Now, in an exciting, fast-paced historical narrative ranging across two centuries, Mark Ronan takes us on an exhilarating tour of this final mathematical quest. Ronan describes how the quest to understand symmetry really began with the tragic young genius Evariste Galois, who died at the age of 20 in a duel. Galois, who spent the night before he died frantically scribbling his unpublished discoveries, used symmetry to understand algebraic equations, and he discovered that there were building blocks or atoms of symmetry. Most of these building blocks fit into a table, rather like the periodic table of elements, but mathematicians have found 26 exceptions. The biggest of these was dubbed the Monster--a giant snowflake in 196,884 dimensions. Ronan, who personally knows the individuals now working on this problem, reveals how the Monster was only dimly seen at first. As more and more mathematicians became involved, the Monster became clearer, and it was found to be not monstrous but a beautiful form that pointed out deep connections between symmetry, string theory, and the very fabric and form of the universe. This story of discovery involves extraordinary characters, and Mark Ronan brings these people to life, vividly recreating the growing excitement of what became the biggest joint project ever in the field of mathematics. Vibrantly written, Symmetry and the Monster is a must-read for all fans of popular science--and especially readers of such books as Fermat's Last Theorem.

    xn + yn = zn, where n represents 3, 4, 5, ...no solution"I have discovered a truly marvelous demonstration of this proposition which this margin is too narrow to contain."With these words, the seventeenth-century French mathematician Pierre de Fermat threw down the gauntlet to future generations.  What came to be known as Fermat's Last Theorem looked simple; proving it, however, became the Holy Grail of mathematics, baffling its finest minds for more than 350 years.  In Fermat's Enigma--based on the author's award-winning documentary film, which aired on PBS's "Nova"--Simon Singh tells the astonishingly entertaining story of the pursuit of that grail, and the lives that were devoted to, sacrificed for, and saved by it.  Here is a mesmerizing tale of heartbreak and mastery that will forever change your feelings about mathematics.

    Really big. You just won't believe how vastly, hugely, mind-bogglingly big it is. I mean, you may think it's a long way down the street to the chemist, but that's just peanuts to space.' Douglas Adams, Hitch-hiker's Guide to the GalaxyWe human beings have trouble with infinity - yet infinity is a surprisingly human subject. Philosophers and mathematicians have gone mad contemplating its nature and complexity - yet it is a concept routinely used by schoolchildren. Exploring the infinite is a journey into paradox. Here is a quantity that turns arithmetic on its head, making it feasible that 1 = 0. Here is a concept that enables us to cram as many extra guests as we like into an already full hotel. Most bizarrely of all, it is quite easy to show that there must be something bigger than infinity - when it surely should be the biggest thing that could possibly be. Brian Clegg takes us on a fascinating tour of that borderland between the extremely large and the ultimate that takes us from Archimedes, counting the grains of sand that would fill the universe, to the latest theories on the physical reality of the infinite. Full of unexpected delights, whether St Augustine contemplating the nature of creation, Newton and Leibniz battling over ownership of calculus, or Cantor struggling to publicise his vision of the transfinite, infinity's fascination is in the way it brings together the everyday and the extraordinary, prosaic daily life and the esoteric.Whether your interest in infinity is mathematical, philosophical, spiritual or just plain curious, this accessible book offers a stimulating and entertaining read.

    Most of the time this math works quietly behind the scenes . . . until it doesn't. All sorts of seemingly innocuous mathematical mistakes can have significant consequences.Math is easy to ignore until a misplaced decimal point upends the stock market, a unit conversion error causes a plane to crash, or someone divides by zero and stalls a battleship in the middle of the ocean.Exploring and explaining a litany of glitches, near misses, and mathematical mishaps involving the internet, big data, elections, street signs, lotteries, the Roman Empire, and an Olympic team, Matt Parker uncovers the bizarre ways math trips us up, and what this reveals about its essential place in our world. Getting it wrong has never been more fun.

    From the very first attempts by the Greeks to grapple with the complexities of our known world to the latest application of infinity in physics, The Road to Reality carefully explores the movement of the smallest atomic particles and reaches into the vastness of intergalactic space. Here, Penrose examines the mathematical foundations of the physical universe, exposing the underlying beauty of physics and giving us one the most important works in modern science writing.

    The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory. Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory accessible to a non-specialist audience. Starting with the simplest knots, Adams guides readers through increasingly more intricate twists and turns of knot theory, exploring problems and theorems mathematicians can now solve, as well as those that remain open. He also explores how knot theory is providing important insights in biology, chemistry, physics, and other fields. The new paperback edition has been updated to include the latest research results, and includes hundreds of illustrations of knots, as well as worked examples, exercises and problems. With a simple piece of string, an elementary mathematical background, and The Knot Book, anyone can start learning about some of the most advanced ideas in contemporary mathematics.

    Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts, mathematical discussions, and the application of complex numbers and functions to important problems.

    Based on a National Magazine Award-winning article, this masterful biography of Hungarian-born Paul Erdos is both a vivid portrait of an eccentric genius and a layman's guide to some of this century's most startling mathematical discoveries.

    It is a bridge from the computational courses (such as calculus or differential equations) that students typically encounter in their first year of college to a more abstract outlook. It lays a foundation for more theoretical courses such as topology, analysis and abstract algebra. Although it may be more meaningful to the student who has had some calculus, there is really no prerequisite other than a measure of mathematical maturity. Topics include sets, logic, counting, methods of conditional and non-conditional proof, disproof, induction, relations, functions and infinite cardinality.

    It shouldn't be like that. Learning calculus without mechanics is incredibly boring. Learning mechanics without calculus is missing the point. This textbook integrates both subjects and highlights the profound connections between them.This is the deal. Give me 350 pages of your attention, and I'll teach you everything you need to know about functions, limits, derivatives, integrals, vectors, forces, and accelerations. This book is the only math book you'll need for the first semester of undergraduate studies in science.With concise, jargon-free lessons on topics in math and physics, each section covers one concept at the level required for a first-year university course. Anyone can pick up this book and become proficient in calculus and mechanics, regardless of their mathematical background.Visit http://minireference.com for more details.

    Crease tells the stories behind ten of the greatest equations in human history. Was Nobel laureate Richard Feynman really joking when he called Maxwell's electromagnetic equations the most significant event of the nineteenth century? How did Newton's law of gravitation influence young revolutionaries? Why has Euler's formula been called "God's equation," and why did a mysterious ecoterrorist make it his calling card? What role do betrayal, insanity, and suicide play in the second law of thermodynamics?The Great Equations tells the stories of how these equations were discovered, revealing the personal struggles of their ingenious originators. From "1 + 1 = 2" to Heisenberg's uncertainty principle, Crease locates these equations in the panoramic sweep of Western history, showing how they are as integral to their time and place of creation as are great works of art.

    Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of "new math" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor and anecdote to illuminate the concepts underlying "new math": groups, sets, subsets, topology, Boolean algebra, and more. According to Professor Stewart, an understanding of these concepts offers the best route to grasping the true nature of mathematics, in particular the power, beauty, and utility of pure mathematics. No advanced mathematical background is needed (a smattering of algebra, geometry, and trigonometry is helpful) to follow the author's lucid and thought-provoking discussions of such topics as functions, symmetry, axiomatics, counting, topology, hyperspace, linear algebra, real analysis, probability, computers, applications of modern mathematics, and much more.By the time readers have finished this book, they'll have a much clearer grasp of how modern mathematicians look at figures, functions, and formulas and how a firm grasp of the ideas underlying "new math" leads toward a genuine comprehension of the nature of mathematics itself.

    Would you believe that these five pieces can be reassembled in such a fashion so as to create two apples equal in shape and size to the original? Would you believe that you could make something as large as the sun by breaking a pea into a finite number of pieces and putting it back together again? Neither did Leonard Wapner, author of The Pea and the Sun, when he was first introduced to the Banach-Tarski paradox, which asserts exactly such a notion. Written in an engaging style, The Pea and the Sun catalogues the people, events, and mathematics that contributed to the discovery of Banach and Tarski's magical paradox. Wapner makes one of the most interesting problems of advanced mathematics accessible to the non-mathematician.

    Integration is treated before differentiation -- this is a departure from most modern texts, but it is historically correct, and it is the best way to establish the true connection between the integral and the derivative. Proofs of all the important theorems are given, generally preceded by geometric or intuitive discussion. This Second Edition introduces the mean-value theorems and their applications earlier in the text, incorporates a treatment of linear algebra, and contains many new and easier exercises. As in the first edition, an interesting historical introduction precedes each important new concept.

    Einstein's Heroes takes you on a journey of discovery about just such a miraculous language--the language of mathematics--one of humanity's mostamazing accomplishments. Blending science, history, and biography, this remarkable book reveals the mysteries of mathematics, focusing on the life and work of three of Albert Einstein's heroes: Isaac Newton, Michael Faraday, and especially James Clerk Maxwell, whose work directly inspired the theory of relativity. RobynArianrhod bridges the gap between science and literature, portraying mathematics as a language and arguing that a physical theory is a work of imagination involving the elegant and clever use of this language. The heart of the book illuminates how Maxwell, using the language of mathematics in a newand radical way, resolved the seemingly insoluble controversy between Faraday's idea of lines of force and Newton's theory of action-at-a-distance. In so doing, Maxwell not only produced the first complete mathematical description of electromagnetism, but actually predicted the existence of theradio wave, teasing it out of the mathematical language itself. Here then is a fascinating look at mathematics: its colorful characters, its historical intrigues, and above all its role as the uncannily accurate language of nature.