Amazon.com

The product of an agreeably dotty cleric named Edwin Abbott Abbott and first published in 1884, Flatland distills all that the Victorian era knew of higher mathematics--and then some--into a witty, complex novel of ideas.

Ian Stewart, the author of the equally witty sequel, Flatterland--which adds to Abbott's store of science the key discoveries made since--does a superb job of explaining the original book's enigmas, allusions, ironies, implausibilities, and what Douglas Hofstadter would call "metamagical themas." Among other things, Stewart comments on Abbott's comments on such things as the nature/nurture controversy, the fourth dimension and beyond, the role of multidimensional spaces in economic systems, infinite series and perfect squares, celestial mechanics, and other matters close to the hearts of cosmologists and science buffs alike.

Stewart's notes make an entertaining and learned addition to an already classic bit of writing--one that has never been out of print since its first publication. For both devoted Abbott fans and newcomers to his work, this is the edition to have. --Gregory McNamee ... Read more

Reviews (6)

A true classic!
Written over a hundred years ago, this book by Edwin A. Abbott is still by far the best introduction to the mathematics of many dimensions. This does not mean that it is a college-text-type of math books that contain complicated derivations and proofs. It is a novel. Ian Stewart's commentary makes it even easier to understand. Even the appendix written by Stewart is a valuable read which gives a brief intro to 4-dimensional mathematics.

A book for all philosophy fans
I understand this book was written by a mathematician and possesses a juvenalian look at Victorian satire- but this book is so much more!! It is philosophy embedded in delicious metaphor and social commentary threaded in the tapestry of extended metaphor. And who said math was boring? This book is a must for every intellectual!!

Intellectual Fun with Commentary
Flatland is a novel originally published in 1884 by Edwin A. Abbott. It is told from the point of view of A. Square, that four-sided resident of the titular country. The first part of the book consists of a description of what it is like to live in a two-dimensional world. The second part concerns A. Square's encounter with a sphere and his subsequent "visions" of pointland, lineland and spaceland.

The purpose of this novel is two-fold: to introduce the casual reader into the concepts of multi-dimensional spaces (i.e. what will become the concept of four dimensional space-time) and to provide social commentary on Victorian society. I cannot comment much on what he achieves in terms of opening the eyes of the Victorian reader to the ills of that society; however, I find his ability to illuminate the concepts of dimensionality extra-ordinary. As a math and physics teacher, I am always looking for ways to open my students' minds to visualizing what they are doing. Even after well over 100 years, few people have approached Abbott's clarity in helping people visualize the difference between different dimensions. One of the best examples: a square only "looks" like a square to someone who can see in three dimensions. A square itself, trapped in a plane, would see another square (or, indeed, any figure) only as a line. This leads to intriguing thoughts on what creatures who live in higher dimensions than our own see as they look at us.

Of course, the story of Flatland alone is wonderful but Stewart's annotation and commentary take the book to another level. On nearly every page, Stewart offers insight and background into the text. Unable to resist the pun: he added another dimension to the book. Having read Flatland many years ago and enjoyed it, I felt I understood the book much better this time around with Stewart's help. Anyone with an interest in math and physics should not pass up the opportunity to read this edition of Flatland.

An Excellent Classic
Contrary to this silly form I am actully 14. I am an eighth grader and I read this for my Algebra 1 class. I fell in love with it instanly. The themes, ideas, and satires all intertwined create one of the best books ever written. The paralle of the unique twist between Euclidian and Non-Euclidian and the satire of Victorian England are wonderful. This book makes you both laugh-out-loud and cry, but most of all it makes you think. Edwin Abbot Abbot was not only a mathamatican but also a brillent liggest. His pros style makes the book all the better... BUY THIS BRILLENT BOOK

Flatland is boring
Flatland is for advanced students -seniors and up- who are participating in a physchological study class. This book warps your thinking about the geometric rules. Unfortunately, it is written in such a way that even if you are a very concentrated reader, you cannot read a paragraph withouth being distracted. The diction in this story is made to be boring. A teacher assigned freshmen students-in high school- to read this and everyone complained because it literally takes and hour to get through a couple of pages. You must also reread the text to find some sort of meaning. This book is not meant for anyone under 18 and is certainly not enjoyable for leisurely purposes. ... Read more

Book Description

This book is an introduction to a new rapidly developing theory of quantum computing. It begins with the basics of classical theory of computation: Turing machines, Boolean circuits, parallel algorithms, probabilistic computation, NP-complete problems, and the idea of complexity of an algorithm. The second part of the book provides an exposition of quantum computation theory. It starts with the introduction of general quantum formalism (pure states, density matrices, and superoperators), universal gate sets and approximation theorems. Then the authors study various quantum computation algorithms: Grover's algorithm, Shor's factoring algorithm, and the Abelian hidden subgroup problem. In concluding sections, several related topics are discussed (parallel quantum computation, a quantum analog of NP-completeness, and quantum error-correcting codes).

Rapid development of quantum computing started in 1994 with a stunning suggestion by Peter Shor to use quantum computation for factoring large numbers--an extremely difficult and time-consuming problem when using a conventional computer. Shor's result spawned a burst of activity in designing new algorithms and in attempting to actually build quantum computers. Currently, the progress is much more significant in the former: A sound theoretical basis of quantum computing is under development and many algorithms have been suggested.

In this concise text, the authors provide solid foundations to the theory--in particular, a careful analysis of the quantum circuit model--and cover selected topics in depth. Included are a complete proof of the Solovay-Kitaev theorem with accurate algorithm complexity bounds, approximation of unitary operators by circuits of doubly logarithmic depth. Among other interesting topics are toric codes and their relation to the anyon approach to quantum computing. ... Read more

Reviews (1)

Complexity of algorithms.
The book covers classical and quantum algorithms;-- of the 250 or so, pages of text, roughly the first 50 pages are "classical", the rest quantum;-- and indeed the aim of the book is to teach the wonders of the qubit-algorithms. While other books, such as Nielsen-Chuang, serve as (more or less)comprehensive references, the present book (by Kitaev et al) is focussed on complexity. The mathematical prerequisits are minimal, but a reader with some understanding of basic ideas from CS, and from quantum theory (at the level of ch 1 in Nielsen-Chuang), will get more out of Kitaev et al. The book is a translation of a Russian 1999 original, but it is really well done, and nicely updated;-- for example, a handy appendix was added, covering elementary math terms that are used.
The book does a great job in explaining the fundamentals, both at the level of the *intuitive ideas*, as well as the mathematical proofs. The big question is why some qubit-algorithms (such as P Shor's factoring algorithm), are a lot better than classical counterparts(for example polynomial vs exponential), and a reader comes away with a good understanding of this in the end. ... Read more

