Book Description

The Penguin Desk Encyclopedia of Science and Mathematics has thousands of entries that go beyond simply defining concepts or identifying the components of our natural world. It includes:

* Detailed drawings throughout
* Tables that provide succinct and complete data
* An exhaustive index to help locate information tied to the main entries
* Cross-references to aid in finding all the information about a particular topic

This is a book that will help readers and students straighten out the meaning of science and mathematics in relation not only to our planet, but also to the universe. ... Read more

Reviews (1)

How many teeth does an aardvark have?
This is one excellent resource for lay people and students that helps understanding scientific concepts and terminology that bombards us today.While the television tells us that we will be blasted into an ice age through the greenhouse effect, we can enjoy browsing through this to find out the whys and hows.There are plenty of cross-references within entries that make it easy to locate information.It's a good read and worth putting into your library. ... Read more

Book Description

This book is devoted to differential forms and their applications in various areas of mathematics and physics. Well-written and with plenty of examples, this introductory textbook originated from courses on geometry and analysis and presents a widely used mathematical technique in a lucid and very readable style. The authors introduce readers to the world of differential forms while covering relevant topics from analysis, differential geometry, and mathematical physics.

The book begins with a self-contained introduction to the calculus of differential forms in Euclidean space and on manifolds. Next, the focus is on Stokes' theorem, the classical integral formulas and their applications to harmonic functions and topology. The authors then discuss the integrability conditions of a Pfaffian system (Frobenius's theorem). Chapter 5 is a thorough exposition of the theory of curves and surfaces in Euclidean space in the spirit of Cartan. The following chapter covers Lie groups and homogeneous spaces. Chapter 7 addresses symplectic geometry and classical mechanics. The basic tools for the integration of the Hamiltonian equations are the moment map and completely integrable systems (Liouville-Arnold Theorem). The authors discuss Newton, Lagrange, and Hamilton formulations of mechanics. Chapter 8 contains an introduction to statistical mechanics and thermodynamics. The final chapter deals with electrodynamics. The material in the book is carefully illustrated with figures and examples, and there are over 100 exercises.

Readers should be familiar with first-year algebra and advanced calculus. The book is intended for graduate students and researchers interested in delving into geometric analysis and its applications to mathematical physics. ... Read more

Book Description

In differential geometry and topology one often deals with systems of partial differential equations, as well as partial differential inequalities, that have infinitely many solutions whatever boundary conditions are imposed. It was discovered in the fifties that the solvability of differential relations (i.e. equations and inequalities) of this kind can often be reduced to a problem of a purely homotopy-theoretic nature. One says in this case that the corresponding differential relation satisfies the $h$-principle. Two famous examples of the $h$-principle, the Nash-Kuiper $C^1$-isometric embedding theory in Riemannian geometry and the Smale-Hirsch immersion theory in differential topology, were later transformed by Gromov into powerful general methods for establishing the $h$-principle.

The authors cover two main methods for proving the $h$-principle: holonomic approximation and convex integration. The reader will find that, with a few notable exceptions, most instances of the $h$-principle can be treated by the methods considered here. A special emphasis in the book is made on applications to symplectic and contact geometry.

Gromov's famous book "Partial Differential Relations", which is devoted to the same subject, is an encyclopedia of the $h$-principle, written for experts, while the present book is the first broadly accessible exposition of the theory and its applications. The book would be an excellent text for a graduate course on geometric methods for solving partial differential equations and inequalities. Geometers, topologists and analysts will also find much value in this very readable exposition of an important and remarkable topic. ... Read more

Book Description

Mathematics for the Imagination provides an accessible and entertaining investigation into mathematical problems in the world around us. From world navigation, family trees, and calendars to patterns, tessellations, and number tricks, this informative and fun new book helps you to understand the maths behind real-life questions and rediscover your arithmetical mind. This is a follow-up to the popular Mathematics for the Curious, Peter Higgins's first investigation into real-life mathematical problems. This is a highly involving book which encourages the reader to enter into the spirit of mathematical exploration. ... Read more

Reviews (1)

