Did you find maths boring at school? That’s because it was! When he was fourteen, Ian Stewart, now undoubtedly one of the best know mathematicians alive, started a maths notebook. Like a magpie he collected every interesting thing he could find out about the maths that wasn’t taught at school. And that meant all the fun and intriguing stuff.
His notebook finally became six, then spilled over into Professor Stewart’s Cabinet of Mathematical Curiosities. Open its drawers and discover a fabulous lifetime collection of games, puzzles, stories, jokes and factoids, odd items of mathematical culture, buzzwords, card tricks, things to make and things to do.
You’ll find out how to extract a cherry from a coctail glass or make money simple by proving the obvious – oh, and what the deal is with Fermat’s last thorem, the Poincaré Conjecture, Chaos Theory, Fractals and Penrose Patterns, and the real reason you can’t divide anything by zero.
As it presents problems and conundrums for the seasoned aificionado and adventurous novice alike, Professor Stewart’s Cabinet guarantees to stimulate and instruct, delight and surprise.
James Gleick - Chaos
Chaos records the birth of a new science. This new science offers a way of seeing order and pattern where formerly only the random, the erratic, the unpredictable - in short, the chaotic - had been observed. In the words of Douglas Hofstadter, "It turns out that an eerie type of chaos can lurk just behind a facade of order - and yet, deep inside the chaos lurks an even eerier type of order." Although highly mathematical in origin, chaos is a science of the everyday world, addressing questions every child has wondered about: how clouds form, how smoke rises, how water eddies in a stream. Chaos is a history of discovery. It chronicles, in the words of the scientists themselves, their conflicts and frustrations, their emotions and moments of revelation. After reading Chaos, you will never look at the world in quite the same way again.
Ismeretlen szerző - The Penguin Dictionary of Mathematics
The Penguin Dictionary of Mathematics takes in all branches of pure and applied mathematics, from algebra to mechanics and from number theory to statistics. Invaluable for students at all levels, it is also a useful and versatile source book for economists, business people, engineers, technicians and scientists of all kinds who use mathematics in the course of their work.
Mark S. Gockenbach - Understanding and Implementing the Finite Element Method
The ﬁnite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the ﬁnite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics. Understanding and Implementing the Finite Element Method includes a carefully documented collection of MATLAB® programs implementing the ideas presented in the book. Readers will beneﬁt from a careful explanation of data structures and speciﬁc coding strategies and will learn how to write a ﬁnite element code from scratch. Students can use the MATLAB codes to experiment with the method and extend them in various ways to learn more about programming ﬁnite elements. This practical book should provide an excellent foundation for those who wish to delve into advanced texts on the subject, including advanced undergraduates and beginning graduate students in mathematics, engineering, and the physical sciences. Preface; Part I: The Basic Framework for Stationary Problems. Chapter 1: Some Model PDEs; Chapter 2: The weak form of a BVP; Chapter 3: The Galerkin method; Chapter 4: Piecewise polynomials and the finite element method; Chapter 5: Convergence of the finite element method; Part II Data Structures and Implementation. Chapter 6: The mesh data structure; Chapter 7: Programming the finite element method: Linear Lagrange triangles; Chapter 8: Lagrange triangles of arbitrary degree; Chapter 9: The finite element method for general BVPs; Part III: Solving the Finite Element Equations. Chapter 10: Direct solution of sparse linear systems; Chapter 11: Iterative methods: Conjugate gradients; Chapter 12: The classical stationary iterations; Chapter 13: The multigrid method; Part IV: Adaptive Methods. Chapter 14: Adaptive mesh generation; Chapter 15: Error estimators and indicators; Bibliography; Index. "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." — Anthony Kearsley, research mathematician, National Institute of Standards and Technology.
Constance Reid - Hilbert
"It presents a sensitive portrait of a great human being. It describes accurately and intelligibly on a nontechnical level the world of mathematical ideas in which Hilbert created his masterpieces. And it illuminates the background of German social history against which the drama of Hilberts life was played. Beyond this, it is a poem in praise of mathematics." -SCIENCE
Ismeretlen szerző - Fractal Art - The Mandelbröt Set
This portfolio of postcards presents a collection of thirty computer-generated fractals from the Mandelbröt set. The images included in this book are created by computer interpretation of millions of calculations of the Mandelbröt equation and its derivatives. Designed as a flip book, each postcard is part of a zoom sequence exploring the wondrous self-replication of Mandelbröt-set fractals. Each consecutive image is a highly focused section of the previous card. A flip through this book is a fascinating tour that delves ever deeper into the original fractal image.
