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Can anyone suggest a reference (or set of references) that simply list the core definitions/theorems from any (or all) of the listed subject areas:

  • Precalculus (Elementary Algebra, Trig, Analytic Geometry)
  • Algebra (Abstract/Linear)
  • Real Analysis (Single/Multi-variable)
  • Complex Analysis
  • Topology (Basic Point-Set and fundamental algebraic concepts)

The depth of the references should be sufficient to at least cover typical undergraduate mathematics and possibly some graduate-level material. I am open to either dead-tree or on-line references. I don't need something that actually develops theory or concepts as I have many, many textbooks that do this and I don't need something that has solved problems such as Schaum's. What I really need is a concise, pithy collection of references that lists definitions and theorems in a logical order.

To help you understand the context of my question, as one of my projects, I'm working through problem sets that cover a broad range of undergraduate and lower-level graduate material. I think it would be really beneficial if I could reference the material I need from a minimal number of sources.

I realize I could make my own reference as I go along and, indeed, this activity in itself could be worthwhile, but I'm hoping something like this already exists.

  • 0
    You could fare worse than looking at the magnificent books of Pólya and Szegő, *[Problems and Theorems in Analysis, I/II](http://books.google.com/books?id=b9l2NqGEFzgC)*. They cover at least points 1,3,4 of your requirements, and much more. (but maybe I misunderstand your question).2011-06-21
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    I don't think it goes as deep as you are requiring, but **CRC Standard Mathematical Tables and Formulae** includes material in all the subjects you mention (but, for example, topology is only included via the basic definition and a few comments, in half a page).2011-06-21
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    @Theo Buehler Those are indeed nice books but am really looking for something very spartan that contains only definitions and theorems, not something that develops the material or contains problem/solutions and proofs.2011-06-21
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    *[Handbook of Mathematics](http://www.amazon.com/dp/3540721215)*, by Bronshtein, Semendyayev, Musiol, Mühlig, is pretty comprehensive. For some reason I can't get Amazon to preview this (and Google Books doesn't have a preview either), but [here](http://www.knovel.com/web/portal/browse/display?_EXT_KNOVEL_DISPLAY_bookid=1867) is a table of contents, and there are... other... ways of seeing the rest of it. It doesn't have topology, unfortunately.2011-06-21
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    Are you familiar with the [Springer EOM](http://eom.springer.de/)?2011-06-24

2 Answers 2

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Garrity's All the Mathematics You Missed But Need to Know for Graduate School seems to be what you are looking for. It covers everything you listed and more!

  • 0
    I bought this book a while back, and recall being very disappointed with the amount of algebra covered. I don't remember how it did with other subjects.2011-06-21
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    I actually have Garrity's book and, unfortunately, find it lacking for my puposes. It covers a fair amount of math but the depth is missing and an cosiderable amount of prose is dedicated to conceptual development which is, again, at odds with what I seeek.2011-06-21
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    @Zev Chonoles My take on this book is that if you want a nice conceptual overview of a broad swath of mathematics then its not a bad read. For any reference/study purposes, however, its not really useful.2011-06-21
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    @3Sphere: I suppose I had just been expecting something else. Though looking at it again, I think you're right about its value as a conceptual overview.2011-06-21
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More wordy that what you're asking for, but maybe very useable until something more spot-on shows up: Math Reference Project http://www.mathreference.com/main.html

edit: Also, somewhat tangential to what you are asking for, but perhaps still germane, is the following website with a long list of (standard? / famous?) problems: http://www.mathproblems.info/

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    Thanks for the references, I'll look them up2011-06-23