Book Description

This guidebook to mathematics contains, in handbook form, the fundamental working knowledge of mathematics that is needed as an everyday guide for working scientists, engineers, and students. Easy to understand, and convenient to use, this guidebook provides the information necessary to evaluate most problems which occur in concrete applications. This fourth edition has been fully revised and now contains a new emphasis on those fields of mathematics that have become more important for the formulation and modeling of technical and natural processes, namely Numerical Mathematics, Probability Theory and Statistics, as well as Information Processing. ... Read more

Reviews (9)

Clasic
For me it was a remarkable fact, how few of the people in western countries have heard about this handbook. In the east this is probably the most popular mathematical handbook ever. I dont know any eastern european scientist in a field of mathematics, engineering and physics who don't have it. The main reason is it's extensivity and usefulness. In Croatian print it has about 1000 pages in very small format covering all possible parts of applied mathematics up to special functions/markov chains/complex integration/vector algebra. It's "allways in backpack book" and my hot recomandation to any technical scientist.

Treasure Island
The original title of this book was "The Mathematical Handbook for Engineers and Technical Colleges' Students". This reflects the essence of what it is about: well rounded Math coverage for those who did not earn Ph.D. in Math yet.
For each of the topics covered the book gives you not only theoretical explanations, but plenty of examples as well. This feature allows anyone to get good understanding of the specific subject, and in most cases this knowledge is more than adequate for the problem solving.
The countless editions of this gemstone had been used by the generations of Russian students and engineers since, I believe 1940s. In my family alone it was the most used reference book for more than 50 years.

not a good reference book for mathematician
It's probably a good book for engineers, but definitely not the right one for mathematician or anybody who needs to do serious math.

Una herramienta valiosa
Cuando comence a estudiar en la universidad, uno de los profesores tenía una edición de 1977 de la editorial MIR en español del libro Manual de Matemáticas para Estudiantes e Ingenieros, a todos nos parecio un libro excepcional, pero increiblemente difícil de hallar, luego cuando comenzamos a estudiar los cálculos, geometría análitica, siempre utilizamos diferentes autores, muchos de ellos eran principlamente de alemania y la unión sovietica. La claridad con la que se refiere a los conceptos que fundamentan el ejercicio de la ingenieria, hacen de este libro la mano derecha de cualquier ingeniero, en la actualidad dispongo de un ejemplar de esta 3era edición y lo utilizó como como herramienta de referencia. En algunas oportunidades he tenido la oportunidad de preparar clases informales para amigas/os o familiares de ellos que aún estudian en la universidad y siempre llevo conmigo este manual.

*The* reference book
I have been using it during my studies and never regrettec the price. It has some mistakes (I got the 2nd edition) but apart from that it is just excellent. ... Read more

Amazon.com

"Pure mathematics," Albert Einstein once remarked, "is, in its way, the poetry of logical ideas." In The Universe and the Teacup, Los Angeles Times science writer K. C. Cole discusses some of the ways this "poetry" can be used to look at science and other realms of experience.

Mathematics, Cole explains, enables us to "translate the complexity of the world into manageable patterns," whether we're trying to comprehend the risks of smoking or the usefulness of DNA matches in criminal investigations. Cole also looks at how mathematical principles apply in unexpected fields. One chapter, for example, vindicates the theories on voting rights that cost Lani Guinier her Justice Department nomination in 1993.

Without relying on a single equation, Cole's gently humorous prose helps make mathematics unthreatening to laypeople, enabling them to better understand the world in which they live. ... Read more

Reviews (33)

The Politics of Truth and Beauty
Despite the title, not once in this book is an actual mathematical problem presented coherently. Instead, Cole drones on about the virtues of cooperation, the importance of minorities, and other left-wing philosophical themes. I'm a liberal and would tend to agree with her politically, but that ignores the central problem with this book: Cole's failure to make the distinction between mathematics itself and beliefs that just happen to be justified by statistics or quasi-mathematical reasoning.

Perhaps The Universe and the Teacup is best described as a meta-popularization, since virtually all of Cole's sources are themselves popularizations. She hypes such familiar staples of popular science writing as fuzzy logic, chaos and complexity theory ("all the rage these days" -- I thought that's what they said back in the 80's), and Godel's theorem (both "a shattering blow" AND "a staggering blow to our sense of certainty"), without showing that she understands any of these things on more than a superficial level. (I don't claim to be an expert on these topics, either, but then again I didn't write a book about them.)

For general readers interested in how mathematics relates to everyday life, I'd recommend John Allen Paulos "Innumeracy"; for a survey of modern mathematics, both "From Here To Infinity" by Ian Stewart and "Archimedes' Revenge" by Paul Hoffman succeed where "The Universe and the Teacup" fails.

The Leonardo da Vinci of science writing!
That's a direct quote from Amazon, and boy, were they right. Only Cole would link the O.J. Simpson trial to the discovery of the top quark in order to explain various roads to truth. The best part is the relationship between beauty and truth, in which she explains the unexplainable--showing how Einstein's theories (and in fact, all modern physics) is based on the notion of symmetry. But there's also so much less etheral food for thought here: the geometry of fairness, for example!

what is truth exactly
Being disenchanted with religion, I picked up this and other books in search of some other kind of truth. I do feel as though after reading this book I have a much better understanding of what 'truth' is and what it's not. I think those who nit-pick about their claims of little discrepancies in the book are really missing out on the bigger picture. The book is full of interesting little facts and factoids but the interesting thing to me was to see how she's pulled together these common insights that are gained from so many fields of study. I think this was just about my favorite book ever.

