Book Description

This invaluable resource will guide general readers and students alike through the often bewildering maze of equations and theorems encountered within the mathematical universe. Nearly 1,000 entries have been added for this new edition covering everything from pure and applied mathematics to statistics. Also included are entries on mathematics of more general interest, such as fractals, game theory, and chaos. Providing succinct definitions and clear explanations to a wealth of terms, A ConciseOxford Dictionary of Mathematics also enables readers to make new discoveries as they browse and check cross-references.

With explanatory figures, diagrams, and tables for ready reference to compliment the text, clear and precise definitions with helpful examples of a wide range of mathematical terms and concepts, and brief biographical sketches of the great mathematicians, this comprehensive dictionary will serve as an indispensable and trustworthy guide to the dynamic world of mathematics. ... Read more

Reviews (1)

There's a better one
I find this reference book a little disappointing. While not a bad book, it's not comprehensive enough and explanations are (in many cases) too concise. If you don't already know the meaning of the term you're looking up, chances are you won't understand it after reading the item. I also purchased the Harper Collins Dictionary of Mathematics, and here are the good news - it's much better than the Oxford. Much more comprehensive and more readable. It's not perfect either, but if you're going to have only one of these, I recommend the Harper Collins. ... Read more

Book Description

Non-compact Riemannian symmetric spaces and their quotients byarithmetically defined groups of isometries occur in many parts ofmathematics. For many purposes it has been necessary to compactifythem. This monograph attempts to give a systematic, and in part newexposition of these compactifications, of new ones, theirinterrelations and of the context out of which they arose.Compactifications of the more general semisimple symmetric spaces arealso considered. The book is divided into three main parts. Part I is devoted tofive types of compactifications, some related even isomorphic, all G-spaces, of the quotient X=3DG/K of a semisimple linear real Lie group Gwith finitely many connected components by a maximal compact subgroupK. The second part treats compactifications of the quotientsGamma\X, where Gamma is an arithmetic subgroup of G, assumed to bedefined over the field Q of the rational numbers. In the third part,three new types of compactifications are examined: the directconstructions of T. Oshima and T. Oshima--T. Sekiguchi, the gluing ofa certain number of copies of a compact manifold with corners, and thereal points of the so-called wonderful compactification of thecomplexification of X, or more generally G/H. The compactification of noncompact Riemannian symmetric spacesleads to a rich area of research in which many mathematicaldisciplines come together: algebraic topology, geometry, number theoryand representation theory. Familiarity with the theory of realsemisimple Lie groups and symmetric spaces, and in Part II, of linearalgebraic groups over Q is assumed although much material is recalledalong the way. Of interest and use to researchers and graduatestudents in Lie Theory or Representation Theory. ... Read more

Book Description

What is the largest number less than 1?

If x and y are any of two different positive numbers, which is larger, x2 + y2 or 2xy?

What do you get if you cross a cube and an octahedron?

Discover the surprising answers as David Wells conclusively proves that: you Are a mathematician

Praise for David Wells's

The Penguin Dictionary of Curious and Interesting Numbers.

"This is a fascinating, strange, and probably unique book, one that I will look at again and again. As soon as I had taken a good look at it, I went out and bought three more copies to give to friends." —New Scientist.

"David Wells's book about curious and interesting numbers is a quirky classic." —William Dunham Author, Journey Through Genius.

Are you on friendly terms with numbers? You will be after reading this delightful introduction to the fascinating and challenging world of mathematics. Bestselling author David Wells, a Cambridge math scholar and former teacher, explores the many patterns, properties —and problems —associated with numbers in a witty, thoroughly engaging style that is both entertaining and informative. Whether you are a math aficionado or whether you, as the author puts it, "panic and start sweating at the sight of a sum," Wells makes one point abundantly clear: You Are a Mathematician.