More good maths for the masses from Mr. Higgins
This is a popular maths book and it continues on where 'maths for the curious' left off. I didn't give it 5 stars because although well written it is structured less well than the first book but nevertheless there is some good stuff here for those non-mathematicians wanting to know more about the subject. The section on 'possible and impossible constructions' for instance is a good guide to the whole 'squaring the circle' problem. My only criticism is the structure which includes the 'for connoiseurs' section at the end. I think the structure problem is partly to do with not saying enough about how each chapter relates to the big mathematical picture. Separating out really hard stuff to the end is another structural mistake since it's nicer (IMHO) if the book flows from beginning to end with the hard stuff set in context and maybe bracketed with a warning that 'this is difficult'. But that's me. Anyway Peter should keep writing because those of us who are fascinated by the subject and only have time to read about it in odd moments need all the simplified explanations of complex maths we can get. ... Read more

Book Description

In this volume the author presents, in great detail and with manyexamples, a basic collection of principles, techniques, andapplications needed to conduct independent research in gaugetheory and its use in geometry and topology. Complete andself-contained computations of the Seiberg-Witten invariants ofmost simply connected algebraic surfaces using only Witten'sfactorization method are included. Also given is a new approachto cutting and pasting Seiberg-Witten invariants, which isillustrated by examples such as the connected sum theorem, theblow-up formula, and a proof of a vanishing result of Fintusheland Stern. The book is a suitable textbook for advanced graduatecourses in differential geometry, algebraic topology, basic PDEsand functional analysis. ... Read more

Book Description

Another brand-new title in Barron’s Essential Atlas science series explains principles of mathematics, which is the universal language of all science. This volume opens with a brief, enlightening description of the differing numeric systems devised by various cultures. The multitude of practical applications involving mathematics are then shown and explained, including measurements of weight and volume, monetary calculations, the binary system and its application in computer science, and much more. Architecture is discussed in terms of its fundamental relationship to principles of geometry. The circle, angles, and trigonometric functions are described, and fundamental principles of calculus and probability are touched upon. This easy-to-comprehend volume makes imaginative use of charts and diagrams to explain mathematical reasoning. There are color photos and illustrations on every page. ... Read more

Amazon.com

How are the great pyramids like seashells? Ask mathematician Midhat J. Gazale, then brace yourself for a heady ride through the wilds of self-similar geometry in Gnomon: From Pharaohs to Fractals, his paean to the roiling mysteries that lie beneath the tranquil surfaces of such objects. The great mathematician Hero of Alexandria defined a gnomon as an object that, when added to another, creates a new object similar in form to the original. Gazale, also of Alexandria, goes much further and uses 20th-century concepts to fully explore "gnomonicity"--the property of self-similarity.

Be prepared for slow going: Gnomon is densely packed with information and concepts foreign to all but the professional mathematician, but Gazale's enthusiasm and brilliant illustrations win the day. Whether he's moving on from the familiar golden rectangle to his own "silver pentagon" or rooting around in the numbers underlying the groovy fractal images popping up on T-shirts worldwide, he takes care to explain to the reader not just what's going on mathematically but what all this abstraction really means to us. Few science books, and even fewer mathematics books, achieve that kind of depth. --Rob Lightner ... Read more

Reviews (4)

Well written, but tediously boring book
....I found this book to be relatively well written, but tediously boring. This book should probably be considered "Recreational Mathematics" and is jammed with math; very little prose accompanies it. Indeed, if you do not love math, or do not love math for the sake of math (rather than, say, a physicist who merely loves math for the sake of his primary interest in physics) then you will probably not enjoy this book.

The prose that the book contains seems to attempt to relate the various math that Gazale demonstrates to practical problems, especially in electrical engineering. I found these analogies to be difficult to follow and did not create much understanding of the material. For example, he discusses resonant LCR circuits and power transmission lines, and his descriptions pale in comparison to those I found in Feynman's "Lectures on Physics."

Now,... this book has a number of useful things in it which is why I say it's "well written." It does include mathematical summaries in the end of every chapter. In my opinion, this was the best part of the book. By reading only the summaries, the reader "takes away" most of what the author is trying to say, without having to suffer through the rest of it. If the summary is not self-evident, the reader can always go back to the chapter to divine how one of the entries in the summary was derived.

All in all, I would not recommend this book to those interested in anything other than math for math's sake. If your interest lies elsewhere, or even only obliquely in math (such as in learning math for a specific use), then avoid this book. However, if you do enjoy a mathematical romp, then this book could well be the one for you.

Slow going, but worth it
According to Gazale', "Hero of Alexandria defined the gnomon as that figure (a number or a geometric figure) which, when added to another figure, results in a figure similar to the original." Gazale's book is, therefore, about self-similarity in numbers and geometry.

