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I left college many years ago and now I've forgotten a lot about multivariate calculus. I've also never taken a real analysis course of any kind before. Now I'm planning to go back to school for a graduate degree in econ. The school says that I must havegood skills in real analysis to survive those econ core courses because exercises are all proof-based.

I have with me nowApostol 1andKenneth A. Ross's "". Reading 3 chapters from both texts, I'm surprised that Ross is an easier read than Apostol 1, even though Apostol is about calculus and Ross about intro real analysis.Elementary Analysis: The Theory of Calculus

Questions:

1) Is calculus (single and multivariable) a pre-requisite for real analysis? On Wikebook course in real analysis, it says that to learn real analysis requires no background in calculus!!! I'm not sure if this statement is correct or not.

2) Should I go straight to Ross or stick with Apostol 1, given that I don't have much time left to prepare before I go to grad school in econ?

2) On the UC Berkeley econ dept website, there is a course called Econ 204, which is basically a math camp for PhD econ students, here, http://elsa.berkeley.edu/users/cshannon/e204_11.html

I've seen a few lectures from this Econ 204 course and found that they are pretty hard material. However, the syllabus says that students can get a waive provided they've taken a course in real analysis comparable to UC Berkeley's Math 104. I then googled for UC Berkeley's Math 104, http://math.berkeley.edu/~chr/104.S12/index.html , and found that they used Kenneth Ross's text for the course.

My question is, why is it that the instructor consider a course closely based on Ross's text a substitute for her Econ 204 course when the latter touches on far advanced topics like optimization, differential equations, etc...? Does she imply that her course, i..e Econ 204 stresses proof writing and not on topics?

Thank you very much.

Best,

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# Apostol 1 vs Ross's Elementary Analysis

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