David J. Hand - The Improbability Principle
In The Improbability Principle, the renowned statistician David J. Hand argues that extraordinarily rare events are anything but. In fact, they’re commonplace. Not only that, we should all expect to experience a miracle roughly once every month. But Hand is no believer in superstitions, prophecies, or the paranormal. His definition of “miracle” is thoroughly rational. No mystical or supernatural explanation is necessary to understand why someone is lucky enough to win the lottery twice, or is destined to be hit by lightning three times and still survive. All we need, Hand argues, is a firm grounding in a powerful set of laws: the laws of inevitability, of truly large numbers, of selection, of the probability lever, and of near enough. Together, these constitute Hand’s groundbreaking Improbability Principle. And together, they explain why we should not be so surprised to bump into a friend in a foreign country, or to come across the same unfamiliar word four times in one day. Hand wrestles with seemingly less explicable questions as well: what the Bible and Shakespeare have in common, why financial crashes are par for the course, and why lightning does strike the same place (and the same person) twice. Along the way, he teaches us how to use the Improbability Principle in our own lives—including how to cash in at a casino and how to recognize when a medicine is truly effective. An irresistible adventure into the laws behind “chance” moments and a trusty guide for understanding the world and universe we live in, The Improbability Principle will transform how you think about serendipity and luck, whether it’s in the world of business and finance or you’re merely sitting in your backyard, tossing a ball into the air and wondering where it will land.
Barbara Oakley - A Mind For Numbers
Whether you are a student struggling to fulfill a math or science requirement, or you are embarking on a career change that requires a higher level of math competency, A Mind for Numbers offers the tools you need to get a better grasp of that intimidating but inescapable field. Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. She flunked her way through high school math and science courses, before enlisting in the army immediately after graduation. When she saw how her lack of mathematical and technical savvy severely limited her options—both to rise in the military and to explore other careers—she returned to school with a newfound determination to re-tool her brain to master the very subjects that had given her so much trouble throughout her entire life. In A Mind for Numbers, Dr. Oakley lets us in on the secrets to effectively learning math and science—secrets that even dedicated and successful students wish they'd known earlier. Contrary to popular belief, math requires creative, as well as analytical, thinking. Most people think that there's only one way to do a problem, when in actuality, there are often a number of different solutions—you just need the creativity to see them. For example, there are more than three hundred different known proofs of the Pythagorean Theorem. In short, studying a problem in a laser-focused way until you reach a solution is not an effective way to learn math. Rather, it involves taking the time to step away from a problem and allow the more relaxed and creative part of the brain to take over. A Mind for Numbers shows us that we all have what it takes to excel in math, and learning it is not as painful as some might think!
Daniel J. Levitin - The Organized Mind
New York Times bestselling author and neuroscientist Daniel J. Levitin shifts his keen insights from your brain on music to your brain in a sea of details. The information age is drowning us with an unprecedented deluge of data. At the same time, we’re expected to make more—and faster—decisions about our lives than ever before. No wonder, then, that the average American reports frequently losing car keys or reading glasses, missing appointments, and feeling worn out by the effort required just to keep up. But somehow some people become quite accomplished at managing information flow. In The Organized Mind, Daniel J. Levitin, PhD, uses the latest brain science to demonstrate how those people excel—and how readers can use their methods to regain a sense of mastery over the way they organize their homes, workplaces, and time. With lively, entertaining chapters on everything from the kitchen junk drawer to health care to executive office workflow, Levitin reveals how new research into the cognitive neuroscience of attention and memory can be applied to the challenges of our daily lives. This Is Your Brain on Music showed how to better play and appreciate music through an understanding of how the brain works. The Organized Mind shows how to navigate the churning flood of information in the twenty-first century with the same neuroscientific perspective.
Randall Munroe - What If?
From the creator of the wildly popular webcomic xkcd, hilarious and informative answers to important questions you probably never thought to ask. Millions of people visit xkcd.com each week to read Randall Munroe’s iconic webcomic. His stick-figure drawings about science, technology, language, and love have a large and passionate following. Fans of xkcd ask Munroe a lot of strange questions. What if you tried to hit a baseball pitched at 90 percent the speed of light? How fast can you hit a speed bump while driving and live? If there was a robot apocalypse, how long would humanity last? In pursuit of answers, Munroe runs computer simulations, pores over stacks of declassified military research memos, solves differential equations, and consults with nuclear reactor operators. His responses are masterpieces of clarity and hilarity, complemented by signature xkcd comics. They often predict the complete annihilation of humankind, or at least a really big explosion. The book features new and never-before-answered questions, along with updated and expanded versions of the most popular answers from the xkcd website. What If? will be required reading for xkcd fans and anyone who loves to ponder the hypothetical.
Shing-Tung Yau - Steve Nadis - The Shape of Inner Space
String theory says we live in a ten-dimensional universe, but that only four are accessible to our everyday senses. According to theorists, the missing six are curled up in bizarre structures known as Calabi-Yau manifolds. In The Shape of Inner Space, Shing-Tung Yau, the man who mathematically proved that these manifolds exist, argues that not only is geometry fundamental to string theory, it is also fundamental to the very nature of our universe. Time and again, where Yau has gone, physics has followed. Now for the first time, readers will follow Yau’s penetrating thinking on where we’ve been, and where mathematics will take us next. A fascinating exploration of a world we are only just beginning to grasp, The Shape of Inner Space will change the way we consider the universe on both its grandest and smallest scales.
Mark Ronan - Symmetry and the Monster
Chronicles the history of a mathematical quest that began two hundred years ago in revolutionary France, led to the biggest collaboration ever between mathematicians around the world, and revealed the "Monster" of symmetry--a giant snowflake that exists in 196,884 dimensions.
