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Seventeen Equations that Changed the World [Kindle Edition]

Ian Stewart
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"'Stewart has a genius for explanation... Find a comfortable chair for some holiday puzzling: mathematics doesn't come more entertaining than this.' (New Scientist) 'Stewart has served up the instructive equivalent of a Michelin-starred tasting menu' (Guardian)"


From Newton's Law of Gravity to the Black-Scholes model used by bankers to predict the markets, equations, are everywhere - and they are fundamental to everyday life.

Seventeen Equations that Changed the World examines seventeen groundbreaking equations that have altered the course of human history. He explores how Pythagoras's Theorem led to GPS and SatNav; how logarithms are applied in architecture; why imaginary numbers were important in the development of the digital camera, and what is really going on with Schrödinger's cat.

Entertaining, surprising and vastly informative, Seventeen Equations that Changed the World is a highly original exploration - and explanation - of life on earth.


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5.0 von 5 Sternen Mathematik uninteressant? 17. Dezember 2012
Von John
Format:Kindle Edition|Verifizierter Kauf
Ian Stewart hat es verstanden, einige Komplexitäten der Mathematik und vor allem die Auswirkungen der Mathematiker auf unser Leben zu erklären. Dieses Buch setzt ein gewisses Grundwissen der Mathematik voraus, um der Argumentation von Stewart zu folgen, Aber das Buch ist auch für den absoluten Laien durchaus interessant, der den Text verstehen kann, ohne sich mit den ganzen Formeln auseinandersetzen zu müssen.
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5.0 von 5 Sternen Fantastic book for the inquisitive. 25. März 2012
Von Charles Chen - Veröffentlicht auf
Format:Gebundene Ausgabe
What could be more boring than mathematical equations? The majority of folks would be hard pressed to find something to answer that hypothetical query. Myself included :) I'll be honest, I'm a math minor and I picked up this book on a whim in a bookstore thinking to myself "Now why would anyone want to write or _buy_ a book on 17 equations?" I flipped through it and immediately knew that I had to consume the rest of this book.

What Stewart is able to do is to take these 17 equations that manifest in everything we do, everything we observe, every bit of space around us and bring life to them. To be clear, this is more a book about history than pure math, but there is no doubt that these 17 core equations are at the heart of the book. He presents the opening of each chapter with a concise summary of these equations in laymen's terms that helps immensely in revealing the underlying nature of the equations and then goes into the history of the creation (discovery?) of each of these equations and it's been an eye-opening read.

As an example, having majored in computer science, I worked constantly with logarithms and natural logs (there's lumber joke here somewhere) but never once understood the nature of logarithms. How did they come about? Why do they exist? What problem do they address? Just what in the heck _is_ a logarithm? I knew them only in the abstract -- as operations that yielded a result; I knew them as a general pattern but not the nature of the logarithm. The second chapter simply blew me away with the clarity and simplicity with which Stewart was able to pull back the covers on what logarithms actually mean -- there's actually a very good reason why they're called logs. No one in my years of formal education had bothered to explain it in the same way that Stewart does in this book; the existence of logarithms finally makes sense to me.

While I cannot say that this book is for everyone (I'm sure my wife would be asleep after the first chapter :), I will say that I find it is surprisingly approachable for most folks who are scientifically or mathematically inclined. Certainly, there are many equations and plenty of mathematics and it gets especially complex (pun intended :) in the later chapters; you WILL get lost in the math. However, I think this book is still immensely readable and approachable, even for those who have never ventured deep into the vast field of mathematics or have long moved past their days of calculus, linear algebra, and so on. I, for one, will make sure that my daughter reads the chapter on logarithms as it starts to seep into her curriculum one day to make sure she understands the "why" and so that she has an appreciation for all of the history and magic behind that little "log n" button on her calculator.

