A New York Times Science BestsellerWhat if you had to take an art class in which you were only taught how to paint a fence? What if you were never shown the paintings of van Gogh and Picasso, weren't even told they existed? Alas, this is how math is taught, and so for most of us it becomes the intellectual equivalent of watching paint dry.In Love and Math , renowned mathematician Edward Frenkel reveals a side of math we've never seen, suffused with all the beauty and elegance of a work of art. In this heartfelt and passionate book, Frenkel shows that mathematics, far from occupying a specialist niche, goes to the heart of all matter, uniting us across cultures, time, and space. Love and Math tells two intertwined stories: of the wonders of mathematics and of one young man's journey learning and living it. Having braved a discriminatory educational system to become one of the twenty-first century's leading mathematicians, Frenkel now works on one of the biggest ideas to come out of math in the last 50 years: the Langlands Program. Considered by many to be a Grand Unified Theory of mathematics, the Langlands Program enables researchers to translate findings from one field to another so that they can solve problems, such as Fermat's last theorem, that had seemed intractable before.At its core, Love and Math is a story about accessing a new way of thinking, which can enrich our lives and empower us to better understand the world and our place in it. It is an invitation to discover the magic hidden universe of mathematics.
Bestselling author and worst-drawing artist Ben Orlin expands his oeuvre with this interactive collection of mathematical games. With 70-plus games, each taking a minute to learn and a lifetime to master, this treasure trove will delight, educate, and entertain.From beloved math popularizer Ben Orlin comes a masterfully compiled collection of dozens of playable mathematical games. This ultimate game chest draws on mathematical curios, childhood classics, and soon-to-be classics, each hand-chosen to be (1) fun, (2) thought-provoking, and (3) easy to play. With just paper, pens, and the occasional handful of coins, you and a partner can enjoy hours of fun-and hours of challenge.Orlin's sly humor, expansive knowledge, and so-bad-they're-good drawings show us how simple rules summon our best thinking.Games include:* Ultimate Tic-Tac-Toe* Sprouts* Battleship* Quantum Go Fish* Dots and Boxes* Black Hole* Order and Chaos* Sequencium* Paper Boxing* Prophecies* Arpeggios* Banker* Francoprussian Labyrinth* Cats and Dogs* And many more.
The second edition of this bestselling book provides an overview of the key topics in undergraduate mathematics, allowing beginning graduate students to fill in any gaps in their knowledge. With numerous examples, exercises and suggestions for further reading, it is a must-have for anyone looking to learn some serious mathematics quickly.
"In MATH WITH BAD DRAWINGS, Ben Orlin answers math's three big questions: Why do I need to learn this? When am I ever going to use it? Why is it so hard? The answers come in various forms-cartoons, drawings, jokes, and the stories and insights of an empathetic teacher who believes that math should belong to everyone. Eschewing the tired old curriculum that begins in the wading pool of addition and subtraction and progresses to the shark infested waters of calculus (AKA the Great Weed Out Course), Orlin instead shows us how to think like a mathematician by teaching us a new game of Tic-Tac-Toe, how to understand an economic crisis by rolling a pair of dice, and the mathematical reason why you should never buy a second lottery ticket. Every example in the book is illustrated with his trademark "bad drawings
"A perennial bestseller by eminent mathematician G. Polya, How to Solve It will show anyone in any field how to think straight. In lucid and appealing prose, Polya reveals how the mathematical method of demonstrating a proof or finding an unknown can be of help in attacking any problem that can be "reasoned" out--from building a bridge to winning a game of anagrams. Generations of readers have relished Polya's deft--indeed
An outrageous graphic novel that investigates key concepts in mathematicsIntegers and permutations—two of the most basic mathematical objects—are born of different fields and analyzed with separate techniques. Yet when the Mathematical Sciences Investigation team of crack forensic mathematicians, led by Professor Gauss, begins its autopsies of the victims of two seemingly unrelated homicides, Arnie Integer and Daisy Permutation, they discover the most extraordinary similarities between the structures of each body.Prime Suspects is a graphic novel that takes you on a voyage of forensic discovery, exploring some of the most fundamental ideas in mathematics. Travel with Detective von Neumann as he leaves no clue unturned, from shepherds’ huts in the Pyrenees to secret societies in the cafés of Paris, from the hidden codes in the music of the stones to the grisly discoveries in Finite Fields. Tremble at the ferocity of the believers in deep and rigid abstraction. Feel the frustration—and the excitement—of our young heroine, Emmy Germain, as she blazes a trail for women in mathematical research and learns from Professor Gauss, the greatest forensic detective of them all.Beautifully drawn and exquisitely detailed, Prime Suspects is unique, astonishing, and witty—a once-in-a-lifetime opportunity to experience mathematics like never before.