From basic arithmetic to algebraic equations, from the purely practical to the abstract, this is an ideal guide to the potential and pleasures of math. Surprising patterns emerge from the simplest groupings of numbers. The many secrets hidden inside of triangles are revealed, as are the origins of a host of mathematical theories and principles, from Aristotle to Euclid and Galileo. On a journey from the ancient Greeks to quantum theory, Wells shares intriguing anecdotes from history, such as how eighteenth-century European military commanders calculated how many cannonballs their enemies had stacked up next to their cannons.

David Wells invites us to discover the sense of wonder and fun that is so much a part of mathematics. Mathematical thinking is often very much like a game, relying on cunning tactics, deep strategy, and brilliant combinations as much as on observation, analogy, and informed guesswork. To illustrate, Wells includes over 100 brainteasing puzzles and problems, ranging from Ptolemy's theorem to Euler's famous solution to the Königsberg bridge problem and Koch's snowflake curve. Modern-day computer buffs will also enjoy the underground classic, the Game of Life, invented by Princeton mathematician John Conway.

Offering a comprehensive and stimulating look at the myriad aspects of mathematics —whether as a household helper or an invaluable tool of science —You Are a Mathematician covers a wide range of topics and applications. It is an ideal guide to the potential and pleasures to be found in math. ... Read more

Reviews (3)

Help for you to understand and appreciate what math can do
Some great mathematicians are born and others are made by having ability that is well applied. Furthermore, even if they do not understand it, nearly all people appreciate mathematics and all it is used for. The last group is more to the point of this book, in that the definition of a mathematician as referenced in the title is being extended to include those who appreciate what mathematics can do. Functions in math libraries are what I use as first examples as objects in my programming courses. Even though the students do not understand the behavior of functions such as the sine and cosine, they do understand the concept of a function call better when it is presented in a mathematical context.
This book is a collection of many mathematical discoveries that have occurred down through the centuries. Some have significant applications, but most would be excellent fits within the definition of recreational mathematics. Topics such as patterns in numbers, mathematical games and mathematics for enjoyment are covered. Problems for examination and clarification are interspersed throughout the chapters with solutions at the end of the chapter. It is an ideal book for those who are interested in mathematics as a subject to explore for the purity of expression. As is pointed out in the text, there is a finality found in mathematics that exists nowhere else. Once something is proven and the proof is completely verified, the theorem is then an absolute truth. The level of difficulty is such that a solid background in algebra is the only requirement for understanding what is being described.
While the level of student performance in mathematics at all levels is often depressing, it is gratifying to see so many popular mathematics books being published. It is clear that there is a solid market for such material, which uplifts the spirits of all who appreciate the beauty and power of math. Reading this book will help place you in that category if you are not already a member.

Published in Journal of Recreational Mathematics, reprinted with permission.

Amazing Journey into Mathematics
This is certainly an interesting ride through the forests of mathematics.

The book is a very detailed and deep look at all branches of mathematics, and a very good look at many different curiosities and bewilderments. D.G. Wells starts with a brief look at triangles, numbers, and patterns and goes on to talk about the enjoyment of mathematics and certainty and proof. In between, he ventures into the world of mathematical games, the most famous of which is Conway's Game of Life. He also talks of modeling the universe, or at least certain aspects of it, using mathematics - and using mathematics to search for the truth. He concludes with a "mathematical adventure," where you, the reader, travels through a series of linked frames exploring a certain mathematical curiousity.

I recommend this book for teenagers developing an interest in mathematics, but also for those who think that mathematics can't be interesting, and even for math teachers - so that they can take a look at their work and all its wonderful applications.

Not for the mathematically-declined!
This book is a very intense look at mathematics; however, it is not so far out of reach that the average persion couldn't understand. It doesn't take more than a high school understanding of some basic algebra and geometry to truly enjoy this book. But be warned! This book is tough, and best tackled with plenty of scrap paper to try some of the problems. If you complete the book, you will have learned some very clever problem- solving skills. ... Read more

Book Description

Over the past 20 years, the study of superprocesses has expandedinto a major industry and can now be regarded as a central themein modern probability theory. This book is intended as a rapidintroduction to the subject, geared toward graduate students andresearchers in stochastic analysis.