This book is incredibly well written, well presented such that it is approachable for a large audience, an entertaining read, and highly recommended. If you've read this review to this point, you should probably just go ahead and by this book!
44 von 47 Kunden fanden die folgende Rezension hilfreich
5.0 von 5 Sternen Equations We Non-Mathematicians Use Every Day 12. März 2012
Von R. Hardy - Veröffentlicht auf
Format:Gebundene Ausgabe
The mathematician Ian Stewart knows the famous story about equations versus book sales. Stephen Hawking's publisher told him that every equation published in _A Brief History of Time_ would halve the number of books sold. One equation got in: E = mc^2, and maybe it really did cut the sales of the book by half. If this rule is true, Stewart is in real trouble with his newest book, _In Pursuit of the Unknown: 17 Equations That Changed the World_ (Basic Books). Readers who know his work, however, know that they are in good hands. Stewart has undoubtedly written mathematical papers that would be over the heads of us other mortals, but his books for the public on the problems, range, and philosophy of mathematics are clear, funny, entertaining, and educational. His seventeen chapters include some simple equations that everyone knows; that E = mc^2 is here, simple to write and to memorize, but pointing to complexities that most of us cannot easily comprehend, even a hundred or so years after it was developed. Some of the equations, like Schrödinger's Equation, are full of Greek letters and only physics experts will recognize them. Throughout the book, however, Stewart shows that these are equations that run our lives in our technical age. The equations may be used professionally just by the egghead experts, but in a wider sense, we all use them, every day.

The first chapter here is on the old familiar a^2 + b^2 = c^2, the Pythagorean Theorem. This is pure math, straight from Euclid, and not (as are many of the equations here) from applied mathematics or mathematical physics. But that does not mean the Pythagorean Theorem is forever locked within the mathematicians' ivory tower; it led to trigonometry. When he does get to E = mc^2, Stewart reflects about how Pythagoras helps understand relativity, because of light paths understood as sides of triangles. All of the equations here have improved our understanding of how nature works, and have supplied reason to wonder at how consistently mathematics underlies everything. The basic equation for calculus is here, which is responsible for most of mathematical physics. Among the simplest of equations here is Euler's formula that shows how faces, edges, and corners of a solid shape are related. Like each simple formula, it has created complications, including the powerful pure mathematics of topology, which has implications for how DNA works and why planets may move in a chaotic way. Another simple one is i^2 = -1, indicating that minus one, which should have no square root since it is negative, does have one, the imaginary number i. Although i may be called imaginary, it is essential for understanding waves and electricity, not to mention quantum mechanics. Chaos theory is here, with an equation that helps show how the flapping of that butterfly's wing may lead to a tornado later on; that's the most famous effect, but the equation models, for instance, how a population of creatures changes over generations if they have to be curtailed by limited resources or predators. Stewart gives clear explanations, but they are relatively deep for the non-mathematician. Many people who read this book will want to take long breaks between its pithy chapters, each of which has been expanded elsewhere into many volumes. Equations are useful for explaining the world, but like any tool they can be misused. Stewart's final chapter is on the Black-Scholes Equation, invented in 1973 and since then used to analyze the changes of price of a financial derivative. Derivatives could thus be traded before they matured. It was a useful formula as long as it was applied only when market situations fit, but it was abused. Stewart makes clear that the formula didn't cause the 2008 - 2009 financial crisis, but abuse of it, along with financial and political ineptitude and lax regulation, made for a crash that didn't have to happen.

In an epilogue, Stewart reflects that most equations aren't important: "I write them down all the time, and believe me, I know." Here are some important ones, though, equations that run our world, always in ways that the inventors of the equations could never have predicted. It may be, Stewart writes at the end, that the cellular automata famously championed by Stephen Wolfram do a better job of explaining the universe than equations do, and maybe algorithms are going to be more important than equations. His engrossing book, showing the vital importance of equations not just for explanation but as causation of historic and social change, makes clear that it will be a long time before any other modeling becomes more important.
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5.0 von 5 Sternen Important Equations: Their History and Meaning 7. April 2012
Von G. Poirier - Veröffentlicht auf
Format:Gebundene Ausgabe
As a quick glance through this book will indicate, some of the equations presented are well-known and simple whereas others can look awfully intimidating. A given reader may be intimately familiar with several of these equations while at the same time be totally unaware of some of the others or their significance. The author does not provide mathematical derivations of these equations. Instead, he describes how they came about, explains their meanings and applications and then discusses their legacy. Several fields are covered in this fascinating book: physics, engineering, mathematics, statistics, information theory, chaos and economics.

