We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket. Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down‑to‑earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real‑world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous. Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS. As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

      Statistics are everywhere, as integral to science as they are to business, and in the popular media hundreds of times a day. In this age of big data, a basic grasp of statistical literacy is more important than ever if we want to separate the fact from the fiction, the ostentatious embellishments from the raw evidence -- and even more so if we hope to participate in the future, rather than being simple bystanders. In The Art of Statistics, world-renowned statistician David Spiegelhalter shows readers how to derive knowledge from raw data by focusing on the concepts and connections behind the math. Drawing on real world examples to introduce complex issues, he shows us how statistics can help us determine the luckiest passenger on the Titanic, whether a notorious serial killer could have been caught earlier, and if screening for ovarian cancer is beneficial. The Art of Statistics not only shows us how mathematicians have used statistical science to solve these problems -- it teaches us how we too can think like statisticians. We learn how to clarify our questions, assumptions, and expectations when approaching a problem, and -- perhaps even more importantly -- we learn how to responsibly interpret the answers we receive. Combining the incomparable insight of an expert with the playful enthusiasm of an aficionado, The Art of Statistics is the definitive guide to stats that every modern person needs.

    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.

    By spinning 28 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," and drawing on everyone from Sherlock Holmes to Mark Twain to David Foster Wallace, Change is the Only Constant unearths connections between calculus, art, literature, and a beloved dog named Elvis. This is not just math for math's sake; it's math for the sake of becoming a wiser and more thoughtful human.

    But many people use data in ways they don't even understand, meaning they aren't getting the most from it. Bayesian Statistics the Fun Way will change that.This book will give you a complete understanding of Bayesian statistics through simple explanations and un-boring examples. Find out the probability of UFOs landing in your garden, how likely Han Solo is to survive a flight through an asteroid shower, how to win an argument about conspiracy theories, and whether a burglary really was a burglary, to name a few examples.By using these off-the-beaten-track examples, the author actually makes learning statistics fun. And you'll learn real skills, like how to:- How to measure your own level of uncertainty in a conclusion or belief- Calculate Bayes theorem and understand what it's useful for- Find the posterior, likelihood, and prior to check the accuracy of your conclusions- Calculate distributions to see the range of your data- Compare hypotheses and draw reliable conclusions from themNext time you find yourself with a sheaf of survey results and no idea what to do with them, turn to Bayesian Statistics the Fun Way to get the most value from your data.

    Most educators also agree that success at higher levels of math hinges on this fundamental skill. But what's the best way to get there? Are flash cards, drills, and timed tests the answer? If so, then why do students go into the upper elementary grades (and beyond) still counting on their fingers or experiencing math anxiety? What does research say about teaching basic math facts so they will stick?In Math Fact Fluency, experts Jennifer Bay-Williams and Gina Kling provide the answers to these questions--and so much more. This book offers everything a teacher needs to teach, assess, and communicate with parents about basic math fact instruction, includingThe five fundamentals of fact fluency, which provide a research-based framework for effective instruction in the basic facts.Strategies students can use to find facts that are not yet committed to memory.More than 40 easy-to-make, easy-to-use games that provide engaging fact practice.More than 20 assessment tools that provide useful data on fact fluency and mastery.Suggestions and strategies for collaborating with families to help their children master the basic math facts.Math Fact Fluency is an indispensable guide for any educator who needs to teach basic math facts.

    Take a journey through the fascinating story of fractions, numbers, patterns, and shapes in order to better understand the complex world we live in.Continuing the "Big Ideas" series' trademark combination of authoritative, clear text and bold graphics to chart the development of maths through history, the book explores and explains some of the most complex and fascinating mathematical subjects. Delve into everything from the mathematical ideas and inventions of the ancient world such as the first number systems, magic squares, and the Chinese abacus, through to the developments in mathematics during medieval and Renaissance Europe, to the rise of group theory and cryptography more recently.This diverse and inclusive account of mathematics will have something for everybody: for those interested in the maths behind world economies, secret spies, modern technology and plenty more, taking readers around the world from Babylon to Bletchley Park. Tracing maths through the Scientific Revolution to its 21st-century use in computers, the internet, and AI, The Maths Book uses an innovative visual approach to make the subject accessible to everyone, casual readers and students alike.

