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May 25th, 2017, 12:06 PM   #1
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Smile Help self-studying algebra

Hello,

One of my goals this summer is to self-study algebra to learn about groups/rings. I'm using the online textbook Basic Algebra by Anthony W. Knapp.
I plan to do the two chapters which seem to cover the prerequisites, and then skip inner product spaces (chapter 3), and go into chapter 4 (groups).

I'm finding it hard because it seems that the majority of textbooks, including this one, are a lot of theories, corollaries, and lemmas, and if I were to make sense out of a whole page, it would take me like 2 - 3 hours of googling.

I don't necessarily mind this.. but is this the right way to do it?

Or another way I've thought to do it is look at the problems first, and then read with the intention of solving a specific problem.

So my question is how should I be reading the textbook?

Also, this textbook doesn't have solutions, so I try to give my best guess. Is this ok? Will it hurt me? There is also a Schaum's outline of abstract algebra at the library that I'll probably use after working through the book's problems..

Do you have any recommendations on learning about groups/rings?
I've taken discrete math and linear algebra (up to eigenvalues), but not a formal proof course.

Last edited by skipjack; May 25th, 2017 at 01:17 PM.
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May 25th, 2017, 07:44 PM   #2
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Make sure you have multiple textbooks on the same topic handy. This is very useful when tackling a new concept or even definitions which may appear 'simple', but have complicated meanings. You can quickly go to the glossary of other books, read a paragraph on that topic and hopefully gain new perspective.

The 2-3 hours of googling sounds like something i would do when self-studying, so i understand your requirement to be more efficient. I would recommend not to stagnate for too long. It may feel strange at first, but if something isn't quite clicking after an hour or so, just move on to the next section.

Chances are that the next section will rely on the previous sections ideas, but this is ok. Try to go with it for a while. Pay attention to the way the new section refers to ideas from the previous section, it may give you insight.
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May 25th, 2017, 08:14 PM   #3
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I actually found a pdf of A Book of Abstract Algebra by Charles C. Pinter, which seems to be less rigorous, so I think I will use it along with the 2-3 books that there are in the library.

And moving on if a concept isn't clicking to see how it is built on, sounds like a good idea.

Thank you for the advice
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May 25th, 2017, 08:20 PM   #4
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Originally Posted by Choboy11 View Post
I actually found a pdf of A Book of Abstract Algebra by Charles C. Pinter, which seems to be less rigorous, so I think I will use it along with the 2-3 books that there are in the library.

And moving on if a concept isn't clicking to see how it is built on, sounds like a good idea.

Thank you for the advice
Yes definitely finding a 'bridging' text is crucial too, i forgot to mention that.

It is worth spending some time finding a book that best suits your current expertise. I am no expert in Abstract Algebra so i couldn't recommend anything . However, if you provide some detail on your current mathematical maturity, others may be able to identify a good bridging text.
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May 25th, 2017, 08:41 PM   #5
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Ok here goes, here is my comfort areas:

With proofs, I got a taste of them in discrete math. I know what proof by contradiction, induction, direct proof are but actually applying them is still hard.
Other than that I've taken calculus up to multivariable calculus, linear algebra up to eigenvalues, and intro to complex analysis which covered up to the residue theorem.

The book i'm reading is basically a presentation of theorems, corollaries, and lemmas, and then a problem set with hints, and it feels a little out of my league.

But I found A Book of Abstract Algebra by Charles C. Pinter which seems to have a reputation of being a less rigorous introduction to this subject. So i've switched over to using that. But i'd be interested if anyone has a different recommendation for an introduction to abstract algebra.
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