The author writes very clearly and in a friendly, lively and engaging style. In some sections the author seems to assume very little or no pertinent knowledge on the part of the reader and as a result is very careful and detailed in his explanations, e.g., logarithms, calculus. In other cases, the discussions are much more challenging, and although new terms are briefly defined, the discussions may still result in some head scratching, e.g., quantum mechanics, Black-Scholes equation. Consequently, it is difficult to determine at what population this book is aimed. Science buffs may be bored by some of the more elementary discussions but find themselves more challenged by the topics on which they know very little. On the other hand, a younger (or less-informed) reader may learn quite a bit from the elementary discussions but get lost in some of the other sections.

Overall, I think that it is safe to say that this book has something for everyone. Although I did find some sections rather challenging, I must admit that I thoroughly enjoyed it.
32 von 37 Kunden fanden die folgende Rezension hilfreich
2.0 von 5 Sternen Sitck with the Facts! 13. August 2012
Von Amazon Customer - Veröffentlicht auf
Format:Gebundene Ausgabe|Verifizierter Kauf
While I enjoyed the stories and anecdotes about the history of the equations, I found that the author often punctuated his discussions with his own opinions about...nearly everything. When I purchased the book, I didn't expect to get an op-ed on Mr. Stewarts stances on politics and the environmet.

For example, at least half of the chapter on the Navier-Stokes equations - one of the fundamental tools for thermo-fluid scientists - is devoted to the author's position on global warming. As a practicing thermo-fluid scientist, I was terribly disappointed that the opportunity to share the wonders of this relationship were lost.
6 von 6 Kunden fanden die folgende Rezension hilfreich
4.0 von 5 Sternen Inspiring but occasionally challenging look at the maths behind the modern world 30. Mai 2012
Von Andrew Johnston - Veröffentlicht auf
Stephen Hawking wrote A Brief History of Time with only a single equation, accepting that more might "scare the punters off". Bill Bryson wrote A Short History of Nearly Everything with neither equations nor pictures. Ian Stewart is therefore being very brave writing a popular science book which explains the mathematical basis for our modern world, unashamedly focusing on the key equations themselves.

That said, the equations are used more as milestones than intensively studied subjects. This is not a "book full of maths", and each chapter is largely a textual exploration around the subject starring the featured equation, explaining what it means, and what it led to.

The scope is vast, from Pythagoras through to the underpinnings of quantum theory, chaos and derivatives trading, taking in key scientific developments and their mathematical explanations along the way. Stewart does a remarkable job of compacting this scope into just 17 chapters and about 300 pages.

If you're a skilled mathematician you will gloss over the maths and still take value from the following discussions. If, however, your maths is more limited or, like mine, rather rusty, you'll find you don't need to follow all the mathematical details. You don't need to really understand about grads, divs and curls, for example, to appreciate the similarity in "shape" between the key equations in several different areas of science. The author does a very fine job of both explaining this structure, and also where the reader must understand, and where detailed understanding is less important.

Some of the explanations are quite complex, especially where Stewart is exploring the most recent applications of older ideas. I did get lost a couple of times and had to re-read short sections, but overall I came away thinking that I had built a decent grasp.

The book has an admirable focus on the practical applications of science, but some of this is presented with such limited detail that in a couple of places it devolves into lists of applications rather than real explanations. As well as positive stories, Stewart is not afraid to show where mis-interpretation of the mathematics or its limitations has failed us, most notably in the last chapter on financial derivatives and how their abuse has caused the current crises.

Although eminently readable and often amusing, this book is best read in chunks of a couple of chapters at a time, allowing the ideas to sink in. Do so, and invest a little effort, and you'll be well rewarded.
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