    Each chapter solves an otherwise unremarkable equation in distinct historical, formal, and imaginative styles that range from Medieval, Topological, and Doggerel to Chromatic, Electrostatic, and Psychedelic. With a rare blend of humor and scholarly aplomb, Philip Ording weaves these variations into an accessible and wide-ranging narrative on the nature and practice of mathematics.Inspired by the experiments of the Paris-based writing group known as the Oulipo--whose members included Raymond Queneau, Italo Calvino, and Marcel Duchamp--Ording explores new ways to examine the aesthetic possibilities of mathematical activity. 99 Variations on a Proof is a mathematical take on Queneau's Exercises in Style, a collection of 99 retellings of the same story, and it draws unexpected connections to everything from mysticism and technology to architecture and sign language. Through diagrams, found material, and other imagery, Ording illustrates the flexibility and creative potential of mathematics despite its reputation for precision and rigor.Readers will gain not only a bird's-eye view of the discipline and its major branches but also new insights into its historical, philosophical, and cultural nuances. Readers, no matter their level of expertise, will discover in these proofs and accompanying commentary surprising new aspects of the mathematical landscape.

      The worlds of visual art and mathematics come together in this spectacular volume by award-winning writer Stephen Ornes. He explores the growing sensation of math art, presenting more than 80 pieces, including a crocheted, colorful representation of non-Euclidian geometry that looks like sea coral and a 65-ton, 28-foot-tall bronze sculpture covered in a space-filling curve. For each work, we get the artist’s story followed by accessible and thought-provoking explanations of the mathematical concept and equations behind the art. From 3D-printed objects that give real form to abstract mathematical theories, to mystic fractals, to Andy Warhol as a solution to the Traveling Salesman Problem, these artworks embody some of strangest, most beautiful relationships among numbers and across dimensions.

    

    This textbook brings together machine learning, engineering mathematics, and mathematical physics to integrate modeling and control of dynamical systems with modern methods in data science. It highlights many of the recent advances in scientific computing that enable data-driven methods to be applied to a diverse range of complex systems, such as turbulence, the brain, climate, epidemiology, finance, robotics, and autonomy. Aimed at advanced undergraduate and beginning graduate students in the engineering and physical sciences, the text presents a range of topics and methods from introductory to state of the art.

    . . like a pendulum? These may not look like math questions, but they are-because they all have to do with patterns. And mathematics, at heart, is the study of patterns. That realization changed Eddie Woo's life-by turning the "dry" subject he dreaded in high school into a boundless quest for discovery. Now an award-winning math teacher, Woo sees patterns everywhere: in the "branches" of blood vessels and lightning, in the growth of a savings account and a sunflower, even in his morning cup of tea! Here are twenty-six bite-size chapters on the hidden mathematical marvels that encrypt our email, enchant our senses, and even keep us alive-from the sine waves we hear as "music" to the mysterious golden ratio. This book will change your mind about what math can be. We are all born mathematicians-and It's a Numberful World.

    

    One or more pages will remind you of a friend, spouse, relative, or your dog, and most will remind you of how ridiculous we all are.

    In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the sixth-grade level through visualization, play, and investigation.During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message--that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

     Part I makes key concepts in statistics readily clear. Parts I and II give an overview of the most common tests (t-test, ANOVA, correlations) and work out their statistical principles. Part III provides insight into meta-statistics (statistics of statistics) and demonstrates why experiments often do not replicate. Finally, the textbook shows how complex statistics can be avoided by using clever experimental design.  Both non-scientists and students in Biology, Biomedicine and Engineering will benefit from the book by learning the statistical basis of scientific claims and by discovering ways to evaluate the quality of scientific reports in academic journals and news outlets.

    Inside, you’ll find:Inspirational stories of students debating math in real classroomsConcrete structures and routines that will get your students talking, listening, and debatingSpecific techniques you can use to transform existing math problems into debatable onesYou'll begin with short speaking and listening routines that take just a few minutes to introduce. When you and your students are ready, you can layer on additional debate routines, until your class is engaged in full-class debates using mathematical reasoning. With this easy-to-read guide, you don't need to wait any longer. You will be able to start debating in your classroom, tomorrow.