The subject sounds simple enough, but I found this to be a pretty tough book. That might be partly due to the fact that I've always had a hard time focusing my attention on number theory. This book has a lot of basic stuff about numbers, and I found much of that subject rather tedious and (dare I say it?) boring. I know that's an ignorant thing to say - after all, mathematics is a beautiful subject in its own right, and there is some really neat stuff in number theory. But it was still a tough book for me to wade through.

The introduction is mostly historical background, and a little truncated. It serves primarily to illustrate a few basic concepts in self-similarity. The author continues this theme with a short description of figurate and m-adic numbers. Gazale tends to use more technical language than many casual readers are likely to recognize. Yet this really isn't a book on formal mathematics, either. It's really somewhere in between.

Gazale often draws on themes from Martin Gardner's series of articles in Scientific American, and in some ways, his book reflects Gardner's style. And, while much of this book seems focused on abstract details, there are occasional forays that illustrate amazing connections between what looks like pure mathematics and the real world.

Chapter 2, titled "Continued Fractions," is foundational. I really enjoyed this section, and think the book is worth having for this chapter alone. Beginning with Euclid's algorithm, Gazale offers a natural introduction to continued fractions. Then, in his characteristic style, he continues to explore every nook and cranny of this fascinating branch of mathematics. Among the most pleasing results of this chapter is his demonstration of the mirrored similarity in the appearance of numbers as they are represented by continued fractions, and as they are represented by our traditional positional number system. For example, he shows that both representations are always convergent and uniquely correspond to a number. However, while infinite periodic representations correspond to rational numbers in the positional system, they correspond to quadratic irrationals in the system of continue fractions. And, while transcendental and irrationals are infinite nonperiodic representations in both systems, there are some beautiful expressions of some transcendental numbers in the system of continued fractions that left me mesmerized.

One particularly nice feature is the way the author summarizes the important equations at the back of each chapter. Some of these summaries are several pages long, and they actually do a good job of encapsulating the essential material. In fact, the summaries are so well done that, if you read the book, you probably will be able to go back and use the formulas in the back of the chapters without having to refer back to the text.

If you ever wanted to know about the Fibonacci sequence, I can hardly imagine a book that will satisfy you better than this one. The first thing you will learn is that the Fibonacci sequence you met in grade school is just a small subset of a more general form. Then, in a whirlwind of mathematical activity you will see the general recursive formula (which depends, of course, on the seed and gnomonic numbers). This is followed by explicit formulae for the terms of the sequence and even a demonstration of how some of these equations, in the limit, model the behavior of wave propagation in an electronic transducer ladder, and the movement of a ganged series of pulleys.

A continuing source of amazement is the way in which the mathematical themes in this book are so interconnected. That's fitting, I suppose, for a book called Gnomon. In the chapter on whorled figures we see many of the other subjects in this book reappearing.

The book also has an excellent chapter on the golden number, and another on the silver number. The golden number, as you may know, shows up all over the place, and not just in Gazale's book. Here, he connects it with the Fibonacci sequence, whorled spirals, and golden rectangles. And for every example using the golden number, not surprisingly, there is another using the silver number. It's fascinating to read of all the ways in which these numbers shows up, and try to contemplate the underlying order that makes it happen this way.

Things get a little more abstract toward the end of the book (but no less interesting), and a bit harder to read. There are some very interesting developments with spirals and the rotation matrix, along with some interesting construction techniques for making your own spirals with paper and pen.

The last chapter, on fractals, exercised my little gray cells more than the rest of the book. This is not your typical discussion about fractals, with pretty pictures and non-technical explanations about self-similarity at any level. While Gazale does not dive in with the sort of mathematical rigor to which a pure mathematician would aspire, he claims to have written an unusual chapter on the subject, derived directly from number-theoretic considerations. This chapter will keep you busy following all the ins and outs of some pretty involve matrix mathematics. If you like the fast-Fourier algorithm, I think you'll love it.

This book is definitely not for everyone. But if you really, really like mathematics, and especially number-theoretic mathematics, I think you will like it. It will most definitely exercise your mind, but then again, that's what a good book on mathematics is supposed to do. Isn't it?

It would be better if this guy could write
I'm a regular reader of all sorts of books on math, and so Gnomon seemed a natural for me. I have a master's degree in computer science (bachelors, too, but i digress) and this sort of thing is right up my alley. The book doesn't really cover any new ground, but it does gather separate things into one volume, which makes it nice as a reference. The biggest problem with the book is with the actual text. This guy can't write. Yes, the material is technical, yes it's slow going, but that is no excuse for poorly structured arguments and incoherent organization of the material.

