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First Experience of Real Analysis

  1. Nov 8, 2005 #1
    Hey guys.

    I was just wondering how your first experiences with real analysis was, such as "how it was taught," "how the exams were like," etc.

    I thought it was relatively easy since the lectures emphasized the proofs of theorems and a sufficient amount of examples. The exams were to prove a couple of theorems and do some problems related to what was previously lectured.

    Also, I was wondering why many people think real analysis I is hard, or aka "hardest course in an undergraduate curriculum."
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  3. Nov 8, 2005 #2


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    My first experience with real analysis was brutal. I took an undergrad 3 quarter sequence that used Walter Rudin's Principles of Mathematical Analysis (affectionately known as Baby Rudin). The homework was arduous, the text rigorous, and the exams were unrelenting and frigid. I miss that class.:rolleyes:
    Now I'm taking the graduate version of that sequence with Rudin's Real and Complex Variables a.k.a. Papa Rudin. It's now a week or so past mid-terms my first quarter into the sequence: I was unable to solve even one of the five problems given on our take home exam. Our prof. authors some of the area exams in analysis at our university (UCSB).:grumpy: I have homework I should be suffering...
  4. Nov 8, 2005 #3


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    my first calculus course was my first encounter with real analysis. I had never had calculus in high school and the lecturer handed out axioms for the reals the first day and we proved evrything in the course from them. I thought it was very hard. the book was courant's calculus which was not quite as rigorous as the course but still hard to read for me. I liked it and the course though.

    Our first hw set included a challenge to prove e is irrational from its taylor series. (we started the course with sequences and seires, and defined cos and sin by their series, and also e^x, and also used both real and complex variables in our series.)

    One reason I think many people find reals hard is that baby rudin is used so frequently. this is a notoriously unfriendly treatment from the student's point of view, and makes the course memorably diffcult or even unpleasant for many people.
  5. Nov 8, 2005 #4
    undergraduate analysis is not that bad, unless your text was Rudin. The real bad/painfull analysis starts at the gradute level. They assume you know almost everything from Rudin's text (even if you didnt use it as an undergrad). And they assume you know everything about topology.
  6. Nov 8, 2005 #5
    I had Pfaffenberger/Johnsonbaugh's text when I did my intro analysis course & I would have much preferred that one over Rudin's. Pfaffenberger/Johnsonbaigh don't construct the real numbers like Rudin does, so they spend more time on limits & functions. instead they just give a list of axioms that the real numbers satisfy & then get on with limits & functions asap. first very thoroughly on the real line, & then when we got to metric spaces they were no problem, even with the added abstractness. i guess that was the idea; to get us used to the epsilon/delta stuff so it was automatic by the time we got to metric spaces, & then we could concentrate more on dealing with absract metric spaces. i always heard that the course was a nightmare but i didn't think it was so bad. having the 'right' textbook helps a lot i think.
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