    First posed by the ancient Greeks, these compass and straightedge problems--squaring the circle, trisecting an angle, doubling the cube, and inscribing regular polygons in a circle--have served as ever-present muses for mathematicians for more than two millennia. David Richeson follows the trail of these problems to show that ultimately their proofs--which demonstrated the impossibility of solving them using only a compass and straightedge--depended on and resulted in the growth of mathematics.Richeson investigates how celebrated luminaries, including Euclid, Archimedes, Vi�te, Descartes, Newton, and Gauss, labored to understand these problems and how many major mathematical discoveries were related to their explorations. Although the problems were based in geometry, their resolutions were not, and had to wait until the nineteenth century, when mathematicians had developed the theory of real and complex numbers, analytic geometry, algebra, and calculus. Pierre Wantzel, a little-known mathematician, and Ferdinand von Lindemann, through his work on pi, finally determined the problems were impossible to solve. Along the way, Richeson provides entertaining anecdotes connected to the problems, such as how the Indiana state legislature passed a bill setting an incorrect value for pi and how Leonardo da Vinci made elegant contributions in his own study of these problems.Taking readers from the classical period to the present, Tales of Impossibility chronicles how four unsolvable problems have captivated mathematical thinking for centuries.

    This book covers not only the standard topics but also some more advanced numerical methods being used by computational scientists and engineers--topics such as compression, forward and backward error analysis, and iterative methods of solving equations--all while maintaining a level of discussion appropriate for undergraduates. Each chapter contains a Reality Check, which is an extended exploration of relevant application areas that can launch individual or team projects. MATLAB(R) is used throughout to demonstrate and implement numerical methods. The Second Edition features many noteworthy improvements based on feedback from users, such as new coverage of Cholesky factorization, GMRES methods, and nonlinear PDEs.

    Many people learning math ask “Why is math so hard for me while everyone else understand it?” and “Am I good enough to succeed in math?” In answering these questions the book shares personal stories from many now-accomplished mathematicians affirming that “You are not alone; math is hard for everyone” and “yes; you are good enough.” Along the way the book addresses other issues such as biases and prejudices that mathematicians encounter, and it provides inspiration and emotional support for mathematicians ranging from the experienced professor to the struggling mathematics student.” —Michael Dorff, MAA President“This book is a remarkable collection of personal reflections on what it means to be, and to become, a mathematician. Each story reveals a unique and refreshing understanding of the barriers erected by our cultural focus on “math is hard”. Indeed, mathematics is hard, and so are many other things - as Stephen Kennedy points out in his cogent introduction. This collection of essays offers inspiration to students of mathemtics and to mathematicians at every career stage.” —Jill Pipher, AMS President

    This changes who we are as people and what we can achieve. Many people grow up being told they are ‘not a maths person’ or perhaps ‘not smart’. They come to believe their potential is limited.Now, however, the latest science has revealed that our identities are constantly in flux; when we learn new things, we can change our identities, increase our potential and broaden our capacity to receive new information.Drawing from the latest research, Professor Boaler followed thousands of school students, studied their learning practices and examined the most effective ways to transform pupils from low to high achievers. Throughout her study, Boaler has collaborated with Stanford University neuroscience experts, harnessing their expertise to reinforce her advanced understanding of learning and educational development.In Limitless Mind, Boaler presents original groundbreaking research that proves that limiting beliefs really do hold us back from fulfilling our potential and that with a few careful life hacks we can transform our potential for good.

    Not many of those same people are excited at the prospect of learning applied statistics to better inform their choices. You can't entirely blame them. Statistics has a well-earned reputation for being somewhat inaccessible by non-academics. It is a field filled with heavy terminology, confusing formulaic notation and concepts not fully relevant to the beginning sports bettor. To make matters worse, nobody in possession of a positive edge model is all that keen to show you how it works. As a result of this, sports modelling successfully requires a toolbox that you largely have to assemble for yourself. This book is my attempt to correct that, as I pull back the curtain on Excel spreadsheet models and techniques I developed in my first few years of sports betting. It is designed to give you an accessible crash course on modelling that will get you up to speed on the key relevant principles of statistics with a minimum amount of heavy technical jargon. You'll learn the most effective concepts in an easy-to-understand way and greatly speed up your learning curve in the process. Best of all, I'll walk you through sports betting models for many major sports: NFL, NBA, NHL, AFL and the English Premier League. You'll even be able to download these spreadsheet models and work your way through them while following this book. We'll be doing all of this in one of the most user friendly programs available: Excel. This program might not be the expert's first choice of platform for modelling work, but you'll be surprised just how much you can do with a spreadsheet or two. If you're ready to take your sports modelling to the next level - open this book, fire up Excel, and let's get to work. See you on the inside.

