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Abstract Algebra is actually the first proofs intensive course I am taking and its not a simple topic. There are many definitions and theorems that I have to know right on the spot for a proof and i find that quite difficult to do. It takes me quite a while to finish my problem sets but I know on an exam I don't have the luxury of time. Can any of you provide some advice for doing well on the exams.

I mean I have been reading definitions, going over notes and proving theorems already but how should I study or ask myself questions in a way that I can do well on my exams? My weakness, in particular, is in dissecting hard proofs and applying theorems on the spot. My first exam will be on Groups, subgroups, cyclic groups, cosets/lagrange and orbits/alternating groups.

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    $\begingroup$ Practice. Do as many problems as you can before the exam. $\endgroup$
    – user121880
    Oct 2, 2014 at 21:43
  • $\begingroup$ I had the same problem in abstract algebra 1. I solved it by doing every problem in every chapter in the week leading up to the exam. Then anything he gave me had to be (or look pretty close to) a problem I had done. $\endgroup$
    – Alexander Gruber
    Oct 2, 2014 at 23:23

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I find it helpful to write some kind of 'exam'of my own - Write down some questions on a page that you feel describe what you should know such as define this term and quote and prove that theorem.

Also add in a few exercises given as homework or were done during lectures or recitations and learn the material.

Then sit down and try to solve the exam, see where are you having difficulties with - do you still don't remember the exact definition of something ? Do you understand proofs ? (You will see that when it is you writing the arguments down you will see exactly which ones seems right and where you feel you don't really understand but rather just knows its a step in the proof).

Finally the exercises are there to see if you can make it all work together - working with the theorems on abstract groups on special cases, this would also be a good practice for seeing definitions in concrete examples - such as subgroups, cosets and orbits

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