Make trigonometry as easy as 1-2-3 Believe it or not, trigonometry is easier than it looks! With the right help, you can breeze through your next trig class, test, or exam and be ready for your next math challenge. In Trigonometry For Dummies, you’ll learn to understand the basics of sines, cosines, and tangents, graph functions, solve tough formulas, and even discover how to use trig outside the classroom in some cool and interesting ways. Ditch the confusing jargon and take a plain-English tour of one of the most useful disciplines in math. In this lifesaving guide, you’ll learn how to: Graph trig functions, including sine, cosine, tangent, and cotangent functions Understand inverse trig functions and solve trig equations Relate triangles to circular functions and get a handle on basic identities So, whether you’re looking for an easy-to-use study guide, to boost your math grade, or get a refresher on some basic trig concepts after a long absence from studying, Trigonometry For Dummies is your ticket to understanding the mathematical mysteries of the triangle.
The easy (okay, easier) way to master advanced calculus topics and theories Calculus II For Dummies will help you get through your (notoriously difficult) calc class—or pass a standardized test like the MCAT with flying colors. Calculus is required for many majors, but not everyone’s a natural at it. This friendly book breaks down tricky concepts in plain English, in a way that you can understand. Practical examples and detailed walkthroughs help you manage differentiation, integration, and everything in between. You’ll refresh your knowledge of algebra, pre-calc and Calculus I topics, then move on to the more advanced stuff, with plenty of problem-solving tips along the way. Review Algebra, Pre-Calculus, and Calculus I concepts Make sense of complicated processes and equations Get clear explanations of how to use trigonometry functions Walk through practice examples to master Calc II Use this essential resource as a supplement to your textbook or as refresher before taking a test—it’s packed with all the helpful knowledge you need to succeed in Calculus II.
Games are everywhere: Drivers manoeuvring in heavy traffic are playing a driving game. Bargain hunters bidding on eBay are playing an auctioning game. A firm negotiating next year's wage is playing a bargaining game. The opposing candidates in an election are playing a political game. The supermarket's price for corn flakes is decided by playing an economic game. Game theory is about how to play such games in a rational way. Even when the players have not thought everything out in advance, game theory often works for the same reason that mindless animals sometimes end up behaving very cleverly: evolutionary forces eliminate irrational play because it is unfit. Game theory has seen spectacular successes in evolutionary biology and economics, and is beginning to revolutionize other disciplines from psychology to political science. This Very Short Introduction introduces the fascinating world of game theory, showing how it can be understood without mathematical equations, and revealing that everything from how to play poker optimally to the sex ratio among bees can be understood by anyone willing to think seriously about the problem. ABOUT THE SERIES: The Very Short Introductions series from Oxford University Press contains hundreds of titles in almost every subject area. These pocket-sized books are the perfect way to get ahead in a new subject quickly. Our expert authors combine facts, analysis, perspective, new ideas, and enthusiasm to make interesting and challenging topics highly readable.