It's all here, but you'll need to work through it slowly and try to infer what he means because he leaves out a bunch of foundation work.

An extremely original book , full of ideas and discoveries.
A very approachable text that appeals to the academic as well as non academic.The simplicity and power of mathematics is demonstrated by this erudite author who promotes this unique and historical approach of the evolution of math. He successfully descibes the self similar processes in math as well as in life forms. Self similarity is the common thread. Very stimulating. ... Read more

Book Description

This book offers a comprehensive and reader-friendly exposition of the theory of linear operators on Banach spaces and Banach lattices using their topological and order structures and properties. Abramovich and Aliprantis give a unique presentation that includes many new and very recent developments in operator theory and also draws together results which are spread over the vast literature. For instance, invariant subspaces of positive operators and the Daugavet equation are presented in monograph form for the first time.

The authors keep the discussion self-contained and use exercises to achieve this goal. The book contains over 600 exercises to help students master the material developed in the text. The exercises are of varying degrees of difficulty and play an important and useful role in the exposition. They help to free the proofs of the main results of some technical details but provide students with accurate and complete accounts of how such details ought to be worked out. The exercises also contain a considerable amount of additional material that includes many well-known results whose proofs are not readily available elsewhere.

The companion volume, Problems in Operator Theory, also by Abramovich and Aliprantis, is available from the AMS as Volume 51 in the Graduate Studies in Mathematics series, and it contains complete solutions to all exercises in An Invitation to Operator Theory.

The solutions demonstrate explicitly technical details in the proofs of many results in operator theory, providing the reader with rigorous and complete accounts of such details. Finally, the book offers a considerable amount of additional material and further developments. By adding extra material to many exercises, the authors have managed to keep the presentation as self-contained as possible. The best way of learning mathematics is by doing mathematics, and the book Problems in Operator Theory will help achieve this goal.

Prerequisites to each book are the standard introductory graduate courses in real analysis, general topology, measure theory, and functional analysis. An Invitation to Operator Theory is suitable for graduate or advanced courses in operator theory, real analysis, integration theory, measure theory, function theory, and functional analysis. Problems in Operator Theory is a very useful supplementary text in the above areas. Both books will be of great interest to researchers and students in mathematics, as well as in physics, economics, finance, engineering, and other related areas, and will make an indispensable reference tool. ... Read more

Book Description

This book is an English translation of the last French edition of Bourbaki's Functions of a Real Variable. The first chapter is devoted to derivatives, Taylor expansions, the finite increment's theorem, convex functions. In the second chapter, primitives and integrals (on arbitrary intervals) are studied, as well as their dependence with respect to parameters. Classical functions (exponential, logarithmic, circular and inverse circular) are investigated in the third chapter. The fourth chapter gives a thorough treatment of differential equations (existence and unicity properties of solutions, approximate solutions, dependence on parameters) and of systems of linear differential equations. The local study of functions (comparison relations, asymptotic expansions) is treated in chapter V, with an appendix on Hardy fields. The theory of generalized Taylor expansions and the Euler-MacLaurin formula are presented in the sixth chapter, and applied in the last one to the study of the Gamma function on the real line as well as on the complex plane. Although the topics of the book are mainly of an advanced undergraduate level, they are presented in the generality needed for more advanced purposes: functions allowed to take values in topological vector spaces, asymptotic expansions are treated on a filtered set equipped with a comparison scale, theorems on the dependance on parameters of differential equations are directly applicable to the study of flows of vector fields on differential manifolds, etc. ... Read more

Reviews (2)

