# Mathematics Books

## Popular mathematics books

# Mathematics Books

## Mathematical Recreations

Isn't "Mathematical Recreations" a contradiction in terms? The classic work on recreational math, Mathematical Recreations and Essays, will convince you that with the right guidance you can find a lot of recreation and fun in modern mathematics. The first edition of the book appeared 106 years ago, and since then was updated by several authors till the current, thirteenth edition. The book contains problems, puzzles, games and paradoxes from all areas of elementary mathematics. Some of the book's chapters: geometrical recreations, magic squares, calculating prodigies, map-coloring problems, cryptography and cryptanalysis.

The book describes mathematical topics in a light and attractive way. These topics include topology, greedy algorithms, cryptography, complexity theory, game theory and other topics of contemporary mathematics. Even if you understand Chinese better than these topics, you can read this book and understand every word, every sentence, and every chapter.

"The man who brought more mathematics to more millions
than anyone else", this is a description of Martin Gardner by three famous
mathematicians. For twenty five years Martin Gardner wrote a monthly column
in the *Scientific American* magazine. These columns are now all gathered
in fifteen volumes. Each volume is without technicalities, but is packed
with brilliant ideas and clear explanations. Complex mathematical ideas are
stated in a simple, funny, straight forward manner. If you are not a
mathematician, but wish to meet the many faces of modern mathematics,
Gardner's books are the best starting point. Each volume in the following
list is a gem by itself, and you may start your collection of Gardner's
books with any of them.

- Hexaflexagons and Other Mathematical Diversions: The First Scientific American Book of Puzzles and Games
- Second Scientific American Book of Mathematical Puzzles and Diversions
- The Unexpected Hanging: And Other Mathematical Diversions
- Mathematical Circus: More Puzzles, Games, Paradoxes, and Other Mathematical Entertainments
- Wheels, Life, and Other Mathematical Amusements
- Knotted Doughnuts and Other Mathematical Entertainments
- Time Travel and Other Mathematical Bewilderments
- Penrose Tiles To Trapdoor Ciphers, And the Return of Dr. Matrix,
- Fractal Music, Hypercards and More...: Mathematical Recreations from Scientific American Magazine
- The Last Recreations: Hydras, Eggs, and Other Mathematical Mystifications

## Mathematically Oriented Novels

Have you heard about a thriller that its hero is a mathematician? Not a cop, not a detective, not a spy - a mathematician. Enigma by Robert Harris is the book. It happens during World War II at Bletchley Park, a British intelligence base working on deciphering German radio messages encrypted with the famous Enigma machine.

Will the British intelligence officers crack on time Nazi Germany's secret codes? Is there a traitor in Bletchley Park? What motivates this unusual spy? The book grabs you and holds you as the plot twists and turns.

The framework of the book is based on reality, and its fictitious hero, Tom Jericho, was designed according to the character of Alan Turing, the real mathematician that conquered the Enigma. The ability to read the encrypted secret messages of the Germans was very useful in the Battle of Britain. From messages deciphered in 1941 the British learned about the beginning of the systematic murder of Eastern Europe's Jews, but nothing has been done with this information.

Evariste Galois, the French mathematician who died in a duel at the age of twenty, is certainly the most romantic and most tragic of all mathematicians. As a mathematician, Galois created group theory. As a young frenchman living in a tumultuous era, he was jailed twice. The French Mathematician is a novel based on Galois' short life. It gives quite accurately the not so many known details about Galois' life, and the mathematics of Galois is not neglected. In the fictional part of the book Galois reveals his thoughts and dreams. This technique resurrects Galois' life, and makes the book a highly readable one, aimed at the general public.

Goldbach's Conjecture, stated in 1742, in a letter written by Christian Goldbach to the great mathematician Leonard Euler, is one of the most famous unsolved problems in mathematics. The novel Uncle Petros and Goldbach's Conjecture, by Apostolos Doxiadis, is based on this problem. The heroes of the novel are Uncle Petros, an ageing mathematician who devoted his life to Goldbach's Conjecture and his young nephew who tells us the story. Some real mathematicians who take part in the plot are Turing, Ramanujan, Hardy and Littlewood.

Fantasia Mathematica: Being a Set of Stories, Together With a Group of Oddments and Diversions, All Drawn from the Universe of Mathematics is a wonderful collection of mathematical science-fiction stories, poems and anecdotes.