"By spinning 28 engaging mathematical tales, Orlin shows us that calculus is simply another language to express the very things we humans grapple with every day - love, risk, time and, most importantly, change. Divided into two parts, "Moments" and "Eternities
Calculus For Dummies, 2nd Edition (9781119293491) was previously published as Calculus For Dummies, 2nd Edition (9781118791295). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product.
"Baseball is not the only sport to use "moneyball." American football fans
Proofs play a central role in advanced mathematics and theoretical computer science, yet many students struggle the first time they take a course in which proofs play a significant role. This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs. Featuring over 150 new exercises and a new chapter on number theory, this new edition introduces students to the world of advanced mathematics through the mastery of proofs. The book begins with the basic concepts of logic and set theory to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for an analysis of techniques that can be used to build up complex proofs step by step, using detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions. Assuming no background beyond standard high school mathematics, this book will be useful to anyone interested in logic and proofs: computer scientists, philosophers, linguists, and, of course, mathematicians.
Absolutely everything you need to get ready for Algebra Scared of square roots? Suspicious of powers of ten? You’re not alone. Plenty of school-age students and adult learners don’t care for math. But, with the right guide, you can make math basics “click” for you too! In Basic Math & Pre-Algebra All-in-One For Dummies, you’ll find everything you need to be successful in your next math class and tackle basic math tasks in the real world. Whether you’re trying to get a handle on pre-algebra before moving to the next grade or looking to get more comfortable with everyday math—such as tipping calculations or balancing your checkbook—this book walks you through every step—in plain English, and with clear explanations—to help you build a firm foundation in math. You’ll also get: Practice quizzes at the end of each chapter to test your comprehension and understanding A bonus online quiz for each chapter, with answer choices presented in multiple choice format A ton of explanations, examples, and practice problems that prepare you to tackle more advanced algebraic concepts From the different categories of numbers to mathematical operations, fractions, percentages, roots and powers, and a short intro to algebraic expressions and equations, Basic Math & Pre-Algebra All-in-One For Dummies is an essential companion for anyone who wants to get a handle on the foundational math concepts that are the building blocks for Algebra and beyond.
In 1931 Kurt Godel published his fundamental paper, On Formally Undecidable Propositions of Principia Mathematica and Related Systems. This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. The authors provide an explanation of the main ideas and broad implications of Godel's discovery.
Complex Analysis is the powerful fusion of the complex numbers (involving the 'imaginary' square root of -1) with ordinary calculus, resulting in a tool that has been of central importance to science for more than 200 years. This book brings this majestic and powerful subject to life by consistently using geometry (not calculation) as the means of explanation. The 501 diagrams of the original edition embodied geometrical arguments that (for the first time) replaced the long and often opaque computations of the standard approach, in force for the previous 200 years, providing direct, intuitive, visual access to the underlying mathematical reality. This new 25th Anniversary Edition introduces brand-new captions that fully explain the geometrical reasoning, making it possible to read the work in an entirely new wayDLas a highbrow comic book!
The odds-on best way to master stats. Statistics All-in-One For Dummies is packed with lessons, examples, and practice problems to help you slay your stats course. Develop confidence and understanding in statistics with easy-to-understand (even fun) explanations of key concepts. Plus, you’ll get access to online chapter quizzes and other resources that will turn you into a stats master. This book teaches you how to interpret graphs, determine probability, critique data, and so much more. Written by an expert author and serious statistics nerd, Statistics AIO For Dummies explains everything in terms anyone can understand. Get a grasp of basic statistics concepts required in every statistics course Clear up the process of interpreting graphs, understanding polls, and analyzing data Master correlation, regression, and other data analysis tools Score higher on stats tests and get a better grade in your high school or college class Statistics All-in-One For Dummies follows the curriculum of intro college statistics courses (including AP Stats!) so you can learn everything you need to know to get the grade you need—the Dummies way.