So many better choices out there.
Chapter two, second paragraph: "The Milky Way galaxy contains 200 billion stars..."
Chapter two, a few pages later: "Fifteen billion is also more or less the number of stars in the galaxy." Obviously, the number of stars in the galaxy is not precisely known, but we do know that 15 billion and 200 billion are two different things. One of the author's "truths" is self-evidently not true. Purveyors of "truth and beauty", whether scientists, gurus, philosophers, spiritual leaders, or journalists, often regard their subject and their audience far too casually. Here we have a case in point. Perhaps most books contain 'typos' and the miscues inherent to humanity, but here it seems that both the author and the editor were asleep at the wheel, something that needs to be addressed if the book achieves a second printing (and I don't see why that would happen).
The subject is truly fascinating; or at least it should be -- the relationship of aesthetics, mathematics, and logic. At the deepest levels of the human intellect's inquiries, the answers are all about a mysterious mathematical beauty. The reality of this escapes most people, which is why the "National Bestseller" heading on the cover of Cole's book intrigued me. Apparently the book has enjoyed a larger readership than most such popularizations. Unfortunately the superficial, disjoined 'newspaper style' of science serves the material poorly. The writing rambles almost aimlessly. The books of many mathematicians and physicists have examined the relationship of reality, reason, mathematics, and aesthetics. Devlin's 'The Language of Mathematics' is very good. Fairly recent works by Penrose, Davies, Rucker, Berlinski, Greene, and others come to mind. Some of these books are far better than others. This volume is one of the others.

how to write a book in five minutes
Should it be that easy to write a book? Collect all the bits and pieces from newspapers' weekend-supplements and almost scientific coffeetable-talk and toss in some currently fashionable phrases concerning physics and mathematics, stir until the lumps have disappeared and do not bother with the spices of explanation and insight. If you love math and physics, stay off ! ... Read more

Book Description

Besides scheduling problems for single and parallel machines and shop scheduling problems the book covers advanced models involving due-dates, sequence dependent changeover times and batching. Also multiprocessor task scheduling and problems with multipurpose machines are discussed. The methods used to solve these problems are linear programming, dynamic programming, branch-and-bound algorithms, and local search heuristics. Complexity results for the different classes of deterministic scheduling problems are updated and summarized. Also the references are updated. ... Read more

Amazon.com

The Encyclopedic Dictionary of Mathematics, as put out by the Mathematical Society of Japan, is as complete and comprehensive an opus as one could wish for, concisely comprising in its two volumes all significant mathematical results, both pure and applied, elementary to advanced. This second edition is, basically, an English version of the acclaimed Japanese third edition. The EDM2, as it is known, succinctly but thoroughly covers math from A to Z, from Niels Henrik Abel and Abelian groups to Witt vectors and Zeta functions. Within its 2,000-plus pages are elegant explanations of diffusion processes, Fourier series, linear operators, and meromorphic functions. There are pages dedicated to quadratic fields and robust and nonparametric methods, and following each section, all the relevant references are listed. In addition, there are appendices with tables of formulas, numerical tables, and statistical tables, journals, publishers, and special notations, articles listed both systematically and alphabetically, plus a name index and an exhaustive subject index that's 231 pages long. It is a quality product--easily accessible, adhering to rigorous standards, and worth the investment for any school or personal math library. --Stephanie Gold ... Read more

Reviews (8)

Indispensable. How did I ever get on without it?
If my house were on fire and I had only sufficient time to rescue four books, I would likely grab my four-volume Encyclopedic Dictionary of Mathematics, Second Edition (EDM2). Truly, this is one of the most useful books I own. As testimony to this fact one need only observe that there are more bookmarks protruding from my copy of EDM2 than there are pages (well, almost).

If you are a mathematician, or if mathematics is central to what you do, you will likely appreciate this collection as it contains wonderfully concise yet informative and authoritative entries on nearly every branch of modern mathematics. Need to refresh your memory on Radon-Nikodym derivatives and their properties? No problem. Are you up on Grassman algebras? If not, you can look it up in EDM2. Interested in game theory? It's in there. What about semi groups, elliptic integrals, perturbation theory, lattice theory, Hilbert spaces, projective geometry, integral geometry, measure theory, geometrical optics, and non-standard analysis? All there!

But simply listing the topics covered in EDM2 will not give you an adequate picture of its utility. What is amazing about the book is how much information it can pack into very few pages, yet manage to keep the discussion quite readable. Don't get me wrong; it doesn't read like a Stephen King novel (nor would you want it to). But the entries are self-contained and cogent enough that you can actually learn a good bit about topics that are totally new to you. Of course, you will want to avail yourself of the many cited references to gain a more complete understanding of any given topic, but you will be well on your way to getting acquainted with fundamental definitions and techniques of a hitherto unfamiliar branch of mathematics.

Here are several examples: If you look up "polynomial approximation" you will find a succinct discussion that rigorously defines such terms Bernstein polynomials, Chebyshev system, Haar's condition, degree of approximation, moduli of continuity, approximation by Fourier expansions, trigonometric interpolation, Lagrange interpolation, and orthogonal polynomials, and all in FOUR terse but readable pages, with plenty of references at the end. The entry on "geometric optics" covers Fermat's principle, Gauss mappings, Malus's theorem, and aberration, all in TWO pages. The succinct one-page biography of David Hilbert is followed by a one-page synopsis of Hilbert spaces. In a mere eight pages on function spaces it provides what amounts to a condensed survey of functional analysis, covering norms, dual spaces, Besov spaces, the Sobolev-Besov embedding theorem, Kothe spaces, etc.

Of course, what you will not find in this book is a single proof. Nor will you find up-to-the-minute esoteric theorems. But then I cannot imagine how such a reference could encompass such things; mathematics is far too vast. Nonetheless, EDM2 has amazing breadth and depth for a meager four-volume collection. And it is written with mathematicians in mind, so the discussions are crisp and rigorous. It's exceedingly well done.

The Consumate Personal Mathematics Reference
Prepared by the Mathematical Society of Japan, this two-volume set provides an outstanding reference of mathematics. It is considered by many to be the best available work that is both definitive and encompassing. Treatment is in depth, and presentations assume a solid mathematical background of the reader. This reference is excellent for the researcher working at the doctoral level. Cost of the paperback edition is very reasonable.

best all-round math book for the mathematician's bookshelf
I've been using this book in my work as a mathematician since I bought the first english-language edition in 1984. The second english-language edition is not enormously different to the first, but it is an improvement. Both have been by far the most useful reference on my bookshelf for 18 years. I have always found that the coverage is in-depth and yet comprehensible (with a bit of pen-on-paper work). It's especially useful for accessing results from areas other than my own speciality. I've found the differential geometry coverage literally better than the dozen texts on DG which I have bought. It must be worth more than 100 books on the shelf. Indexing and cross-referencing are both excellent. Historical context is very good. I use this encyclopedia at least 10 times a week. Virtually every definition I need is here, and every important theorem is summarised.

Absolutely Must!
This dictionary is great. No other work is as comprehensive and detailed. This is a must buy if you are interested in modern mathematics.

Incomparably Great
The Encyclopedic Dictionary of Mathematics is an astonishing achievement. The result of an extraordinary, decades-long collaboration among literally hundreds of celebrated Japanese mathematicians, it will not only never be equalled but in all probability will never be challenged. In two massive volumes, the EDM surveys the whole of the mathematical sciences, both pure and applied, through a series of pithy articles containing the key definitions, methods, and results of every mathematical subdiscipline sufficiently coherent to have a name. It also tabulates vast amounts of information -- homotopy groups of spheres, symmetries of ordinary differential equations, characters of finite groups, class numbers of algebraic number fields, and so forth, seemingly, ad infinitum -- available, as far as I know, in no other single reference work.