    This readable yet rigorous textbook contains a complete course in the linear algebra and related mathematics that students need to know to get to grips with learning from data. Included are: the four fundamental subspaces, singular value decompositions, special marices, large matrix computation techniques, compressed sensing, probability and statistics, optimization, the architecture of neural nets, stochastic gradient descent and backpropagation.

    It can be used for high school students who hate Physics and Maths and want to get it over with, up to graduate students applying for PhDs. The book covers every single point of student life, from the basics of study to advanced techniques for desperate exam situations. This book takes a holistic approach to your study. That is, not only the proper, special study techniques of Physics and Maths are discussed, but also every other element of student life. To name a few: procrastination, sleep, habits, exam preparation, group works, projects, presentations, scientific writing, and, importantly, a vast section dedicated to your career choices. It ranges from which university to choose, to the purpose of your career, and where you can find meaning and thence happiness.This book aims to give you all the advice possible to master Physics and Maths and score excellent marks, whether in high school or at university. Benoît Seron studied Applied Mathematics at Cambridge University. Before that, he studied five years in Belgium as a Theoretical Physicist, with the best grades of his class every year. He is now a PhD student at the University of Bruxelles.

    Logitica specifically teaches how to approach different types of mathematical problems in a logical manner and presents the concepts in an interesting, fun and unique way. The book has been provided with 200+ problems spread across 7 chapters. An ideal gift for 9+ year olds. An unique book on 3-step approach on logic building: Challenge, Strategy, Answer. Whether your child’s future includes developing the next big app or video game, designing robots or embarking on a professional career in almost any field, they will need highly developed logical and analytical thinking. Why not start now with LOGITICA: The Brain Behind the Brain?Chapter-1: Number Box... Arithmetic Operations, Binary Operators, ReasoningChapter-2: Number Cross....Arithmetic Operations, Binary Operators, ReasoningChapter-3: Marbles in a box….Linear EquationsChapter-4: Average Cell....Linear Equations, Arithmetic Mean.Chapter-5: Wisgo Number Tile....Stimulating the left and right sides of the brain.Chapter-6: Number Pyramid.... Linear Equations, pyramidChapter-7: Advanced Number Pyramid....Pascal's Triangle. Coefficient Rule Author: Neelabh Kumar is the creator of Logitica. Having memorized the first 1500 digits of Pi (π) using sequential recollection, he is ranked among the top 150 on the Pi World Ranking List.  He is the creator behind Wisgo Logitica, which stimulates both sides of the brain. One of the Wisgo Logiticas Kumar created has a patent filing in Hong Kong. After earning a Masters Degree from one of the most prestigious universities in India (IIT), Kumar is now employed in Hong Kong at a large financial firm, while also creating and designing a new Logitica, with more to come.

    David Bressoud explains why calculus is credited to seventeenth-century figures Isaac Newton and Gottfried Leibniz, and how its current structure is based on developments that arose in the nineteenth century. Bressoud argues that a pedagogy informed by the historical development of calculus represents a sounder way for students to learn this fascinating area of mathematics.Delving into calculus's birth in the Hellenistic Eastern Mediterranean--particularly in Syracuse, Sicily and Alexandria, Egypt--as well as India and the Islamic Middle East, Bressoud considers how calculus developed in response to essential questions emerging from engineering and astronomy. He looks at how Newton and Leibniz built their work on a flurry of activity that occurred throughout Europe, and how Italian philosophers such as Galileo Galilei played a particularly important role. In describing calculus's evolution, Bressoud reveals problems with the standard ordering of its curriculum: limits, differentiation, integration, and series. He contends that the historical order--integration as accumulation, then differentiation as ratios of change, series as sequences of partial sums, and finally limits as they arise from the algebra of inequalities--makes more sense in the classroom environment.Exploring the motivations behind calculus's discovery, Calculus Reordered highlights how this essential tool of mathematics came to be.

