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BOOKS available in association with

There are many good books available for mathematics.  One key book in my life was my father's copy of Plane Geometry.  I remember, at a young age, looking at the diagrams in this book.  They made some claim, and I thought "that can't be true."  But it was.  A bit later, I got hooked on Martin Gardner.  Am I missing something? Write me with a recommendation.

The fifteen books of Mathematical Games by Martin Gardner
 Hexaflexagons and Other Mathematical Diversions ($11), Second Scientific American Book of Mathematical Puzzles and Diversions ($12), The Unexpected Hanging : And Other Mathematical Diversions ($13), Magic Numbers of Dr Matrix ($17), Knotted Doughnuts and Other Mathematical Entertainments ($12), Wheels, Life, and Other Mathematical Amusements ($12), Time Travel and Other Mathematical Bewilderments ($12), Fractal Music, Hypercards and More ($12), Penrose Tiles to Trapdoor Ciphers ($28), and The Last Recreations ($18).  Two more at the MAA site.

My favorite math books

Particle Physics Booklet by Particle Data Group (Free!) -- My favorite "carry around" book.
Amusements in Mathematics by Dudeney ($8) -- The best 'old' book of puzzles.
Mensa Math & Logic Puzzles by Dave Tuller & Michael Rios ($8) -- The best wordless logic puzzles.
Recreations in the Theory of Numbers  by Albert Beiler ($10) -- The best book on Math Recreations
The Magic Machine: A Handbook in Computer Sorcery by A K Dewdney ($16)
The Planiverse by A K Dewdney ($20) -- Excellent math as fiction book.
The Book of Numbers  by John Horton Conway, Richard K. Guy ($29)  -- The best book on Numbers
Mathematical Circles (Russian Experience) by Dmitri Fomin ($29) -- Great problems.
Proofs from THE BOOK by Aigner and Zeigler ($30) -- A wonderful collection of the best proofs.
The Nature and Growth of Modern Mathematics by Edna Kramer ($32) -- Great Math History
Problem-Solving Strategies by Arthur Engel ($50) -- An amazing book of great problems.
Mathematics Handbook for Science and Engineering by Lennart Rade ($50)
The Algorithm Design Manual by Steven Skiena ($70) -- Comprehensive, with many good links.
Mathematical Thinking by John D'Angelo and Douglas West ($81.33) -- The best book on Proofs
Encyclopedic Dictionary of Mathematics 2 by The Mathematical Society of Japan ($90)
Mathematica in Action by Stan Wagon ($50) -- Really a perfect book.  Scads of neat information, along with the tools needed for further exploration.  Delightful.  You do need Mathematica in order to play, though.



Images from Mathematica in Action by Stan Wagon.

For Younger People
Adventures of Penrose - The Mathematical Cat  by Theoni Pappas ($9)
Secrets of the Maze by Adrian Fisher ($18) (his website)