Equipped with a detailed and extensive system of indexes, the EDM makes its myriad resources readily available even to the befuddled; the vaguest, most dimly remembered hint is generally enough to track down a topic or result quickly and easily. Each entry, too, offers its own references to the mathematical literature -- and these invariably include the seminal contributions to the particular area under discussion. But it is important to note that the EDM was written by the Japanese, for the Japanese: many of its references direct the reader to (untranslated, Japanese-language) works in (often inaccessible) Japanese mathematics journals.

It is likewise only fair to point out that the EDM is a tool for serious research mathematicians. To keep its component articles brief, it makes full, unapologetic use of a wide variety of notational and expositional economies. The EDM seldom if ever provides a heuristic explanation of anything; although it often gives a bare outline of the historical development of a subject area, it resolutely eschews Toeplitz's "genetic" exposition, in which the crucial problems and examples that engendered a field are placed in the foreground. Only those persons comfortable with a very considerable level of compactness and abstraction in the exposition of mathematical ideas will find the EDM easy reading.

A further cautionary note: although the EDM does offer the same tables of integrals and lists of the zeroes of Bessel functions that make up the bulk of a book like Abramowitz and Stegun's, it makes no attempt to be a handy desk reference for the harried engineer who imagines he may someday need a tidbit of mathematical legerdemain to cope with the odd ODE. First and foremost, the EDM is a sophisticated survey of all extant mathematical knowledge. Those who come to it seeking only the solution to some thorny integral will find, besides the solution they seek, a staggeringly vast, undreamt-of universe of profound mathematical ideas. The experience may well leave them stunned and bewildered for days. ... Read more

Book Description

5 b/w photographs, 2 line illustrations, 1 table The overwhelming similarity of human and ape genes is one of the best-known facts of modern genetic science. But what does this similarity mean? Does it, as many have suggested, have profound implications for understanding human nature? Well-known molecular anthropologist Jonathan Marks uses the human-versus-ape controversy as a jumping-off point for a radical reassessment of a range of provocative issues--from the role of science in society to racism, animal rights, and cloning. Full of interesting facts, fascinating personalities, and vivid examples that capture times and places, this work explains and demystifies human genetic science--showing ultimately how it has always been subject to social and political influences and teaching us how to think critically about its modern findings.Marks presents the field of molecular anthropology--a synthesis of the holistic approach of anthropology with the reductive approach of molecular genetics--as a way of improving our understanding of the science of human evolution. As he explores the intellectual terrain of this field, he lays out its broad areas of interest with issues ranging from the differences between apes and humans to the biological and behavioral variations expressed in humans as a species. Marks confronts head-on the problems of racial classification in science. He describes current theories about race and uses work in primatology, comparative anatomy, and molecular anthropology to debunk them. He also sheds new light on the controversial Great Ape Project, the Human Genome Diversity Project, and much more. This iconoclastic, witty, and extremely readable book illuminates the deep background of human variation and asks us to reconsider the role of science in modern society. ... Read more

Reviews (12)

He's yet to meet Ishmael
A catchy and provocative title is now de-rigueur for popular science books on the subject of genetics. It's somewhat surprising then that the message of WHAT IT MEANS TO BE 98% CHIMPANZEE is that it doesn't really mean that much at all. Marks takes a distinctly middle-of-the-road position on most of the scientific debate that has spun off from the human versus ape discussion. Marks says that "the extent to which our DNA resembles an ape's predicts nothing about our genetic similarity to apes, much less about any moral or political consequences arising from it."

In chapters such as "The Ape in You", "How People Differ from One Another" "The Meaning of Human Variation" and "Human Nature" the author lays out his views on hot-button topics such as the biological reality of "races" and "nature vs nurture". Marks is not a believer in strict genetic determinism and therefore does not take a reductionist view of human nature - i.e genetics as a causal factor for everything. He's somewhat more of a humanist but this nod to a more environmentally deterministic view does not extend to an all embracing view of our fellow primates. The non-human primates - Chimpanzees, Bonobos, Gorillas, and Oranutans have an increasing number of human advocates who say that there are moral and ethical consequences that stem from the genetic similarity between apes and humans. Primatologists such as Jane Goodall argue that the higher intelligence and emotional awareness of apes demands a distinction in how we view them, and more importantly, how we treat them. In the chapter "Human Rights for Apes?" Marks discusses the Great Ape Project and the long term objective of getting an U.N. Declaration on the Rights of Apes. Marks will have none of this and sees such positions as pretentiousness on the part of scientists.

The science on animal consciousness is still inconclusive especially as it relates to the Great Apes. It's in the area of self-awareness and higher order thinking ("thinking about thoughts") where much of the debate takes place but this is not Marks' primary interest. Marks' main point is that there is a better approach to understanding these issues, one that is holistic rather than a binary "either/or" argument. Marks introduces us to his speciality in chapter one - "Molecular Anthropology" - and tells us that it combines the reductive power of genetics with the humanistic vision of anthropology. It thus allows practitioners to steer clear of ideologically influenced science.

It's ironic because in arguing about the merits of his field of study, Marks himself comes across as tunnel-visioned and obviously enamored with his own view of things. This is the only problem with this otherwise well written and wide-ranging discussion on some of the current debates in science. Although Marks wouldn't support it because it talks about a sentient Gorilla, for me, Daniel Quinn's book ISHMAEL provides the best overview on this whole debate. Our scientific beliefs give us a view of the world. Ishmael says it's going to be hard for us to give it up because what we're doing is "right" and "giving up would mean that all along [we've] been wrong. It would mean [we've] never known how to rule the world. It would mean relinquishing [our] pretensions to godhood." As if to prove the point, this book can't end without trying to tackle the "big" questions. Marks concludes with a chapter on "Science, Religion, and Worldview".

Enjoy the book for what it is: a good general introduction to genetics, with particular reference to apes and ourselves. Just remember that scientists - even iconoclasts such as Marks who does a great job of cutting through the debate - still are subject to their own biases and particular worldviews. Science itself is still undecided on much of what you read about here.

Post-modernist persiflage
Accepting the fallacy of Marks' title, let us start on a positive note. Marks wants to keep apes and humans separate. Fair enough. I don't want to live on termites on a stick, and it's doubtful chimps want to worry about traffic congestion, tax rates or political corruption. Marks wants scientists to do their job well. Who can argue? Marks has courage - he has the temerity to assault the venerable E. O. Wilson, the articulate Richard Dawkins and the revered Jane Goodall. Marks is against racism. Hardly debatable. Marks seems a pretty upstanding fellow. Why then, is this book such an insult to the intelligence?