The Mathematical Magpie: Being more stories, mainly transcendental, plus subjects of essays, rhymes, music, anecdotes, epigrams, and other prime oddments and diversions, rational and irrational, all derived from the infinite domain of mathematics contains more mathematically oriented stories, cartoons, essays, rhymes, music, anecdotes and aphorisms.

## Puzzles

Each of Martin Gardner's books listed above contains a chapter or two with ingenious puzzles. If that is not enough, try the following superb puzzle books.

Mathematical Bafflers and
Second Book of Mathematical Bafflers are two collection of not so easy
mathematical puzzles (and, thank God, their solutions). Try this one:
*What is the largest amount of money you can have in coins and still not
be able to give change for a dollar?*

Amusements in Mathematics by H.E. Dudeney is a classic puzzles book. It contains 430 ingenious puzzles: arithmetical problems, geometrical problems, mazes, chessboard problems and much more. Try this one: "I have eight sticks, four of them being exactly half the length of the others. I lay every one of these on the table, so that they enclose three squares, all of the same size. How do I do it? There must be no loose ends hanging over."

Raymond Smullyan, professor of mathematics and philosophy, has the unique talent to create new puzzles and to put them in an exciting story. Here are his three most entertaining and thought provoking puzzle stories, which are also a tour in the world of logic:

The Riddle of Scheherazade and Other Amazing Puzzles, Ancient & Modern.

Chess Mysteries of Sherlock Holmes: Fifty Tantalizing Problems of Chess Detection

## Problem Solving

If you have tried to solve puzzles or real life problems, but gained little success, you will find the book How to Solve Mathematical Problems quiet helpful. Mathematical problems, puzzles and science problem are used as examples, and are analyzed thoroughly.

The activity of problem solving, which requires discovery
and invention, seems to be an intuitive activity, an activity with no rules.
George Polya, in his classic book
How to Solve It; A New Aspect of Mathematical Method, presents
systematic ways to solve problems. The main part of the book is *Short
Dictionary of Heuristic*, which contains a detailed discussion, in
alphabetical order, of problem solving techniques, from "analogy" to
"working backwords'. This most famous book on problem solving will add to
your knowledge about the theory and practice of this useful subject.

## History of Mathematics

The greatest mathematical achievement of the last decades is, with no doubt, the proof of Fermat's Last Theorem. Fermat's Enigma: The Quest to Solve the World's Greatest Mathematical Problem tells the exciting story of this theorem. From its roots at ancient Greece to its dramatic end few years ago. This is a very readable book. Although it deals with one of the hardest problems in the history of mathematics, you need no previous knowledge to enjoy this book, which is mainly a book about people.

The quest for a proof to Fermat's Last Theorem took 350 years, but it is a short one compared to the efforts to find a proof to Euclid's fifth postulate. More than 2000 years passed till the creation of the Non-Euclidean Geometry, which demonstrated that such a proof does not exist. The book gives a critical and historical study of development of Non-Euclidean Geometry. The book includes a translation of the original works of Lobachevsky and Bolyai, the men who created, separately, the Non-Euclidean Geometry.

The mathematician Leopold Kronecker said, "God made the natural numbers, all the rest is the work of man." Starting at early Greek mathematics and proceeding through history till the beginning of the twentieth century, Makers of Mathematics gives a detailed account of the development of mathematics, with short descriptions of the many people who made those developments.

Men of Mathematics, the classic history of mathematics by Eric Temple Bell, is written with great affection and puts greater emphasis on the life of the mathematicians. These characteristics make this book delightful even to the general, non-mathematician, reader.

The name of the last book, *Men* of Mathematics,
is not because the book was first published before the politically correct
era, but because women were very, very rare in the history of mathematics.
Things have changed a bit in the last century, and the book
Women In Mathematics: The Addition of Difference tries to push further
this change. It contains profiles of nine contemporary female mathematicians.
With chapters named "What's a Nice Girl Like You Doing in a Place Like
This?" it deals with some myths about women and mathematics.