This accessible introduction to sacred geometry illuminates the beauty and power of nature and explains how we can draw on this mystical energy to enrich our everyday lives Sacred geometry is founded on the belief that everything is connected through the shapes and symmetries that we see repeated in nature all around us, from snowflakes and shells to crystals and honeycombs. These beautiful patterns are part of the mystic architecture of the universe – some even see them as the signature of a deity woven throughout creation. This beginner’s guide clearly explains what sacred geometry is and how it manifests in the natural world. Then, by learning how to harness the power of sacred shapes, you can find healing, energy, peace and oneness with the universe. The Little Book of Sacred Geometry will help you appreciate the cosmic significance of these principles and grasp fascinating insights such as: How the study of sacred geometry has developed since ancient times What the numerous sacred shapes look like What key concepts, such as the golden ratio, refer to How sacred geometrical practices can be applied in your life
There is a logical flaw in the statistical methods used across experimental science. This fault is not a minor academic quibble: it underlies a reproducibility crisis now threatening entire disciplines. In an increasingly statistics-reliant society, this same deeply rooted error shapes decisions in medicine, law, and public policy with profound consequences. The foundation of the problem is a misunderstanding of probability and its role in making inferences from observations.Aubrey Clayton traces the history of how statistics went astray, beginning with the groundbreaking work of the seventeenth-century mathematician Jacob Bernoulli and winding through gambling, astronomy, and genetics. Clayton recounts the feuds among rival schools of statistics, exploring the surprisingly human problems that gave rise to the discipline and the all-too-human shortcomings that derailed it. He highlights how influential nineteenth- and twentieth-century figures developed a statistical methodology they claimed was purely objective in order to silence critics of their political agendas, including eugenics.Clayton provides a clear account of the mathematics and logic of probability, conveying complex concepts accessibly for readers interested in the statistical methods that frame our understanding of the world. He contends that we need to take a Bayesian approach—that is, to incorporate prior knowledge when reasoning with incomplete information—in order to resolve the crisis. Ranging across math, philosophy, and culture, Bernoulli’s Fallacy explains why something has gone wrong with how we use data—and how to fix it.
The Golden Ratio examines the presence of this divine number in art and architecture throughout history, as well as its ubiquity among plants, animals, and even the cosmos. This gorgeous book—with layflat dimensions that closely approximate the golden ratio—features clear, enlightening, and entertaining commentary alongside stunning full-color illustrations by Venezuelan artist and architect Rafael Araujo. From the pyramids of Giza, to quasicrystals, to the proportions of the human face, the golden ratio has an infinite capacity to generate shapes with exquisite properties. This book invites you to take a new look at this timeless topic, with a compilation of research and information worthy of a text book, accompanied by over 200 beautiful color illustrations that transform this into the ultimate coffee table book. Author Gary Meisner shares the results of his twenty-year investigation and collaboration with thousands of people across the globe in dozens of professions and walks of life. The evidence will close the gaps of understanding related to many claims of the golden ratio’s appearances and applications, and present new findings to take our knowledge further yet. Whoever you are, and whatever you may know about this topic, you’ll find something new, interesting, and informative in this book, and may find yourself challenged to see, apply, and share this unique number of mathematics and science in new ways.
Part history, part philosophy, part love letter to the study of mathematics, Everything and More is an illuminating tour of infinity. With his infectious curiosity and trademark verbal pyrotechnics, David Foster Wallace takes us from Aristotle to Newton, Leibniz, Karl Weierstrass, and finally Georg Cantor and his set theory. Through it all, Wallace proves to be an ideal guide—funny, wry, and unfailingly enthusiastic. Featuring an introduction by Neal Stephenson, this edition is a perfect introduction to the beauty of mathematics and the undeniable strangeness of the infinite.
Linear algebra is a fundamental area of mathematics, and arguably the most powerful mathematical tool ever developed. This dynamic and engaging book uses numerous examples, question and answer sections, and historical biographies to provide an introduction to linear algebra for undergraduates in mathematics, the physical sciences and engineering.