Mostly because it is a froth of misleading statements, misdirected wrath, misconceptions and mistaken views of science. Marks goes to unusual lengths in dismissing the research achievements of many scientists in both field and laboratory. He blithely dismisses the disclosure that chimpanzee and human genes are nearly identical as "the most overly exposed factoid in modern science." It's not significant because it confuses precision with accuracy. From there, Marks goes on to castigate a legion of scientists for their failure to "get it right" the first time around. Few escape his lash - even Linneaus, who virtually invented classifying life, is a victim, and perpetrator, of cultural artifacts in naming species. This from a man who finds culture an unbridgeable chasm between humans and animals!

Marks spends much of the remainder of the book discussing racial/cultural undercurrents in science. He finds far too much of it in current anthropology. He's correct in this, but his case is "overblown"- a favourite phrase of his. In a welter of complaints, he finds but two scientists to exonerate of the charge: Richard Leowntin and - himself. He doesn't want any cultural or behavioural relationship between humans and the rest of the animal kingdom, a favourite plaint of Lewontin's. Any hint of sociobiology, which he incorrectly defines as the study of human behaviour, must be rejected. This attitude ignores the wealth of research published during the past generation.

Marks' shots against sociobiology would be amusing except that so many will accept them uncritically. Like his mentor, Marks wants humanity to evolve without any evolutionary baggage. Behavioural studies of modern animals are irrelevant according to Marks. Thus is cast aside the whole realm of Darwin's evolution by natural selection. At least as far as it concerns humans. This attitude fits adroitly with Marks' intended reader community. He blames science for many social attitudes, delving deeply into the history of science to build his case. His brief runs from Plato onward, ending with the efforts to map the human genome. Science has long suffered from its cultural roots. The case is flawed by Marks failure to recognize that all through history, science has sought to reveal natures' secrets. It's a process of fits and starts, each gain a limited success. That inability to "get it all right the first time" is inherent in the process. It accomplishes little to portray the process as invalid. If some people have not performed to his expectations doesn't mean science should give up trying.

The area that Marks clearly wants abandoned is understanding of what drives human beings. That some scientists want to look more deeply into the human genome he perceives as a wasted effort. Along with Lewontin, Marks rails against "genes for" this or that aspect of life - particularly human life. Are we to assume then that we should stop looking? Because faulty genes have been shown to invoke certain disorders but haven't been found for others, is the list now complete? He inveighs against looking for genes for criminal behaviour. We don't know enough about how DNA works to decide one way or another. Do we give up analysing how genes perform? And what exactly is criminal behaviour? Even Marks uses statistics of prison populations to build his case. But none of the Enron executives are in prison, nor are likely to be. Do we exclude them from genetic analysis to unravel what genes lead us to do?

This book will go far in inflaming the already anti-scientific attitude prevalent in North American schools. Statements such as "science is not generally accurate" and "scientific statements are routinely falsified" [p. 279] aren't likely to entice anyone into the scientific fold. Students will not be encouraged to enter science disciplines when they're told "it is no easier to get the average scientist to accept responsibility than it is to get the average four-year-old to accept responsibility. After all, Marks is a scientist himself, his statements must be valid. We must assume, it is supposed, that he and Lewontin stand alone by having donned the mantle of responsibility. Yet his book is permeated with complaints that statements made by other scientists have been uncritically accepted. Marks owes the scientific community an apology. More importantly, he owes every young person interested in science an apology for describing them as likely to become irresponsible children instead of aspiring grown-ups. [stephen a. haines - Ottawa, Canada]

A good book with ideas which need to be expressed now.
Despite the author's raging anger and at times over the top invective, this is a very important book that at once demystifies genetic science and shows how genetic theories of human behavior have always been subject to cultural influence and in most cases in the absence of any hard evidence. Equipped with an arsenal of facts and historical case studies, Marks passionately warns us about the misuses of science. This is not to say he is any way anti-science or " Postmodern" as the armchair Sociobiologist Steven Haines implies. Opening on the offensive with a discussion on the genetic similarity between apes and humans Marks shows the similarity to be merely frivolous when we consider the we also share half our genes with fish and about a third with daffodils

Moving right along Marks addresses issues as diverse as the arbitrary nature of classifications, essentialism, not to mention worldview and religion. We learn that the classificatory schemes of the saintly Linneus perhaps had more to do with the man's views on breast-feeding that on
" how things are in selves" We also get a glimpse of how essentialist views of man have their origins in folk knowledge and societal prejudice which inevitability creeps into the conclusions we draw from empirical data.

While Marks can be overly critical of his field and his colleagues in general, it is a necessary antidote to the appalling bile and misinformation reported in the popular press in the name of science; which more often than not is accepted uncritically and taken as gospel in the pop science community.

From reports of the " Gay gene" to the genetic basis of female coyness and racial theories of intelligence, Marks shows there is simply no experimental evidence for any of these claims, and when there is, it is statistically spurious.

Simply interpreting social and psychological data in light of evolutionary theory and drawing vague inferences from physiology is not science. And Marks exposes it, again and again. This is Speculation and myth and the public should be under no obligation to take it as established science.

Politicized Science
Marks book is not about science in any real sense. It is about politics. Over the course of his examination of biological incursions into anthropology, ranging from sociobiology to genetic testing of ancient skeletons, the only unifying theme to the book is that any conclusion that does not support progressive causes must be wrong and that any research that might hurt someone's feelings should not be attempted. Marks states both tenets explicitly several times.

That is not to say that all of his discussions are bad. If you leave out the irrational political diatribes, his accounts of some of the conclusions of sociobiology, for example, are spot on. His discussion of sociobiology in general, however, is based wholly on his beliefs about the political motivations of sociobiologists.

He does not provide logical arguments against most of his targets, but rather uses examples that seem to be chosen for their ability to offend a modern audience without regard to their relevance. Nazi Germany is invoked continuously, for example, although modern work is not derived from 1930's and 40's continental scholarship. He also misrepresents not only the motivations but also the results and theses of other researchers with the express intent of comparing them to the Nazis. The reader is often left with the impression that Marks bases his discussion on hearsay instead of studying the work of the scientists whose work he examines.

This is why the tone of this book often makes it difficult to finish a section.

Marks inadvertently makes a good case for not listing anthropology among the sciences. Although he has great pretensions for the field--it is supposed to be both a link between the modern and the pre-modern worlds and a link between the sciences and the humanities, while remaining itself a science--, he defines anthropology politically. Its purpose is to help the oppressed, foreign and domestic, deal with their exploiters. Thus, anthropologist's conclusions must face a political test to be considered correct (or, "convincing," as he likes to put it). Any field so construed is not science; any anthropologist following his advice would not be a scientist.