A variety of different approaches to the superprocesses emergedover the last ten years. Yet no one approach superseded anyothers. In this book, readers are exposed to a number ofdifferent ways of thinking about the processes, and each is usedto motivate some key results. The emphasis is on why results aretrue rather than on rigorous proof. Specific results are given,including extensive references to current literature for theirgeneral form. ... Read more

Book Description

Mathematics is one of the most basic—and most ancient—types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists. The two-volume Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences recovers this mathematical heritage, bringing together many of the world's leading historians of mathematics to examine the history and philosophy of the mathematical sciences in a cultural context, tracing their evolution from ancient times to the twentieth century.

In 176 concise articles divided into twelve parts, contributors describe and analyze the variety of problems, theories, proofs, and techniques in all areas of pure and applied mathematics, including probability and statistics. This indispensable reference work demonstrates the continuing importance of mathematics and its use in physics, astronomy, engineering, computer science, philosophy, and the social sciences. Also addressed is the history of higher education in mathematics. Carefully illustrated, with annotated bibliographies of sources for each article, The Companion Encyclopedia is a valuable research tool for students and teachers in all branches of mathematics.

Contents of Volume 1: •Ancient and Non-Western Traditions •The Western Middle Ages and the Renaissance •Calculus and Mathematical Analysis •Functions, Series, and Methods in Analysis •Logic, Set Theories, and the Foundations of Mathematics •Algebras and Number Theory

Contents of Volume 2: •Geometries and Topology •Mechanics and Mechanical Engineering •Physics, Mathematical Physics, and Electrical Engineering •Probability, Statistics, and the Social Sciences •Higher Education and Institutions •Mathematics and Culture •Select Bibliography, Chronology, Biographical Notes, and Index ... Read more

Book Description

"Casti Tours offers the most spectacular vistas of modern applied mathematics" —Nature

Mathematical modeling is about rules—the rules of reality. Reality Rules explores the syntax and semantics of the language in which these rules are written, the language of mathematics. Characterized by the clarity and vision typical of the author's previous books, Reality Rules is a window onto the competing dialects of this language—in the form of mathematical models of real-world phenomena—that researchers use today to frame their views of reality.

Moving from the irreducible basics of modeling to the upper reaches of scientific and philosophical speculation, Volumes 1 and 2, The Fundamentals and The Frontier, are ideal complements, equally matched in difficulty, yet unique in their coverage of issues central to the contemporary modeling of complex systems.

Engagingly written and handsomely illustrated, Reality Rules is a fascinating journey into the conceptual underpinnings of reality itself, one that examines the major themes in dynamical system theory and modeling and the issues related to mathematical models in the broader contexts of science and philosophy. Far-reaching and far-sighted, Reality Rules is destined to shape the insight and work of students, researchers, and scholars in mathematics, science, and the social sciences for generations to come.

Of related interest . . .

ALTERNATE REALITIES

Mathematical Models of Nature and Man

John L. Casti

A thoroughly modern account of the theory and practice of mathematical modeling with a treatment focusing on system-theoretic concepts such as complexity, self-organization, adaptation, bifurcation, resilience, surprise and uncertainty, and the mathematical structures needed to employ these in a formal system.

1989 0-471-61842-X 493pp. ... Read more

Book Description

Quick, simple solutions to life¡¦s pesky math problems in an easy-to-use lighthearted reference book.

„h Millions are "math-phobic" and panic when faced with an everyday math problem.

„h Readers will quickly find solutions to math problems without having to re-learn complicated formulas or principles.

„h Easy to use, practical examples, and lighthearted tone make the book friendly and accessible.