    In this volume, you'll find a collection of low floor, high ceiling tasks that will help you do just that, by looking at the big ideas at the seventh-grade level through visualization, play, and investigation.During their work with tens of thousands of teachers, authors Jo Boaler, Jen Munson, and Cathy Williams heard the same message--that they want to incorporate more brain science into their math instruction, but they need guidance in the techniques that work best to get across the concepts they needed to teach. So the authors designed Mindset Mathematics around the principle of active student engagement, with tasks that reflect the latest brain science on learning. Open, creative, and visual math tasks have been shown to improve student test scores, and more importantly change their relationship with mathematics and start believing in their own potential. The tasks in Mindset Mathematics reflect the lessons from brain science that:There is no such thing as a math person - anyone can learn mathematics to high levels. Mistakes, struggle and challenge are the most important times for brain growth. Speed is unimportant in mathematics. Mathematics is a visual and beautiful subject, and our brains want to think visually about mathematics. With engaging questions, open-ended tasks, and four-color visuals that will help kids get excited about mathematics, Mindset Mathematics is organized around nine big ideas which emphasize the connections within the Common Core State Standards (CCSS) and can be used with any current curriculum.

    It explores ideas at the brink of paradox: infinities of different sizes, time travel, probability and measure theory, computability theory, the Grandfather Paradox, Newcomb's Problem, the Principle of Countable Additivity. The goal is to present some exceptionally beautiful ideas in enough detail to enable readers to understand the ideas themselves (rather than watered-down approximations), but without supplying so much detail that they abandon the effort. The philosophical content requires a mind attuned to subtlety; the most demanding of the mathematical ideas require familiarity with college-level mathematics or mathematical proof.The book covers Cantor's revolutionary thinking about infinity, which leads to the result that some infinities are bigger than others; time travel and free will, decision theory, probability, and the Banach-Tarski Theorem, which states that it is possible to decompose a ball into a finite number of pieces and reassemble the pieces so as to get two balls that are each the same size as the original. Its investigation of computability theory leads to a proof of G�del's Incompleteness Theorem, which yields the amazing result that arithmetic is so complex that no computer could be programmed to output every arithmetical truth and no falsehood. Each chapter is followed by an appendix with answers to exercises. A list of recommended reading points readers to more advanced discussions. The book is based on a popular course (and MOOC) taught by the author at MIT.

    While the rules governing dynamical systems are well-specified and simple, the behavior of many dynamical systems is remarkably complex. Of particular note, simple deterministic dynamical systems produce output that appears random and for which long-term prediction is impossible. Using little math beyond basic algebra, David Feldman gives readers a grounded, concrete, and concise overview.In initial chapters, Feldman introduces iterated functions and differential equations. He then surveys the key concepts and results to emerge from dynamical systems: chaos and the butterfly effect, deterministic randomness, bifurcations, universality, phase space, and strange attractors. Throughout, Feldman examines possible scientific implications of these phenomena for the study of complex systems, highlighting the relationships between simplicity and complexity, order and disorder.Filling the gap between popular accounts of dynamical systems and chaos and textbooks aimed at physicists and mathematicians, Chaos and Dynamical Systems will be highly useful not only to students at the undergraduate and advanced levels, but also to researchers in the natural, social, and biological sciences.

    It is one of today's most important branches of mathematics and computer science--and also a surprisingly rich medium for creating breathtaking works of art. Opt Art takes readers on an entertaining tour of linear optimization and its applications, showing along the way how it can be used to design visual art.Robert Bosch provides a lively and accessible introduction to the geometric, algebraic, and algorithmic foundations of optimization. He presents classical applications, such as the legendary Traveling Salesman Problem, and shows how to adapt them to make optimization art--opt art. Each chapter in this marvelously illustrated book begins with a problem or puzzle and demonstrates how the solution can be derived using a host of artistic methods and media, including 3D printing, laser cutting, and computer-controlled machining. Bosch focuses on mathematical modeling throughout--converting a problem into a workable mathematical form, solving it using optimization techniques, and examining the results, which can take the form of mosaics, line drawings, and even sculpture. All you need is some high-school algebra, geometry, and calculus to follow along.Featuring more than a hundred illustrations and photos of Bosch's own art, Opt Art demonstrates how mathematics and computing can be used to create beauty and express emotion through amazing works of art.