Marks believes, and restates often, that science should be Hippocratic. All science should look at what possible harm, including psychic harm, a discovery could do before the inception of an experimental program. Some knowledge is bad knowledge.

Marks justifies his politicized stance childishly. To paraphrase, "they (e.g., the Nazis) politicized anthropology first, so I can, too."

He has similarly irrational restrictive requirements on experiments. Experiments that wouldn't yield enough data to be conclusive should begin. For experimental sciences physics, perhaps, this might be a good rule, but for forensic sciences like astronomy and biology this would be devastating. Data needs to be added as it comes in.

If you would like a good discussion of the issues Marks addresses, such as human intelligence, crime, and paleoanthropology, you should go elsewhere. If you would like some debating points that occasionally reference scientific work, then you should read this book.

Easy to Dismiss, but very Important
The easiest thing to do about Marks' work is to dismiss it. Maybe we can simply state that herein lies that 'lefty pinko commie propaganda' that tries hopelessly to be 'PC.' And that's all she wrote! But I am afraid it is not so simple...

Jonathan Marks is writing about _my_ field. I have done some similar work. He is fighting against a popular old force, which tries to ignore not only cultural influence, but also ecological and political, and other influences.

Marks is an expert in his field, and this is very evident. It is interesting that one of the reviewers of this book, Mr. Haines, cites research from past ten years as diminishing to this book. I would like to see this research, not published in a newspaper, please. Genetic determinism, for all its promises, has _failed_ to live up to its expectations. It tries to solve _grand_ answers, and this is pretty hard. Marks is right to question evolutionary psychology, as the field has brought almost _nothing_ but the so-called 'just-so' stories. This is not science, this is myth. And Marks exposes it, as he should. I am also at a loss to observe how Marks wants no Darwinist baggage. This is false; he notes in his work that these explanations can contribute--but again, grand theories based on this kind of 'science' avoid about 150 years of anthropology, which has gone through many of the same pitfalls, by the way.

He is right to question the silliness of invoking the 98% chimpanzee argument, as it is a ridiculous one. He is right to note that folk knowledge manages to mingle in with what is supposed to be science. This is easily the best part of the book, and the dripping sarcasm and the molten anger with which Marks writes is immensely entertaining. However, it is also tragic to observe.

While I do not usually attack a particular Amazon review, I will point that Mr. Haines would benefit from a second reading of the book. Science is generally inaccurate in behavioral sciences (but also elsewhere): this is a simple truth, not an extreme claim. It is also _not_ an attack on science. As a matter of fact, as Marks points out rightly, science is accurate _OVER TIME_, but may be hopelessly misguided sometimes even in the long term. IF this was not the case, there would be no need for new paradigms; but, these do happen, I am afraid. This book is in no way trying to disparage science. If this was the case, Marks would not continue his work. But let me stress this: Marks simply notes that scientists should not put their noses where there is no place for them, or where scientific truth cannot be derived. I do not quite understand why this is a preposterous claim.

Linneus is demonized?! No, Marks simply notes the amount of folk knowledge inherited in this supposedly natural classifying system--what is found 'out there,' in nature. This is a clear point, not demonization. He is showing the arbitrary nature of classification. EVERY biologist should know this, but doesn't. Nor did I, before I got my MA in Physical Anthropology after studying Biology as an undergrad

Particularly, I would like to reply to this comment: "[i]nability to 'get it all right the first time' is inherent in the process. It accomplishes little to portray the process as invalid." Marks _does not_ expect science to get it right the first time. As a matter of fact, a careful reading of his book will indicate that he does not want genetics to fall into the same trap for the _SECOND_ time. Furthermore, far from arguing for abandonment of genetics as a whole, Marks asks geneticists to stop making grand claims when small results are observed: if that is not reasonable I am not sure what is.

Overall, Marks has presented an immensely readable work. Not everyone is going to like it, especially sociobiologists. There is actually nothing terribly revolutionary here. However, Marks' prose and his dripping sarcasm make this a book to read. I have yet to see how it is post-Modern or deconstructionist, for that matter. Marks is interested in science, but wants to see that it does not make mistakes it has so often made in the past. Is that really so controversial? ... Read more

Book Description

Learn How To Apply The Theory Of ConstraintsTo Management Accounting.

The Theory of Constraints, a management philosophy derived from physics, assumes that constraints prevent organizations from achieving better performance.The Theory of Constraints (TOC) is based on a scientific method that has been developed and refined for nearly three decades by Dr. Eliyahu M. Goldratt.As a tool for business management, TOC is now accepted as a mainstream alternative to cost accounting.

Throughput Accounting

Reveals a new management tool for managerial accounting and shows an alternative path for other management practices.

Enables managers to quickly see if their decisions increase profitability.

Demonstrates some of cost accounting's flaws, and shows how these errors will lead to bad decision making.

Compares the paradigm of TOC-based throughput accounting with more conventional cost accounting methodologies and in the process, demonstrates a new way to solve the complex problems of modern management. ... Read more

Reviews (8)

Good if you're familiar with TOC
This is a good explaination of why the various allocation based account methods lead to poor management decisions and a good introduction to a better way of accounting. It does not include how to reconcile throughput accounting with required GAAP reporting. The only book I know that does is The Measurement Nightmare, which is a rather difficult read. It would be very helpful to have a book with example problems to work, an explaination of the GAAP reconciliation process, and more detail into what costs are totally variable and non-totally variable.

Stop waisting time and start making money!
This is a funny little book. It's not too well written and the content is not that new, once you have read Eli Goldratt's basics on the topic.
However, Thomas Corbett simply put the stuff together and proves, beyond any doubt, the fallacy of classical cost accounting as well as the "new & improved" fallacy of ABC.
Examples are quite simple to follow and the outcome is very exiting!
Makes you seriously wonder if there is add-on software out there that extracts the relevant data from present accounting systems, and helps top and middle management make the right decdions for a change on a daily basis. Key question is; how can this software help non-TOC companies help establish their bottle neck?

Helpful book
People who did not understand the message, find the Throughput Accounting a useless framework. But if you are a smart and open mind person, this book is for you.

The theory is very well explained illustrating an alternative path to the old and nosense cost accounting.

I advice you to buy it.

Useless book
I really think I have lost money buying this useless book I advice you not to buy it.
The nosense theory explained is even explained bad.