"Use Your Fingers, Use Your Toes" offers relief to millions of math-phobes who, while generally bright and educated, panic when faced with an everyday math problem. Included are common, but puzzling problems such as adjusting recipes, calculating calorie counts and fat grams, measuring for new carpets, drapes and wallpaper, figuring percentage discounts, mortgage interest, taxes, sports statistics, miles per gallon, and, of course, tipping.The book moves at the pace of today¡¦s busy lifestyle. By reading through the clear step-by-step solution to a given problem, the reader can solve the problem in as little as five minutes. Other books concentrate on reteaching math; this book concentrates on offering quick, accessible, example-oriented solutions for today¡¦s busy lifestyles. ... Read more

Reviews (2)

Great reference book
This is a great reference book. It's saving me alot of time and aggravation. It's easy to find what you're looking for, get an understandable answer, and be on your way. It simplifies things so they're easily doable using real life situations which is very helpful. An added bonus is that they put a quick reference appendix in the back that's absolutely wonderful.

Use Your Fingers, Use Your Toes: Quick and Easy Step-By-Step
Offers relief to millions of math-phobes who, while generally bright and educated, panic when faced with an everyday math problems like adjusting recipes, calculating calorie counts and fat grams, measuring for new carpets, drapes and wallpaper, figuring percentage discounts, mortgage interest, taxes, sports statistics, miles per gallon, and tipping ... Read more

Book Description

This fully updated edition of Practical Problems in Mathematics for Drafting and CAD features contemporary drafting problems, CAD drawings, and industry applications and practicesessential information designed to enhance the math skills of students concentrating their studies in the field of drafting.A comprehensive compilation of integrated math problems and CAD operations facilitates critical thinking, problem solving, and basic mathematics literacy.Real-world, everyday applications include use of a scientific calculator to solve math problems in drafting and CAD.Examples and figures cover a range of skills and levels of difficulty, and math principles provide a challenge for a variety of ability levels. ... Read more

Book Description

Boiled-down essentials of the top-selling Schaum's Outline series for the student with limited time

What could be better than the bestselling Schaum's Outline series? For students looking for a quick nuts-and-bolts overview, it would have to be Schaum's Easy Outline series. Every book in this series is a pared-down, simplified, and tightly focused version of its predecessor. With an emphasis on clarity and brevity, each new title features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form.

Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give students quick pointers to the essentials.

• Designed to appeal to underprepared students and readers turned off by dense text
• Cartoons, sidebars, icons, and other graphic pointers get the material across fast
• Concise text focuses on the essence of the subject
• Delivers expert help from teachers who are authorities in their fields
• Perfect for last-minute test preparation
• So small and light that they fit in a backpack!

Reviews (1)

commentary & selected ECC papers (1'st 25 years)
A collection of selected famous coding theory papers written in 1974. Easier than collecting the papers individually, plus Berlekamp's comments make interesting reading. ... Read more

Book Description

Motivate students with math lessons based on real life problem-solving situations with food. Even the most hard to manage students are interested in the lesson when something worthwhile is being asked, solved, and eaten! ... Read more

Reviews (3)

One path to learning mathematics
Ambivalence surrounds me when I attempt to review this book. As someone who learned arithmetic in the pre-calculator days, many of the ideas in this book bring back deep memories. One of my favorite things to do when in my teen years and later was to keep track of the items in the grocery cart and estimate the total cost. It was considered a failure when the guess and true total differed by more than $0.25. While this skill did succeed in amazing people, I cannot recall a single instance where it actually was financially beneficial. And eventually I gave it up, going on to mathematics and computers.
But those days are gone, and calculators (computers) do free the mind for other things. So the question becomes, is it beneficial to read books of this type and learn the "lost" art of estimation? The history of mathematics informs us that early mental manipulation of numbers is a strong indicator of the future development of mathematical ability. Gauss and Hardy are two excellent examples of this. However, in later years Hardy in particular looked down on those who were mere number crunchers.
Which leads to the clearest use for the techniques demonstrated in this book, namely to instruct children in the mental manipulation of symbols. By having young minds compete against a calculator, mental techniques are developed that most likely cannot be created any other way. And those methods are excellent training for future careers in the quantitative sciences. And this book does an excellent job in introducing these "tricks." All are clearly explained and detailed solutions to the problems are in the back of the book. Anyone wishing to learn how to perform efficient mental computations will find what they are looking for.
If your goal is to teach or learn how to perform calculations in your head, then this book is for you. However, one should make an effort to keep everything in perspective. The ability to perform mental arithmetic should be considered as a step toward mathematical ability and not a stand-alone indicator of such skill.