For High School Students
Along with any of the books above, the following books should be enjoyable for bright high school students.
Calculus Made Easy  by Silvanus Thompson and Martin Gardner ($16)
Chess Mysteries of Sherlock Holmes by Raymond Smullyan ($10)
Codes, Puzzles, and Conspiracy by Dennis Shasha ($11)
Concepts of Modern Mathematics   by Ian Stewart ($8)
Dissections: Plane & Fancy by Greg Frederickson ($35) (his website)
Elementary Theory of Numbers by William Leveque ($7)
From Erdos to Kiev by Ross Honsberger ($34)
A Gamut of Games by Sid Sackson ($6)
Geometry, Relativity, and the Fourth Dimension by Rudolf V B Rucker ($6)
Godel, Escher, Bach by Douglas R. Hofstadter ($16)
How to Lie with Statistics by Darrell Huff ($7)
An Imaginary Tale by Paul Nahin ($18)
Ingenuity in Mathematics by Ross Honsberger ($20)
Introductory Graph Theory by Gary Chartrand ($9)
Introduction to Graph Theory by Richard J. Trudeau ($8)
Journey Through Genius : The Great Theorems of Mathematics by William Dunham ($12)
Manhattan Research (the collected works of Raymond Scott) ($26)
Mathematics as Problem Solving by Alexander Soifer ($19) (his website)
Mathematical Gems II by Ross Honsberger ($12)
Mathematical Gems III by Ross Honsberger ($12)
Mathematical Puzzles of Sam Lloyd by Martin Gardner ($5)
Mathematical Recreations : A Collection in Honor of Martin Gardner  by David Klarner ($15)
Mathematical Tourist by Ivars Peterson ($12) (his MAA Column)
The Mathematical Universe  by William W. Dunham ($16)
More Mathematical Morsels by Ross Honsberger ($20)
New Ambidextrous Universe by Martin Gardner ($12)
New Rules for Classic Games by Wayne Schmittberger ($8)
The Penguin Dictionary of Curious and Interesting Numbers by David Wells ($12)
The Penguin Dictionary of Curious and Interesting Geometry by David Wells ($18)
The Pursuit of Perfect Packing by Aste and Weaire ($29)
The Puzzling Adventures of Dr. Ecco by Dennis Shasha ($7)
The Puzzling World of Polyhedral Dissections by Rausch and Coffin ($25) (online version)
Supermazes by Robert Abbott ($14) (his website)
What's Happening in the Mathematical Sciences by Barry Cipra ($14)
Winning Ways by Conway, Berlekamp, and Guy ($69)
The Cambridge Encyclopedia of the English Language by David Crystal ($24)
Making the Alphabet Dance by Ross Eckler ($12)
Sound and Sense by Perrine and Arp (my favorite book of poetry) ($36)
The Harry Potter Series:  Sorcerer's Stone, Chamber of Secrets, Prisoner of Azkaban by J K Rowling ($9, $9, and $10)

For College Students
Ah, college.  Who can forget their first $100 book? 
Analysis of Numerical Methods  by Eugene Isaacson ($12)
Applied Analysis   by Cornellius Lanczos ($14)
Art of Computer Programming Vol 1 by Knuth ($50) (his website)
Art of Computer Programming Vol 2 by Knuth ($50)
Art of Computer Programming Vol 3 by Knuth ($50)
Basic Complex Analysis by Marsden and Hoffman ($112)
Calculus and Analytic Geometry by Thomas and Finney ($107.40)
A Combinatorial Introduction to Topology  by Michael Henle ($8)
The Four Color Problem by Saaty and Kainen ($7)
Games of No Chance by Nowakowski ($30) (online version)
generatingfunctionology by Herbert Wilf ($50) (online version)
Geometry and Symmetry by Paul Yale ($10)
Group Theory by W R Scott ($12)
An Introduction to Knot Theory by W B Raymond Lickorish ($50)
Linear Differential Operators  by Cornelius Lanczos ($12)
The Mathemagician and the Pied Puzzler by Berlekamp and Rodgers ($34)
Matrices and Linear Transforms by Charles Cullen ($11)
Number Theory and its History by Oystein Ore ($9)
Numerical Recipes in C by Press, Teukolsky, Vetterling, and Flannery ($58) (online version)
Proofs from the Book by  Martin Aigner ($30)
Principles of Mathematical Analysis by Walter Rudin ($102)
Regular Polytopes by H S M Coxeter ($8)
Theory of Functions by Konrad Knopp ($8)
Three-Dimensional Geometry and Topology by William Thurston ($45)
Tracking the Automatic Ant by David Gale ($21)
Visual Complex Analysis by Tristan Needham ($45) (his website)
Watchmen by Alan Moore and Dave Gibbons ($16)
What is Mathematics?  by Richard Courant, Herbert Robbins, and Ian Stewart ($16)

For Hardcore Mathematicians
At this level, you usually need to appeal to the mathematician's specialty.  Do not dream of giving a book on partial boundary value problems to an algebraist, for example.  Here are a few of the high level books I like.
Algebraic Topology by C R F Maunder ($10)
Counterexamples in Topology   by Steen and Seebach ($8)
Handbook of Discrete and Computational Geometry by Goodman and O'Rourke ($110)
Real and Complex Analysis by Walter Rudin ($82)
Set Theory  by Thomas Jech ($117)  Note:  The 2nd edition is identical to the first edition, save for a few pages of errata that has been added at the back of the book.
Sphere Packings, Lattices, and Groups  by John Horton Conway and N J A Sloane ($70)
Topology by John G. Hocking ($10)