Ismeretlen szerző - Quadrivium
Composed of six previously published works.
Burkard Polster - Gerard Cheshire - Matt Tweed - Matthew Watkins - Moff Betts - Sciencia
From basic mathematical and physical formulas that govern much of our world to the components of matter; from the structure of the cosmos to that of the human body-the discoveries of scientists over the last millennium have been remarkable. Sciencia gathers together "Useful Mathematical and Physical Formulae," " Q.E.D," "Essential Elements," "Evolution," "The Human Body," and "The Compact Cosmos," six elegant and insightful short volumes spanning the realms of mathematics, physics, chemistry, biology, evolution, and astronomy, offering invaluable information to today's readers. Lavishly illustrated with engravings, woodcuts, and original drawings and diagrams, "Sciencia" will inspire readers of all ages to take an interest in the interconnected knowledge of the modern sciences. Beautifully produced in thirteen different colors of ink, "Sciencia" is an essential reference and an elegant gift.
David Wade - Symmetry
Symmetry underlies almost every aspect of nature and our experience of the world, from the subatomic realms of quantum mechanics to the equations of physics, in art, architecture and our concepts of morality and justice. In this little book Welsh writer and artist David Wade paints a picture of one of the most elusive and pervasive concepts known to man.
Ravi Vakil - A Mathematical Mosaic
Ravi Vakil, described in the San Francisco Chronicle as a legend in the world of math competitions has finally released his long-awaited second edition of A Mathematical Mosaic: Patterns & Problem Solving. Regarded by many as a seminal book in the field of mathematics competitions, the first edition of A Mathematical Mosaic has received wide acclaim from mathematics teachers, professors and the mathematics community at large. In the pages of this book, Ravi shares what mathematics is really about: beauty, elegance, and the discovery of deep and interconnected patterns. These patterns of nature are often best understood through puzzles and problems, both easy and hard. He also profiles eleven other Olympiad winners including Noam Elkies, the youngest professor to receive tenure at Harvard. This book is a must for teachers seeking to challenge their best students, and for students preparing for mathematics competitions.
Ian Stewart - Flatterland
First there was Edwin A. Abbott's remarkable Flatland, published in 1884, and one of the all-time classics of popular mathematics. Now, from mathematician and accomplished science writer Ian Stewart, comes what Nature calls "a superb sequel." Through larger-than-life characters and an inspired story line, Flatterland explores our present understanding of the shape and origins of the universe, the nature of space, time, and matter, as well as modern geometries and their applications. The journey begins when our heroine, Victoria Line, comes upon her great-great-grandfather A. Square's diary, hidden in the attic. The writings help her to contact the Space Hopper, who tempts her away from her home and family in Flatland and becomes her guide and mentor through ten dimensions. In the tradition of Alice in Wonderland and The Phantom Toll Booth, this magnificent investigation into the nature of reality is destined to become a modern classic.
Max Tegmark - Our Mathematical Universe
Max Tegmark leads us on an astonishing journey through past, present and future, and through the physics, astronomy and mathematics that are the foundation of his work, most particularly his hypothesis that our physical reality is a mathematical structure and his theory of the ultimate multiverse. In a dazzling combination of both popular and groundbreaking science, he not only helps us grasp his often mind-boggling theories, but he also shares with us some of the often surprising triumphs and disappointments that have shaped his life as a scientist. Fascinating from first to last—this is a book that has already prompted the attention and admiration of some of the most prominent scientists and mathematicians.
John E. Hopcroft - Rajeev Motwani - Jeffrey D. Ullman - Introduction to Automata Theory, Languages, and Computation
It has been more than 30 years since John Hopcroft and Jeffrey Ullman first published this classic book on formal languages, automata theory and computational complexity. With this long-awaited revision, the authors continue to present the material in a concise and straightforward manner, now with an eye out for the practical applications along with the mathematics. This edition has been revised to make it more accessible to today's students, including the addition of more material on writing proofs, more figures and pictures to convey ideas, sidebars to highlight related material, and a less formal writing style. It includes many new exercises in each chapter to help readers confirm and enhance their understanding of the material.
Greg Egan - Permutation City
The good news is that you have just awakened into Eternal Life. You are going to live forever. Immortality is a reality. A medical miracle? Not exactly. The bad news is that you are a scrap of electronic code. The world you see around you, the you that is seeing it, has been digitized, scanned, and downloaded into a virtual reality program. You are a Copy that knows it is a copy. The good news is that there is a way out. By law, every Copy has the option of terminating itself, and waking up to normal flesh-and-blood life again. The bail-out is on the utilities menu. You pull it down... The bad news is that it doesn't work. Someone has blocked the bail-out option. And you know who did it. You did. The other you. The real you. The one that wants to keep you here forever.
László Máté - Hilbert Space Methods in Science and Engineering
This volume aims to present Hilbert space theory as an accessible language for applied mathematicians, engineers and scientists. A knowledge of linear algebra and analysis is assumed. The construction of mathematical models using Hilbert space theory is illustrated with problems and results are evaluated. For the first time, mathematical models based on reproducing kernel Hilbert spaces and causal operators are explained at an introductory level.