(Published in "Journal of Recreational Mathematics" - reprinted with permission.)

Una pequeña joya
He encontrado el libro muy útil , entretenido , y facil de leer.
Muy recomendable para iniciarse en el cálculo mental.

Truly amazing
A truly amazing insight into various ways to mystify others with seemingly impossible mathematical challenges. Learn how to determine the day someone was born on, or guess the missing number in the answer to a multiplication problem. This book provides you with insight to the fun (yes... fun) side of math. You will be greatly impressed by the tricks to amaze your friends and make math interesting ... Read more

Amazon.com

A.K. Dewdney takes readers on a theoretical world tour to answer the question: Did humans make up mathematics, or did mathematics make up everything, including humans? After all, mathematical formulas seem to perfectly govern the cosmos, and the ur-mathematician Pythagoras himself believed that mathematics makes up reality. Dewdney has taken it upon himself to examine this fundamental question, beginning his journey in Miletus, the ancient home of Pythagoras and other deep thinkers. There, he meets the fictional Dr. Petros Pygonopolis, the first of his guides through space and time in search of mathematical meaning in history. His journey continues with stops in the Arabian desert (for insight into ancient Islamic astronomy with Professor al-Flayli), Venice (where Maria Canzoni reveals the mysteries of atomic theory), and England (home of the "engines of thought" in the form of Alan Turing's mind machines, as explained by Sir John Brainard). Dewdney's style is accessible, his knowledge is thorough, and his sense of humor is refreshing, if a bit geeky. A Mathematical Mystery Tour is not a difficult read, although the ideas it attempts to clarify are quite abstract. The fictional tour guides at each port of call are helpful in humanizing the intimidating subject matter. --Adam Fisher ... Read more

Reviews (11)

Some of the greatest achievements in mathematics
To explore the great beauty of mathematics, it is always necessary to go back to the ancient Greeks. It was there that the great intellectual breakthrough of abstract mathematics was made.Dewdney begins his mathematical journey at the logical place, Athens, Greece. His first discussions are with Petros Pygonopolis, a specialist in ancient Greek mathematics. Quite fittingly, Pygonopolis is found measuring the stones of an ancient structure with a ruler. This proves to be an excellent starting point for the explanation of the discovery of irrational numbers. Before the great proof that the square root of two was irrational, it was believed that all values were commensurate. This means that by repeating one length a specific number of times and the other length a different number of times, two distances of the same length could be created. The most interesting part of this discussion is the descriptions of how numbers were represented in ancient Greece. In many ways, it is incredible to realize how cumbersome their notation was.
In keeping with the historical development of mathematics, Dewdney then travels to Amman, Jordan to examine the development of mathematics in the Arab world. After the collapse of the Roman Empire, the development of mathematics essentially ceased in Europe. All mathematical progress for centuries after the collapse took place in the Arab world. He meets with Jusuf al-Flayli, an Egyption astronomer who is an expert in the Arab view of the heavens. The naming of the stars is important in Arab culture, and it is clear when you read Dewdney's account. For where else but in the desert would one see the greatest, clearest spectacle of stars.
Venice, Italy is the next stop, for discussions with Maria Canzoni. These discussions are about the development of numerical operations, the new representations and the notations used in the operations. It is difficult to overstate the significance of positional notation. It is hard to see how modern commerce could have ever developed without it. One thing that it is difficult for math students to appreciate is how clean modern mathematical notation is. Even the simple symbols of addition, subtraction and so on abbreviate some very advanced mathematical concepts.
The last stop on the tour is Oxford, England where Dewdney has discussions with Sir John Brainard. The conversation uses nonsense words such as gadzooks, blorgs, semiblorgs, zooks and horping tables. These terms are actually replacements for the words of group theory. Brainard uses this as an example to illustrate the idea put forward by David Hilbert for geometry. Namely that geometry should be constructed so that the terms point, line and plane can be replaced by chair, table and beer mugs. It was quite fun to read and reminded me of some of the writings of Lewis Carol.
There is great beauty in mathematics, sometimes even practitioners fail to appreciate it. Dewdney does an excellent job in describing some of the more significant events in the history of mathematics. Read it and appreciate what some of the great minds have done.