An exploration of mathematics in traditional peoples
In the current atmosphere of political correctness and emphasis on multicultural attributes, it was inevitable that the mathematical air would be affected. However, any examination of obscure cultures presents an opportunity to lose perspective. It is very easy to examine a cultural attribute, explain it via abstract mathematics, and then call that an example of mathematical sophistication. For as all mathematics teachers know, the ability to do a particular application in no way means that the person knows the theory or can apply it in another context. The author makes an occasional and fairly deep penetration into this pitfall, but on the whole maintains a balanced outlook.
Ethnomathematics is given the definition, "study of the mathematical ideas of traditional peoples," and is a loose marriage of mathematics and anthropology. The primary cultures investigated are the Inuit, Navajo, and Iroquois of North America; the Incas, the Malejula, Warlpiri, Maori, and Caroline Islanders of the Pacific; and the Tshokwe, Bushoong, and Kpelle of Africa. Since the vast majority of potential readers have never heard of most of these cultures, reading the book has value as a simple exercise in horizon expanding. In all cases the level of mathematics is not deep, but some exposure to the particular concept is essential.
Chapter one describes how the Incas stored information by tying knots in cords (called quipu), and is more discourse than mathematics. The second chapter explains the Bushoong, Tshokwe, and Malekula traditions of drawing figures in sand, and uses graph theory to explain how it is possible to draw some of the figures without lifting the stick. The third one deals with the Warlpiri logic of kin relations, with group theory being the mathematical foundation. This is where the author falls the most, as can be seen from the following quote: "To me it is striking to find that a logical structure studied abstractly and extensively by Western mathematicians plays a central and significant role in the day-to-day life of some peoples." Given the ubiquity of modern mathematics, it would be more surprising if no explanation existed.
The fourth chapter deals with the games and puzzles of several of the cultures. Number five describes the perception of geometric shapes by several Native American tribes and how the Caroline Islanders use the heavens to navigate. Here again, it is more a listing of the thoughts than mathematical justification. Chapter Six gives many examples of symmetric patterns of decoration, all of which can be assigned group theoretic analogues.
If you are interested in the mathematical thought of these cultures, then this book is essential. However, given the current academic climate, this is no doubt the first in a string of books of this type. Which, when you think about it, is a good thing for us all.

Published in Journal of Recreational Mathematics, reprinted with permission.

An interesting look at fascinating, and foreign, ideas
This book has two goals: one is defining the field of ``ethnomathematics'', the second is legitimizing the field by giving examples of what it might cover. This is more anthropology than mathematics, but would still appeal to a fan of Martin Gardner.

Memorable topics: the Inuit view of space, a sort of ethnotopology; navigation among the Polynesian islanders (how *do* they steer those tiny boats across five hundred miles of open ocean and arrive at an island a half-mile across? --- this chapter is simply amazing!); deciphering the code of the quipu (the knotted strings that formed the accounting records of the Incan Empire). ... Read more

Book Description

Clear, rigorous definitions of mathematical terms are crucial to good scientific and technical writing-and to understanding the writings of others. Scientists, engineers, mathematicians, economists, technical writers, computer programmers, along with teachers, professors, and students, all have the need for comprehensible, working definitions of mathematical expressions. To meet that need, CRC Press proudly introduces its Dictionary of Algebra, Arithmetic, and Trigonometry- the second published volume in the CRC Comprehensive Dictionary of Mathematics. More than three years in development, top academics and professionals from prestigious institutions around the world bring you more than 2,800 detailed definitions, written in a clear, readable style, complete with alternative meanings, and related references.From Abelian cohomology to zero ring and from the very basic to the highly advanced, this unique lexicon includes terms associated with arithmetic, algebra, and trigonometry, with natural overlap into geometry,topology, and other related areas.Accessible yet rigorous, concise but comprehensive, the Dictionary of Algebra, Arithmetic, and Trigonometry is your key to accuracy in writing or understanding scientific, engineering, and mathematical literature. ... Read more

Book Description

This book gives a broad overview of core topics of finite model theory: expressive power, descriptive complexity, and zero-one laws, together with selected applications to database theory and artificial intelligence, especially constraint databases and constraint satisfaction problems. The final chapter provides a concise modern introduction to modal logic, which emphasizes the continuity in spirit and technique with finite model theory. This underlying spirit involves the use of various fragments of, and hierarchies within, first order, second order, fixed point, and infinitary logics to gain insight into phenomena in complexity theory and combinatorics.

Students of logic and computer science will find here the tools necessary to embark on research in finite model theory, and all readers will experience the excitement of a vibrant area of application of logic to computer science.

Amazon.com

Clifford Pickover is by most standards a mathematics geek (Ph.D. research scientist for IBM, associate editor for two computer journals), but he is the coolest math geek you might ever meet. For this book he has compiled 30 chapters of mathematical puzzles (and one short story), all having some connection to the concept of infinity. These problems are open-ended; in the event that the reader actually solves the main puzzle, there are enough digressions, diversions, and tangents to keep even the fastest computer running for hours. Computer modelers will be happy to find that instructive BASIC and C language has been provided for most of the problems. Many puzzles have been previously posted on the Internet, and the best or weirdest replies have been included in this book.

