# Basic Math Reference

## Proofs

Do you have trouble reading and writing formal proofs and definitions?
Had trouble with the required automata theory class? Tried to read
introductory textbooks on analysis or group theory, but got lost
quickly? Not sure whether you can survive a graduate-level math
class? Then check out
- Daniel Fendel and Diane Resek (1990)
Foundations of Higher Mathematics: Exploration and Proof,
Addision-Wesley, Reading MA.

This book provides clear, detailed descriptions of how formal,
abstract mathematics works. It takes you step-by-step through how to
read definitions and construct formal proofs. It will also give you a
brief introduction to analysis, abstract algebra, and logic. This
book should be read in linear order: random access will not work well.

## High school math and calculus

Can you reproduce the quadratic formula from memory? How about
the formula for the tangent of half an angle? No? This isn't
surprizing: it's probably been years since you last used them. You
should own a book of mathematical formulas.

There are many books of mathematical formulas, in all sizes and
prices, some intended for mathematicians and some for students in the
physical sciences. Examine the collections at your local library and
bookstores and buy one that you like. It should include trig formulas,
formulas for volumes and areas of regular solids and parts of them
(e.g. subsections of a sphere), integral and derivative tables,
and a table of values for the integral of the Gaussian (or normal)
distribution.

The CRC Press (CRC originally stood for "Chemical Rubber Company")
has been publishing such handbooks, including not only several sizes
of math handbooks, but also a giant handbook for chemists and
physicists. Their big math handbook is

- Beyer, William H, Standard Mathematical Tables [& Formulae],
CRC Press, Boca
Raton, FL. [numerous editions, e.g. the 27th edition is 1984 and the
29th is 1991]

This costs about $40 new (hardbound).
Used copies often appear in used bookstores.
Make sure a used copy is recent enough that it does not include
many pages of trig and log tables, redundant now that calculators
are cheap.

They also publish a tiny math handbook: cheaper and fits in your
backpack. It is adequate for most purposes;
your library should have a copy of the larger handbook if you
need to look up something obscure.

- Tallarida, Ronald J. (1990) Pocket Book of Integrals and
Mathematical Formulas, CRC Press, Boca Raton, FL.

Also, a variety of useful formulas can be found in chapters 2 and 3 of

- Cormen, Thomas H., Charles E. Leiserson, and Ronald L. Rivest
(1990) Introduction to Algorithms, MIT Press, Cambridge MA and
McGraw-Hill, New York.

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