Finally a TOC book that addresses accounting specifics!
We've all read Goldratt's work on the Theory of Constraints (TOC) and the improvements that can be made in manufacturing processes. However, what is often overlooked in those books is the reality of getting these changes to work with our traditional cost accounting systems. TOC sounds great in theory, but how do we, as accountants, measure and report financial results in a way which supports TOC, yet still fulfills our responsibilities for external reporting? Don't we still have to apply overhead to products and calculate product costs?

In this book, Corbett does a great job illustrating how our old cost accounting techniques are inadequate, and, more importantly, can lead us to make decisions which actually harm the bottom line. But he doesn't stop at simply pointing out the shortcomings of cost accounting, as most texts do. He takes the additional step of providing real financial statements and measures that support the concepts in TOC, and allow accountants to give production management the data they need. You can begin using these statements right away in your own company. In addition, he shows us how to use TOC to make various financial decisions. He even spends a chapter showing some of the criticisms of Throughput Accounting and provide warnings about its proper use.

After reading this book you will realize that calculating a product cost is like buying a house and then trying to figure out how much of the purchase price to assign to the bathroom faucet. "Product Cost" is a fallacy, and impossible to determine. All that really matters is Throughput, the difference between selling price and totally variable costs.

If you are a controller or cost accountant stuck between production managers who are eager to implement TOC improvements, and financial managers who still insist on overhead application and product costs, this is the book for you. ... Read more

Book Description

Pocket Book of Integrals and Mathematical Formulas, a revision of a very successful pocket book, provides a handy desk-top reference for engineers and scientists seeking essential formulas, concepts, and definitions. Topics range from pre-calculus to vector analysis and from Fourier transforms to statistics.This third edition contains:oA new chapter on business and financial mathematics - providing information on progressions, especially geometric progressions, which is the basis for many formulas related to annuities, growth of funds, and interest paymentsoAdditional topics in statistics - including sample size calculations for testing differences and proportionsFeaturing numerical tables of probability distributions, the book also includes oDiscussions on formula listings and differential equationsoFourier seriesoLaplace and z-transformsoVector analysisoOrthogonal polynomialsMany other handbooks go too far in their attempts, essentially mimicking larger comprehensive texts they try to summarize. The result is a reference less detailed than the full texts and too big to be conveniently portable. Most scientists do not carry them.Through a careful selection of topics and detail, Pocket Book of Integrals and Mathematical Formulas truly meets the needs of engineers and scientists - a convenient, usable supplementary text providing worked examples where most necessary. Its comprehensive information and convenient arrangement of tables makes it an essential and easy to use reference. ... Read more

Reviews (5)

Helpfull little book
This Book is good for general to advance caluations in geometry to advanced calculus and differential equations. Help in Bussiness and other areas too. Very good book for engineers and physics to math majors!!

Handy little reference book.
I've had the 2nd edition of this book for about six years and I can't tell you how many times I have used it. When I was in college, it came in very handy with the tables of derivatives and integrals, along with all those trig identities. After I graduated and started working, it became a great reference for those geometry equations that you start to forget or methods for solving multiple equations. It's also compact, so it will easily fit in a briefcase or a drawer. I would definately recommend it to anyone looking for a good, quick, easy to use math reference.

Lacks some key formulas
Schaum's Mathematical Handbook of Formulas and Tables is slightly less portable but I found it to be more complete

Table of Contents
1. Elementary Algebra and Geometry 2. Determinants, Matrices, and Linear Systems of Equations 3. Trigonometry 4. Analytic Geometry 5. Series 6. Differential Calculus 7. Integral Calculus 8. Vector Analysis 9. Special Functions 10. Differential Equations 11. Statistics Table of Derivatives Table of Integrals Appendix

Must have for all engineering and mathematics students
A great reference for all undergraduate and graduate level engineering and mathematics students. Pocket Size - easy to bring along. Tables of Trig Identities, Integrals, Fourier Series, Laplace Transforms, Statistical Functions... a very convenient tool. It should be issued to all students. ... Read more

Book Description

For those gearing up for pilot interviews, preparing for a check-ride or proficiency check, or looking to improve inflight calculations, this book offers invaluable tips and tricks to help in all areas of cockpit calculations. ... Read more

Reviews (5)

I am a bit puzzled
This book is over rated! It comes across as giving the pilot all these tips and formula's but falls way short on the task. First off, the typeset fills only half the page making the book in reality about 25 pages. It goes on to show you basic math found in any private pilot instruction guide. FH/C temp conversion, subtracting military time, and RVR which is all the same as in the NOS/Jep charts and Ops manuals for the plane you fly. The second half of the book has the times tables, subtraction tables, and division tables. He put fuel dump calculations in along with wet runway computations, this is not only a waste for pilots flying anything short of a jet, but worthless due to FMS and EFIS on bigger airplanes not to mention the F/E sitting sideways behind the captain. In short the book is outdated. finding reciprocals, compass turns to a heading, and ANDS are all in the flight manuals. In short this book fails to teach much. It is not worth the [price] that is for sure.

Essential for interview preperation.
This is an excellent book for anyone preparing for an airline interview. I was recently hired by a regional airline and several interview questions consisted of mental math problems. Buy this book and the ATP test prep....good luck!

Excellent study guide
If you are a little underconfident with your math skills,... Helped me review my math formulas and feel much more confident about having to do math in an airline interview. Good study book!

Way Overpriced!
Mr. McElroy's book has some neat math shortcuts for common aviation problems, but it is a pretty skinny book and not worth near the asking price. I've been an airline pilot for about 5 years, and a military pilot for about 10 before that. I'll admit that there were 2 or 3 shortcuts I didn't know (though less that I'll actually use!), but the prevailing comment among other airline pilots I showed it to were "You can tell the author is an airline pilot!" as they pointed to the $27+ price. I agree, this book is worth $10 or $12 tops. . .I could summarize all the shortcuts in a page or two. As for interview prep, you're better off using one of the books written specically for that purpose.

Excellent Interview Prep
This book covers all the neat little tricks to getting the job done quickly and right. It is also a great book for interview prep. Goes into detail on how to do the math problems and gives several ways to do the problems. There are also review problems at the end of each chapter. A must buy for interviews or if you are just looking for a way to make your flying job easier. ... Read more

Book Description

The idea of chaos figures prominently in mathematics today. It arose in the work of one of the greatest mathematicians of the late 19th century, Henri Poincaré, on a problem in celestial mechanics: the three body problem. This ancient problem--to describe the paths of three bodies in mutual gravitational interaction--is one of those which is simple to pose but impossible to solve precisely.