If phrases like "Monte Carlo bootstrapping approximation" send you off the deep end, not to worry. These are not dry, dusty puzzles. In problems such as "The Loom of Creation," "Grid of the Gods," "Alien Abduction Algebra," and "The Infinity Worms of Callisto," Pickover has couched mathematical puzzles in bizarre science fiction scenarios to make them both fun and challenging. --Eric Warner ... Read more

Reviews (4)

A fascinating exploration of topics on infinity
*The book is a collection of fascinating, thought-provoking essays on
various topics which are not necessarily all concerned with infinite
topics. Some may be discussions of really big numbers or
mathematical constructs, but these may or may not necessarily involve
infinity.

*If you absolutely cannot stand math stuff, this is not your book.
Otherwise, it has a range of math from very simple to really
advanced. I just brushed over the very advanced math stuff that I
either did not understand or had long ago forgotten, but I didn't
really feel like I missed anything.

*There are a slew of amazing visually complex and striking graphical
representations of various advanced functions, etc. All are well
worth exploring, even if they do not directly involve infinite
concepts. The book is loaded with such graphics, a real visual feast.

*The math is rather advanced in some sections but is quite elementary
in others. Best of all, a generous collection of computer programs
is included which can be used to explore almost every chapter.

*There are a few "mystery" type things, but mostly it is just very
exotic, seldom-explored areas of number theories and other areas of
mathematics.

*The chapter on Vampire numbers is really cool, I thought. I have
seen them mentioned in posts here from time to time, now I understand
what they are and why they are so interesting

*The chapter on recursion has loads of really cool pattern-type stuff
that you can easily explore with a PC. A great topic.

*The chapter near the back of the book on random numbers and random
number generators is great background for some anyone interested in quantum theory. I had never seen the RNG cloud graphics before, what a
unique and ideal way to show the effectiveness of an RNG.

As expected, this is a great book, I heartily recommend it for all.

A truly entertaining book on numbers
A perpetual idea machine, Clifford Pickover is one of the most creative, original thinkers in the world today. In most cases using only simple ideas, he follows paths that in many cases must be constructed immediately before traversal. In this, his latest installment in that trek of exploration, he is again at his best.
Each subject starts with a simple premise and the author follows it through to a basic conclusion. Many of the topics involve computer programs, and source code is provided. The programs are in several languages, including C, Pascal, BASIC and Rexx. However, most programs are quite short and represent basic algorithms, so it is not difficult to understand a program even if you are not familiar with the language.
Some of the topics include:

- 10^33, the largest power of 10 that can be represented as the product of two numbers that contain no zero digits.
- A debate as to whether there should be a national computing initiative to compute the first trillion digits of Pi.
- Fractal milkshakes, or creating a collection of fractal "bubbles."

Truly fuN with a capital N for number, this is another of the author's superb creations. A math book that is entertaining, and not just to people who find it so by nature or profession.

Published in Journal of Recreational Mathematics, reprinted with permission.

Infinity got you stumped? Get this book
Having trouble understanding the concept of "infinity"? Know the word but don't have a deep understanding of what it really is? This book is for you! The author can take such a hard-to-grasp concept like infinity and make it accessible to everyone. With a good sprinkling of computer programs for those with access to one, Pickover provides the reader with the ability to experiment with the ideas presented.

The one thing wrong with this book is that it's finite
This book is not just for maths nuts like me. Its for anyone who has a passing interest in the subject.

The author has in a crisp and concise wa,y managed to introduce, and in some cases explain, both the history and the solution, to some of the most mystifying problems to confront mankind in his infinite quest to understand the Ultimate Infinity - The Universe.

The cover notes suggest that the reader requires "no specialised mathematical knowledge " but you will need to understand some maths probably to GCSE level but then you would not buy, borrow or steal this book if you can't add, subtract, multiply and divide.

The computer programs that are sprinkled throughout the book do require a lot of thought and a good knowledge of the particular language, of which there are several, to make them work but, when they do, they demonstrate the beauty of maths as well as illustrate the ideas under discussion extremely well.

In all a very good read. ... Read more

Book Description

In the Dictionary of Mathematics, key ideas, terms, and concepts are clearly explained in an accessible and easy-to-use format.

Each entry begins with a short definition and is followed by an explanation and/or worked example. The more complex and important the term, the more detailed the entry.

In writing each entry, the authors kept three questions in mind: what does the entry mean? why do I need to know it? how is it used? The method follows the familiar concept that knowledge in mathematics consists of "concept, context, and skill." ... Read more