Lofty goals unachieved
The book tries to explore some of the more philisophical aspects of mathematics, and cannot be faulted for its failure to reach any real conclusions there.If an answer were easy to come by, it would indicate that the questions were not so philisophical after all.

Unfortunately, the book also fails to achieve secondary goals.Both the historical and mathematical topics it covers could be covered just as well in 1/5 the pages.The extra length comes from trying to work the material into a journey, a technique possibly used in an attempt to make the topics less intimidating or more interesting, but which in fact just makes them boring.If one travels to see and talk to somebody, the travel itself (plane ride, taxi, carrying of the bags) is oftentimes a boring chore needed to get where you are going.Why describe it here?It is not more interesting to read about than to experience.

Instead, this book seems to combine all of the filler material needed to make a fictional story consistant and realistic, but there is not really any story being told here.If one wants a story with some math worked in, try A. K. Doxiadis's "Uncle Petros and Goldbach's Conjecture" instead.

When I saw the title of the book, it reminded me of Ivars Peterson's "The Mathematical Tourist", which I have only looked at briefly, but which explores interesting areas of mathematics.If one wants an overview of some interesting math topics, this is a much more appropriate book.

In Dewdney's book, we get a "tourist" book with few points of interest, mathematical, historical, or geographical.Given the interesting people, places, and material covered, it really misses the mark.

Interesting subject, disappointing errors
I started reading this book like all others: with anticipation to learn something new and exiting but instead mistakes hit me over my head. On page 85 the author calls the angle between the zenith and a star its declination. Wrong name: It is (90 degrees minus altitude), also called the complementary angle. The declination is the distance from the equator. On page 97 the author gives the impression that the polar star (Polaris) is moving with the seasons; that is not so. Polaris is fixed on the celestial sphere except for a very small daily circle of about 1.5 degree radius. Page 101 makes Kepler a priest which he was not. He just studied Lutheran theology before turning completely to natural philosophy and teaching for a living. Kepler never ignored Copernicus as claimed by Dewdney and neither is the Earth in the middle of the Platonic Solids but the Sun as described in the Mysterium Cosmographicum. On page 103 the author makes us believe that the geographical latitude of Baghdad as measured by the altitude of Polaris is 33 degrees 19 minutes at the beginning of spring; the altitude of Polaris for Baghdad is the same all the time except for that small daily variation mentioned before. On page 110 the author gives the title of Fibonacci's main work as "Algorismus"; there is no work of this title, the common name of his major work is given as "Liber abaci (or abbacy)" - The Book of Abacus. On page 113 the author attributes the spectral lines of the Balmer Series to "vibration" of the atoms. Not so. In Bohr's model the spectral lines are caused by transition of electrons between different levels of energy or different orbits. Vibrations are involved in the spectra of molecules. Finally, why has the author forgotten Mr. Balmer while attributing the different Hydrogen series with changing parameter n to (1) Lyman, (2) Paschen, (3) Brackett and (4) Pfund? The correct attribution is (1) Lyman, (2) Balmer, (3) Paschen, (4) Brackett and (5) Pfund.
I think that I lost my patience reading this book at that point.

