Like Douglas Hofstadter's G del, Escher, Bach, and David Berlinski's A Tour of the Calculus, Euclid in the Rainforest combines the literary with the mathematical to explore
logic--the one indispensable tool in man's quest to understand the world. Underpinning both math and science, it is the foundation of every major advancement in knowledge since the time of the ancient Greeks. Through adventure stories and historical narratives populated with a rich and quirky cast of characters, Mazur artfully reveals the less-than-airtight nature of logic and the muddled relationship between math and the real world. Ultimately, Mazur argues, logical reasoning is not purely robotic. At its most basic level, it is a creative process guided by our intuitions and beliefs about the world.
Get all you need to know with Super Reviews Each Super Review is packed with in-depth, student-friendly topic reviews that fully explain everything about the subject. The Statistics Super Review includes frequency distributions, numerical methods of describing data, measures of variability, probability, distributions, sampling theory, statistical inference, general linear model inferences, experimental design, the chi-square test, and time series. Take the Super Review quizzes to see how much you've learned - and where you need more study. Makes an excellent study aid and textbook companion. Great for self-study DETAILS- From cover to cover, each in-depth topic review is easy-to-follow and easy-to-grasp - Perfect when preparing for homework, quizzes, and exams - Review questions after each topic that highlight and reinforce key areas and concepts- Student-friendly language for easy reading and comprehension- Includes quizzes that test your understanding of the subject
The international best-seller that makes mathematics a thrilling explorationIn twelve dreams, Robert, a boy who hates math, meets a Number Devil, who leads him to discover the amazing world of numbers: infinite numbers, prime numbers, Fibonacci numbers, numbers that magically appear in triangles, and numbers that expand without end. As we dream with him, we are taken further and further into mathematical theory, where ideas eventually take flight, until everyone--from those who fumble over fractions to those who solve complex equations in their heads--winds up marveling at what numbers can do. Hans Magnus Enzensberger is a true polymath, the kind of superb intellectual who loves thinking and marshals all of his charm and wit to share his passions with the world. In The Number Devil, he brings together the surreal logic of Alice in Wonderland and the existential geometry of Flatland with the kind of math everyone would love, if only they had a number devil to teach them.
Optimization models play an increasingly important role in financial decisions. This is the first textbook devoted to explaining how recent advances in optimization models, methods and software can be applied to solve problems in computational finance more efficiently and accurately. Chapters discussing the theory and efficient solution methods for all major classes of optimization problems alternate with chapters illustrating their use in modeling problems of mathematical finance. The reader is guided through topics such as volatility estimation, portfolio optimization problems and constructing an index fund, using techniques such as nonlinear optimization models, quadratic programming formulations and integer programming models respectively. The book is based on Master's courses in financial engineering and comes with worked examples, exercises and case studies. It will be welcomed by applied mathematicians, operational researchers and others who work in mathematical and computational finance and who are seeking a text for self-learning or for use with courses.
"Altogether a most instructive, entertaining, and esthetically pleasing book." -- Science.
Since the ancient Greeks, the visualization of space has been a challenge that has intrigued men of learning. Through centuries of thoughtful looking, a number of three-dimensional figures or polyhedral, as the Greeks called them, have been discovered, admired, and wondered at for their mathematical elegance and beauty. And they have been put to use in remarkably diverse ways by engineers and builders, chemists and crystallographers, architects and sculptors.
This book describes very clearly and simply, and illustrates with beautiful photographs of models, a great number of three-dimensional figures, all but a few consisting of plane faces bounded by straight lines. It examines the nine regular solids -- the five commonly called Platonic, described by Theaetetus in the fourth century B.C., and the four called Kepler-Poinsot, two each of which were discovered by Kepler and Poinsot many centuries later. And it examines many variations obtained by truncation, stellation, dualization, and compounding.
Writing for the layman as well as the student or professional in mathematics, Alan Holden explains the structure of the figures and demonstrates how they can be used to explain mathematics visually rather than by symbol systems, an effort hailed by Scientific American magazine as "a victory of clear, connected thinking over the theorematic method." At the end of the book the author includes a section containing instructions for constructing cardboard models.
"I have discovered a truly marvelous proof, which this margin is too narrow to contain". With these tantalizing 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, yet the finest mathematical minds would be baffled for more than three and a half centuries.
Fermat's Last Theorem became the Holy Grail of mathematics. Whole and colorful lives were devoted, and even sacrificed, to finding a solution. Leonhard Euler, the greatest mathematician of the 18th century, had to admit defeat. Sophie Germain had to take on the identity of a man to do research in a field forbidden to females, and made the most significant breakthrough of the 19th century. The clashing Evariste Galois scribbled down the results of his research deep into the night before venturing out to die in a duel in 1832. Yutaka Taniyama, whose insights would lead directly to the ultimate solution to Fermat, tragically killed himself in despair. On the other hand, Paul Wolfskehl, a famous German industrialist, claimed Fermat had saved him from suicide, and established a rich prize for the first person to prove the theorem.
And then came Princeton Professor Andrew Wiles, who had dreamed of proving Fermat ever since he first read of it as a boy of ten in his local library. In 1993, some 356 years after Fermat's challenge, and after seven years of working in isolation and secrecy, Wiles stunned the world by announcing a proof -- though his own journey would be far from over.
"Fermat's Enigma" is the story of the epic quest to solve the greatest math problem of all time. Written by the award-winningfilm-maker who has had more access to Andrew Wiles than any other journalist, it is a human drama of high dreams, intellectual brilliance, and extraordinary determination.
If you have ever looked for P-values by shopping at P mart, tried to watch the Bernoulli Trails on People's Court, or think that the standard deviation is a criminal offense in six states, then you need The Cartoon Guide to Statistics to put you on the road to statistical literacy.
The Cartoon Guide to Statistics covers all the central ideas of modern statistics: the summary and display of data, probability in gambling and medicine, random variables, Bernoulli Trails, the Central Limit Theorem, hypothesis testing, confidence interval estimation, and much more--all explained in simple, clear, and yes, funny illustrations. Never again will you order the Poisson Distribution in a French restaurant
This updated version features all new material.
An experienced math instructor and teacher trainer helps to make PreCalculus easy--even for students who feel intimidated by more advanced math topics. His orderly, step-by-step approach begins with concepts and skills typically introduced in a first-year high-school-level algebra course then progresses to advanced algebra and trigonometry, needed for the study of calculus. The lesson format and step-by-step demonstration examples are designed for self-teaching and rapid learning. Special math tips help resolve student difficulties and are strategically located throughout the text. Major topics include: algebra; graphs and graphing calculator methods; complex numbers; polynomial and rational functions; exponential and logarithmic functions; fitting lines and curves to data; trigonometry and polar coordinates; conic sections and parametric equations; counting and probability; binomial theorem; and probabilities. Check-up exercises at the end of each chapter help students monitor their progress.
Praised by Entertainment Weekly as "the man who put the fizz into physics," Dr. Len Fisher turns his attention to the science of cooperation in his lively and thought-provoking book. Fisher shows how the modern science of game theory has helped biologists to understand the evolution of cooperation in nature, and investigates how we might apply those lessons to our own society. In a series of experiments that take him from the polite confines of an English dinner party to crowded supermarkets, congested Indian roads, and the wilds of outback Australia, not to mention baseball strategies and the intricacies of quantum mechanics, Fisher sheds light on the problem of global cooperation. The outcomes are sometimes hilarious, sometimes alarming, but always revealing. A witty romp through a serious science, Rock, Paper, Scissors will both teach and delight anyone interested in what it what it takes to get people to work together.