

I'd suggest scattering a few of the earlier problems (every third problem, say), but putting most of your energy into the last half of the exercises: Those are the exercises that will ensure (or require) that you "really know your stuff"!

At any rate, save a few problems for giving your self "examinations" periodically, for the sake of personal accountability: In a typical semester-length (4-5 months or so), there is at least one midterm, and a final exam. So you might aim, say, for testing to return every month or two, first spending a little time reviewing the material covered during that time (studying for your exam), and then returning to some of the problems you left "unsolved" to "test yourself". If you find yourself struggling to complete those exercises, you might want to spend a bit of time reviewing the relevant material in order to recall (and/or deepen your understanding of) what you need to know to solve them, before moving on.

Then, "back to the books" and moving forward from where you left off!

Good luck!

ADDED: Here is a syllabus from an abstract algebra class taught last fall at Standford University. It includes assigned exercises from the class text (Dummit and Foote), and most of the assignments have solutions available for downloading.

You can also try googling "Dummit and Foote: .edu" to search for other links to course syllabi in which Dummit and Foote is the class text.

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I hope this helps, MrWhy! If you'd like, we can occasionally open a private chat to discuss some of Dummit and Foote, as you're studying it. I can't do that daily, but we can figure out some time each week to do so. Any way, let me know if you still have a question on the last grouptheory question you posted! the maximal sugroup question...If you still would like clarification, I can post something by tomorrow. If you're okay with it now (the question/answers), that's great. –  amWhy Feb 4 '13 at 3:35
i'm ok with it now :) , yes this disscussion will be great ! , i'll googling as you mentioned in your answer , if you found other things likes notes , videos , exercises ! this may hepl . i noticed that the course in stanford didn't cover chapter 5 or 6 in dummnit and foote ! this was strange for me !! do you have an idea about the reason of this ? on the disscusion , can we make first one after finishing chapter 4 - group actions - ?? what do you think ? if you agree , i'll contact with you here in a comment or on the way you like to determine the time to disscus . i wait your reply –  Maths Lover Feb 5 '13 at 3:03
Yes, I'll look for some more syllabi with exercises, maybe even solutions. This may have been the first semester of a year long class, so I'll see if there's a follow-up site for that class this spring. Yes, feel free to comment when you'd like to "meet" in chat. Feel free, to, to accept my answer here ;-). –  amWhy Feb 5 '13 at 3:06
last thing , i want to thank you very much for stanford course's link :) i think it'll be useful for me :) also , i want to thank you for the disscusion :) I'm Maths Lover , but i changed my name , it's similar to yours , but i liked it as one of the greatest mathematician - godel if my memory is good ! - was called Mr Why when he was a child ! if this is annoying for you , i will change it –  Maths Lover Feb 5 '13 at 3:07
Not at all annoying...I like "Why" and "MrWhy"! Just be sure to accept my answer ;-) –  amWhy Feb 5 '13 at 3:10

What I do in general is that I try to solve a couple of the problems which are more mechanic (like the ones on the euclidean algorithm and the totient function at the beginning) and then try to tackle the difficult ones at the end.) Try all of the hard ones. Especially because in that book they tell you a lot of stuff in the problems that they don't in the general text.

I save some of them for later so I can go back and consolidate what I have learned. Some of the harder problems make the text more juicy and give clues to what will be developed in future pages.

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hello , thanks for your advices , you look in high school like me and study the same subject , maybe you are intersted in knowing people interested in the same subjects and in the same age level - i'm also a high school student - . if you are interested in communicating with me to be a friends or help each other , that will be nice for me ! what do you think ?! –  Maths Lover Feb 4 '13 at 2:34