For Reference Nuts
Some books are purely designed as reference material.  There is nothing really readable in any of the following books.  All of them are packed with facts, though.
The Encyclopedia of Integer Sequences by Sloane and Plouffe ($57) (online version)
The Mathematica Book by Stephan Wolfram ($35) (online version)
Standard Mathematical Tables and Formula by Zwillinger ($50)
The Merriam Webster Collegiate Dictionary ($18) (online version)
Cambridge International Dictionary of English ($27) (online version)

Out of Print books
Tilings and Patterns   by Grunbaum and Shephard
The VNR Concise Encyclopedia of Mathematics
The Master Crossword Puzzle Dictionary   by Hebert Baus
On Numbers and Games   by John H Conway
A Budget of Trisections by Underwood Dudley
Encyclopedia of Chess Variants   by D B Pritchard
Patterns in Nature by Peter S. Stevens
Mad Mazes  by Robert Abbott (available from the author at his site)
From Polychords to Polya by Mike Kieth (available from the author at his site)
The Ins & Outs of Peg Solitaire by John Beasley
Satan, Cantor and Infinity by Raymond Smullyan
The Penguin Book of Curious and Interesting Puzzles  by David Wells
Books I plan to buy and evaluate
Another Fine Math by Ian Stewart ($12)
Challenging Brainteasers (Sterling).  Bernardo Recaman
Applied Combinatorics by Alan Tucker ($90)
Combinatorial Theory by Martin Aigner ($35)
Computability and Logic   by George Boolos and Richard Jeffrey ($27)
A Course in Combinatorics   by J H Van Lint, R M Wilson ($40)
Elementary Number Theory by Landau ($20)
Fractals Geometry of Nature by Benoit Mandelbrot ($28)
Geometry and Trigonometry for Calculus by Peter H. Selby ($16)
Geometric Patterns from Islamic Art and Architecture by Robert Field ($7)
Geometric Patterns from Churches and Cathedrals by Robert Field ($8)
Geometry by Harold Jacobs ($49)
Graphs and Digraphs by Chartrand and Lesniak ($80)
Handbook of Combinatorics by R L Graham ($185)
An Introduction to the Theory of Numbers by Hardy and Wright ($55)
Introductory Quantum Mechanics  by Richard Liboff ($91)
The Knot Book by Colin Adams ($23)
Knot Theory by Charles Livingston ($42)
The Lighter Side of Mathematics by Richard K. Guy ($20)
Mathematical Discovery by George Polya ($90)
Measure Topology and Fractal Geometry by Gerald Edgar ($33)
The Nature of Mathematical Modeling by Neil A. Gershenfeld
Polyominoes by George E. Martin ($15)
p-Adic Numbers by Fernando Q. Gouvea ($44)
Problems For Mathematicians Young and Old by Paul Halmos ($36)
Problem Solving Through Problems by Loren Larson ($45)
Theory and Application of Infinite Series by Knopp ($12)
Turtle Geometry by Abelson and diSessa ($26)
The Visual Display of Quantitative Information by Edward R. Tufte ($28)
The Pleasures of Counting by T W Korner ($36)

My Favorite Amazon Reviews
From William Lowell Putnam Mathematical Competition Problems and Solutions : 1938-1964 (out of print)
"However, I found the characters somewhat flat. Why, for example, does the set N choose to define himself in such narrow terms? Has he no dreams, no fantasies, no weaknesses, nothing but a recursive definition? Many of the characters had similar problems; I had difficulty relating to the motives behind some of their self-simplifying actions."

From What is Mathematics?
Albert Einstein -- A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable. (Editor's note: "hmmm...")
 

The CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein ($100) (online version)
The CRC Handbook of Chemistry and Physics 80th edition ($91)
The CRC Handbook of Combinatorial Designs by Colbourn and Dinitz ($100) (online version)