Poincaré's famous memoir on the three body problem arose from his entry in the competition celebrating the 60th birthday of King Oscar of Sweden and Norway. His essay won the prize and was set up in print as a paper in Acta Mathematica when it was found to contain a deep and critical error. In correcting this error Poincaré discovered mathematical chaos, as is now clear from Barrow-Green's pioneering study of a copy of the original memoir annotated by Poincaré himself, recently discovered in the Institut Mittag-Leffler in Stockholm.

Poincaré and the Three Body Problem opens with a discussion of the development of the three body problem itself and Poincaré's related earlier work. The book also contains intriguing insights into the contemporary European mathematical community revealed by the workings of the competition. After an account of the discovery of the error and a detailed comparative study of both the original memoir and its rewritten version, the book concludes with an account of the final memoir's reception, influence and impact, and an examination of Poincaré's subsequent highly influential work in celestial mechanics. ... Read more

Reviews (10)

The Best Dictionary of Mathematics I Know Of
The thoroughness of this dictionary makes it great both for browsers like me and for real mathematicians. I can't imagine anyone outgrowing this work. If anything better comes along to take this book's place, odds are it will be the next edition.

Fabulous repository of mathematical terms
This is the best dictionary I have ever seen for undergraduated. This dictionary is complete, clear and not expansive. It is not complete as a CRC encyclopedia for graduated but for an undergraduated and even a beginning graduate it is the best one, because it explains all terms you can encounterand many more. Also it has biographies of great mathematicians. If you look for a dictionary of mathematics buy this one.

Nice Dictionary
I'm yet to find a better maths dictionary. Lots of definitions. Well organized/cross-referenced. As an undergraduate, I'm yet to look up something and be disappointed. Handy tables at the back.

It doesn't get 5 stars because of a few glaring misprints.

So good I own 2 copies
This is by far the best Mathematics Dictionary I have ever come across. My original copy has been so well read it is held together with tape! I keep one copy at work and one at home and reccommend it to all my Math majors. It is really useful for undergraduate and graduate Math majors and still handy for faculty. As well as good definitions for most math terms it also has short bios for many mathematicians which can be useful in adding historical context to a course.

My First (& Only) Choice
A more handy dictionary of math than this one, I have yet to find. Profusely illustrated with equations, graphs, diagrams and charts, it is yet comprehensive enough not to miss items and entries of major importance - and it still stays within a reasonable, user-friendly size. The only dictionary I know of that is sure to be better than this one is soon to be available: the second edition of this book, published just a few months ago. ... Read more

Book Description

A reliable source of definitions, theorems, and formulas, this authoritative handbook provides convenient access to information from every area of mathematics. Coverage includes Fourier transforms, z transforms, linear and nonlinear programming, calculus of variations, random-process theory, special functions, combinatorial analysis, numerical methods, game theory, and much more. Introductions, notes, cross-references show the interrelations of various topics and their significance to science, engineering. Numerous figures and tables.
... Read more

Reviews (8)

an MBA student says:
I've been searching for a math reference book to use while pursuing an MBA. Much of the math that is used in the classes I'm taking is relatively simple and was more then adequately covered by my undergraduate education. But it has been all been forgotten long ago. This book fits the bill.

Pros: Have been able to find everything I've needed quickly. (Chain rule, logarithms, conditional probability, general solution to quadratic equations.) The explanations are terse but clear.

Cons: Crowed typography, could have used more margins, maybe a choice that was made for this reprint. Sections are number x.y-z, makes it hard to notice when the index refers to a range: x.y-za-zb. The index doesn't always lead directly to the desired section, for instance there is no entry for chain rule, but differentiation takes you right there.

Unfortunately, I'm already through most of the classes where I could have made good use of this book, but for those starting out, this might be a handy reference.

an engineer says: thanks korn and korn
over a period of thirty-plus years, i've benefited countless times from this dizzyingly broad and accurate handbook. it must be seen in that light: handbook. but, as such, there is simply no competition, at least for the engineer doing mathematical evaluations or predicting performance. i myself even find it enjoyable to just read in it. also to remember: it is not a compendium of computer-based techniques; indeed, it is a handbook of actual mathematics. i appreciate this small forum as an opportunity to say: Thanks, K&K.

Excellent but not much "applied"
While it has very good structure and layout, this well organized reference book is much more a teoretical rather than an applied mathematical handbook. It covers many engineering issues, but it doesn't shows practical examples in mechanics, thermodynamics and electrics, like the old good Pipes/Harvill.

Mathematical Handbook for Scientists and Engineers (Paperbk)
I have both the "hardcover" and "paperback" copies of this book. I feel that this is the "BEST" handbook of mathematics I have reviewed. It is both through and concise. The topical structure and layout of the book is excellent! The paperback is a convenient size, it fits easily within a briefcase. I most strongly recommend this book to any engineer, mathematician, physicist, etc.

This is the best book of Theorems
This book can teach you every thing you need to know about Mathamatics. ... Read more

Book Description

Praise for David Darling

The Universal Book of Astronomy

"A first-rate resource for readers and students of popular astronomy and general science. . . .Highlyrecommended."
–LibraryJournal

"A comprehensive survey and . . . a rare treat."
–Focus

The Complete Book of Spaceflight

"Darling’s content and presentation will have any reader moving from entry to entry."
–TheObservatorymagazine

Life Everywhere

"This remarkable book exemplifies the best of today’s popular science writing: it is lucid, informative, and thoroughly enjoyable."
–Science Books & Films

"An enthralling introduction to the new science of astrobiology."
–Lynn Margulis

Equations of Eternity

"One of the clearest and most eloquent expositions of the quantum conundrum and its philosophical and metaphysical implications that I have read recently."
–The New York Times

Deep Time

"A wonderful book. The perfect overview of the universe."
–Larry Niven ... Read more

Book Description

Janos Bolyai (1802-1860) was a mathematician who changed our fundamental ideas about space. As a teenager he started to explore a set of nettlesome geometrical problems, including Euclid's parallel postulate, and in 1832 he published a brilliant twenty-four-page paper that eventually shook the foundations of the 2000-year-old tradition of Euclidean geometry. Bolyai's "Appendix" (published as just that--an appendix to a much longer mathematical work by his father) set up a series of mathematical proposals whose implications would blossom into the new field of non-Euclidean geometry, providing essential intellectual background for ideas as varied as the theory of relativity and the work of Marcel Duchamp. In this short book, Jeremy Gray explains Bolyai's ideas and the historical context in which they emerged, were debated, and were eventually recognized as a central achievement in the Western intellectual tradition. Intended for nonspecialists, the book includes facsimiles of Bolyai's original paper and the 1898 English translation by G. B. Halstead, both reproduced from copies in the Burndy Library at MIT. ... Read more