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Strichartz's the Way of Analysis

  1. Aug 9, 2012 #1
    I searched the forum, and found some information on this book, but I am looking for some more. It is a pretty lengthy book coming in at 700+ pages. Front to back, it looks like it covers a lot of topics (including Lebesque Integration, which is something I've had my eye on learning). What are some of your thoughts on the book? It appears to very explanatory. Any more input would be very helpful.

    By the way, what I am looking for is an analysis book that aims to teach (since I have no instructor) and one that I can get a lot of mileage out of. This book seems to be it.

    Thank you for your opinions!
     
  2. jcsd
  3. Aug 10, 2012 #2

    jbunniii

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    I own this book, but I'm not a big fan of it. Aiming to teach is a great thing, but I think the book is so verbose that it ends up obfuscating more than enlightening. Also, it's full of typos.

    I highly recommend the following books by Bruckner and Thompson:

    Elementary Real Analysis

    "www.amazon.com/Real-Analysis-Andrew-M-Bruckner/dp/1434844129"[/URL]
     
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  4. Aug 11, 2012 #3
     
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  5. Aug 11, 2012 #4
    Thank you so much for the suggestion. I actually purcharsed the Bruckner and Thompson text (Elementary Real Analysis)! I am very excited to start. I found out about the free PDFs afterwards. But, I would need the text anyway since I get headaches from staring at the computer for too long.

    Now, I am sure getting through this text will take some time since I generally want to at least try every exercise (plus I work full time). But, when the time comes, how is their Real Analysis text? It appears that this is more of a graduate-level text. Looking at the contents of the Elementary text, finishing it would have already put me WAYY past the year-long Real Analysis sequence I took as an undergraduate. Just wondering where finishing both texts will get me in terms of graduate analysis.

    Thanks!
     
  6. Aug 11, 2012 #5
    Just to add some details, we used Lay's Analysis with an Introduction to Proof back when I took Real Analysis. The book was very clear. It appears that these books are too!
     
  7. Aug 11, 2012 #6

    jbunniii

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    Yes, it's a reasonable plan, but beware that some (but not all) of their challenge problems are quite tough, including many old Putnam questions. These often require some kind of ingenious trick which may take a long time to come up with (if ever) and which might not be especially useful in other contexts. If your goal is to master the material in a reasonable amount of time, then skipping the challenge problems entirely may not be a bad idea.

    I think it's a very nice book, one of the best I've seen for providing motivation and insight into measure theory and Lebesgue integration in R^n.

    How far it will take you in terms of graduate analysis depends upon the university and who's teaching the analysis course (and writing the analysis qualifying exam).

    When I took graduate analysis, about half of the first semester was spent on measure and integration (following big Rudin, which my instructor muttered under his breath that he considers to be an undergraduate text "these days"), followed by a race through L^p, Hilbert and Banach spaces, then on to distributions and some Fourier analysis. The second semester was all functional analysis. Within this framework, Bruckner and Thomson would have good coverage for about 40% of the year-long sequence. It also covers many "classical" topics that were completely ignored by my instructor, such as the various covering theorems, absolute continuity, differentiation, Baire category, analytic sets, etc. A lot of this stuff is really interesting, and I find that the book is well suited to self-studying to pick up some of this background that I missed during formal coursework.
     
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