Compendium(s) of Elementary Mathematical Truths

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.


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!

Source : Link , Question Author : ItsNotObvious , Answer Author : Corey

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