Tour is actually Discovering the Truth & Beauty of the Holos
Tour is certainly a rare book, one on mathematical philosophy. After all, it is commonly accepted that physics describes the real world, while metaphysics grapples with the questions of what is real? With that being said, Dewdney turns his attention the tools of mathematics that Physics uses in its descriptions, and ponders if there could be the "meta-mathematical." In Tour, he undertakes to answer two questions. First, why is mathematics so amazingly successful in describing the structure of physical reality, and second, is mathematics discovered or is it created? These are not trifling questions. Consider the discovery of the planet Neptune. In 1845, the 23-year old British John Couch Adams completed calculations pinpointing a new planet that he believed was perturbing the orbit of Uranus. That same year, French astronomer Urban Jean LeVerrier independently published his prediction of the position of the new planet, within a degree of Adams. Alone, this proves almost nothing. Given the same set of data from observations, regardless of how complex the celestial mechanics are, the formulae do not change and accurate algebraic answers should agree (although they do provide standalone verification for each other). What happened next though transforms a merely mathematical exercise into Dewdney's quest to understand the true nature of math. On the same night they read of it, Johann Galle and Heinrich d'Arrest at the Berlin Observatory search and see an eighth magnitude "star" right where LeVerrier envisaged it. Dewdney dares asks, "Why is the physical universe determined (or accurately describable) to so great an extent by Mathematical ideas?"
To answer, Dewdney employs what in the preface he describes as "a fictional narrative," that leads from Greece to Arabia to Italy to England. However, his level of detail and his concluding notes in the postscript lead me to question how fictional the four characters are who elucidate on the subject. I suppose that is to be expected in a work of philosophy, blurring the distinction of who is real. There is one other "character," dead some 2,500 years, but whose mystical and mathematical spirit is still felt: Pythagoras. Carl Sagan credits Pythagoras as the first to "use the word Cosmos to denote a well-ordered and harmonious universe, a world amenable to human understanding" (hence the title for Sagan's series; and now you know the rest of the story!) The followers of Pythagoras developed an entire mathematical cult, a sect that sincerely believed that through math they were glimpsing a perfect reality, a nonmaterial higher realm, of which the physical world was a manifestation. The dwellers of Plato's cave were inheritors indirectly of the Pythagoreans: "The stars that decorate the sky, though we rightly regard them as the finest and most perfect of visible things, are far inferior, just because they are visible, to the true realities; that is, to the true relative velocities, in pure number and perfect figures, of the orbits and what they carry in them, which are perceptible to reason and thought but not visible to the eye. (The Republic, Plato, book VII, 529-E)." In his first stop, along the coast of the Aegean, Dewdney encounters the "holos," the place where all of mathematics, known and unknown, exists. The Cosmos is the manifestation, but the holos is the source, so much so that the Tour is actually Discovering the Truth and Beauty of the Holos. But be cautioned though that a proper frame of mind is a prerequisite. Just as Galileo's journals show he observed Neptune in 1612 but failed to recognize it for what it was, so to Tour benefits from a second or third revisit for complete comprehension.

VERY DUMB
I was forced to read this book for a Pre Calc Class and I must say that it is the most boring book that I have ever read.If this is a teacher reading this, let me tell you that you are going to torture your students if you give them this book. ... Read more

Book Description

In Count Down, Steve Olson sets out to crack a secret: what inspires a select few average-seeming American teens to become wizards at the world's toughest math competition? Olson shadows the six charming U.S. contestants at the 2001 International Mathematical Olympiad, from their free-time games of Ultimate Frisbee to the high-pressure rounds of the competition, getting to the core of what drives theseyoung people and makes them such nimble problem solvers. In each he finds a mix of inspiration, insight, competitiveness, talent, creativity, and experience, and, perhaps most important, an enduring sense of wonder. As he observes the competitors, Olson delves into math culture and education, exploring why many American students dread geometry, why so few girls pursue competitive math, and whether each of us might have a bit of genius waiting to be nurtured. For parents, teachers, students, and kindred puzzle-lovers, Count Down reveals an engaging approach to the art of beautiful solutions. ... Read more

Book Description

Teachers of political science, social studies, and economics, as well as school library media specialists, will find this resource invaluable for incorporating the Internet into their classroom lessons. Over 150 primary source Web sites are referenced and paired with questions and activities designed to encourage critical thinking skills. Completing the activities for the lessons in this book will allow students to evaluate the source of information, the content presented, and it usefulness in the context of their assignments. ... Read more

Book Description

A booklet giving easy access to the most crucial concepts and formulas in basic mathematics. Has the same effect as flash cards, but in a bound form. ... Read more