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So I'm taking my first midterm exam in math analysis soon and I'm confused on how to study for it. I mean in calculus one would be able to just go into the book and take derivatives and integrals until it was second nature, but in analysis, the class is mostly proving theorems and writing proofs of important theorems. I understand that every university and even every class is going to be different but what are some of the essential things that are learned in the first part of an analysis course that would likely be tested on? If anyone is familiar with Charles Pugh's text on Real Analysis the exam covers the whole first chapter and section 1 of chapter 2.

In class we have covered openness and closedness of sets, continuity, the construction of the real number system in the method of Cauchy sequences (professor didnt really touch on them being built on cuts too much, but a little), homeomorphisms, upper and lower bounds, cardinality, etc.

Of course I'm going to study those topics, but is there a good way or a suggested way that tends to help students prepare for those in an exam?

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Could you give a little more information about the material that you have covered so far, and your background in proof writing? Thanks! –  William Stagner Feb 19 '13 at 4:19
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Usually, and in great generality, the things you are most likely to be tested on in an exam are the things you have been tested on in your homework assignments. –  Gerry Myerson Feb 19 '13 at 4:33
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Dear Kyle, you can try to figure out the proofs on your own, but it is even more important to do problems from other texts. For example, if you will be tested on open sets, you should try to get hold of as many problems on open sets as possible. There is an abundance of exams posted online by professors from many schools. –  Haskell Curry Feb 19 '13 at 4:39
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You are asking me questions for which you would get much better answers from the person teaching the course. –  Gerry Myerson Feb 19 '13 at 5:04
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I am currently taking Analysis myself and took a test today. What I found out was know your proofs, theorems and know the concepts inside and out. and the only way you will get better at that is by doing a whole lot of practice problems and not just from your book, go online and search for some more problems. –  Q.matin Feb 19 '13 at 5:44

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Get the definitions. Try to prove the theorems yourself. If you can't , understand the proof idea and why you missed it. Thinking visually and creating examples may help to solve the problems.

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