Paul Erdös, who died in 1996 at age 83, was the most prolific mathematician of the twentieth century, with 1,475 research articles. Moving from one university to the next in search for good mathematical problems, Erdös collaborated with more people than any other mathematician in history. He was totally obsessed with mathematics, ignoring all other aspects of life. The Man Who Loved Only Numbers tells vividly the story of Erdös, a uniquely great mathematician with a highly unusual lifestyle.

The Hilbert Challenge by Jeremy J. Gray describes the history of modern mathematics, viewed through the famous 23 problens posed by David Hilbert address in Paris before the International Congress of Mathematicians on the very beginning of the twentieth century.

## Famous Numbers

All numbers were born equal, but has the most fascinating history, as you can see reading History of Pi, by Peter Beckmann. Starting at 2000 BC, and till the computer age, is in the focus of an intensive research. Douglas Hofstadter describes this book: "Actually, a history of the world, with Pi as its focus. Most entertaining, as well as a useful reference on the history of mathematics".

The number e - the base of natural logarithms - is less famous than and it has a shorter history, but it still has a very interesting history, which involves some of the central people of mathematics. e: The Story of a Number starts with John Napier, the man who created logarithms. The book proceeds with Newton, Leibniz, Laplace, the Bernoullis, Euler and Gauss, and describes various applications of e, saving difficult math to footnotes and appendices.

An Imaginary Tale: The Story of , tells the story of
one more celebrity in the world of numbers, *i* - the squre root of minus 1. The
book tells the 2000-year-old history of the 'imaginary number' , the
people who missed it and the people who successfully used it. The book
contains examples of the application of complex numbers to important problems
in physics and engineering.

The Nothing That Is: A Natural History of Zero deals with the many aspects
of this simple number: zero. The book is intended primarily for mathematical
novices - those who learnt no more than high school math. It takes the reader
to a tour spanning from ancient Babylonian number system to contemporary
calculus and modern cryptography. If you want to know the meaning of 0/0 and
0^{0}, this is the book for you.

Zero: The Biography of a Dangerous Idea.

## Contemporary Mathematics

Learning mathematics in high school gives the impression that God gave math to Euclid, and since then we have to learn it exactly as it was given. Mathematics is, of course, a vivid science, with new achievements and new research topics. Mathematics: The New Golden Age gives an exciting description of eleven topics of contemporary mathematics: Chaos, the Four-Color problem, Knots and Topology etc.

What is Mathematics? An Elementary Approach to Ideas and Methods is a 1996 revision (by Ian Stewart) of a classical masterpiece, by Richard Courant and Herbert Robbins, originally published in 1941. It is a very good introduction to the main topics of current mathematics: calculus, algebra, number theory, geometry, topology, set theory. Not just about technique, the book tries to put the meaning back into mathematics. Albert Einstein said (on the first edition of the book): "It is an easily understandable introduction for the layman and helps to give the mathematical student a general view of the basic principles and methods." May I humbly say that if you are not Einstein, reading this book is not an easy task, but it worth the effort.

"If a family is to have only one mathematics book on the reference shelf, then this is the one." This is what Donald J. Albers says about the book Mathematics: From the Birth of Numbers. Should I add anything to this recommendation? This is a huge book (1120 pages), written for everybody by a non-mathematician (the author, Jan Gullberg, was a surgeon). Written with great passion and a wonderful sense of humor, the book covers many topics of mathematics: arithmetic, algebra, geometry, trigonometry, calculus, differential equations, combinatorics, logic, set theory, topology, fractals, probability, and more. The book is useful not just as a history of mathematics, but also as a reference book, which contains the important formulas and theorems. The book is rich in pictures, illustrations and cartoons.

Life by the Numbers is a companion book to the PBS series bearing the same name. It displays vividly, using many examples and photographs, the beauty and diversity of mathematics.

All the books in the Mathematics department of the *Profession Jokes*
bookstore are about mathematics, but are not for the professional
mathematician. Every book is highly readable, and was written for the
intelligent layperson, who wants to expand his mathematical knowledge and
have fun at the same time. If you seek books for the professional
mathematician or textbooks for students of mathematics, visit
Math Books Online, the
bookstore of the Mathematical Association of America, in association with
Amazon.com.

If you didn't find any interesting book in my recommendations, you can start here a search in the whole catalog of Amazon.com, Earth's Biggest Bookstore. Write the name of the author or the name of the book you wish to find, and click on the "Search" button.