     Trapped on a burning island. And much more besides . . . Everything is at stake in this compendium of more than 150 ingenious puzzles, selected to reveal the wonderful diversity of brainteasers that have confounded and intrigued solvers for the last thousand years. You'll need to pit your wits against probability problems, wrestle with wordplay, grapple with geometry and scrabble for survival.Along the way you will discover stories of whip-smart thinkers, eccentric novelists and a poodle with allegedly supernatural powers. You will absorb fascinating and important mathematical ideas. Some solutions will rely on ingenuity, some will challenge you to spot hidden patterns, others call for extreme rationality. All will surprise, entertain and stretch your brain. Will you make it out with your puzzling pride intact?

    This engaging and refreshingly different guide breaks down the skills into clear step-by-step chunks and explains the theory using brief easy-to-understand language. Rather than bamboozling readers with pages of mind-numbing technical jargon, this book includes 150 practical challenges, putting the power in the reader's hands. Through creating programs to solve these challenges the reader will quickly progress from mastering the basics to confidently using subroutines, a graphical user interface, and linking to external text, csv and SQL files. This book is perfect for anyone who wants to learn how to program with Python. In particular, students starting out in computer science and teachers who want to improve their confidence in Python will find here a set of ready-made challenges for classroom use.

    Wittgenstein pulled off the greatest hoax in philosophical history. By sheer force of personality, he managed to get all the philosopher dweebs to swallow his brilliantly contrived joke to expose the idiocy and gullibility of modern philosophers. Wittgenstein wrote, "My propositions serve as elucidations in the following way: anyone who understands me eventually recognizes them as nonsensical... The right method of philosophy would be this: To say nothing except what can be said, i.e. the propositions of natural science, i.e. something that has nothing to do with philosophy..." Being the comedic genius he was – the finest humorist of his era – Wittgenstein stayed in character as an idiot savant all his adult life and never once revealed his ingenious joke to his credulous target audience. They say that Stanislavsky regarded Wittgenstein as the consummate actor and based his “method” on how brilliantly Wittgenstein, a member of the super-rich elite, pulled off his lifelong act as a shambling, incoherent fan of cowboy movies and musicals, pretending to be a serious, world-historic philosopher, and completely fooling British toffs such as Bertrand Arthur William Russell, 3rd Earl Russell. In the movie "Being There", the character of "Chance", played by Peter Sellers, was inspired by Wittgenstein. Wittgenstein’s biggest fan was Andy Kaufman, the notorious prankster and comedian who tried never to tell a joke - as his homage to the great Austrian straight man. Kaufman wanted to pull off a ruse as big as Wittgenstein’s, resulting in many people believing Kaufman faked his own death as his grandest hoax. Like Wittgenstein, Kaufman was eager to provoke negative and confused reactions from audiences, leaving them in a state of bafflement and disorientation. One rumor was that Kaufmann styled his persona as the obnoxiously rude lounge singer Tony Clifton on Wittgenstein. At one point, Kaufmann considered basing the villain he played in his professional wrestling act on Wittgenstein so that he could insult his audience in German, using cryptic Wittgensteinian utterances. At the last moment, he chose to wrestle women and posture as the “Inter-Gender Wrestling Champion of the World”. His shows were especially appealing to philosophers. It would be easy to imagine Wittgenstein writing a treatise on it, entitled “Transgressing the Boundaries: Towards a Transformative Hermeneutics of Postmodern Wrestling in the light of Hyperreal Language Games.” Actually, we’re only joking. Sadly, Wittgenstein wasn’t. His Tractatus is one of the most pernicious texts in modern philosophy. It amounts to an attempt to assassinate philosophy. All serious philosophers – philosophers in the grand tradition – need to arm themselves against the irrationalism preached by modern philosophy. It’s time to see through the con. It’s time for the rebirth of grand philosophy. This time, it will be centered on the ontology of mathematics, the language of reality. The reign of manmade language - which does nothing but falsify reality - is over. The time for the second and final Enlightenment has come: the Age of Mathematical Rationalism.

    One goal of the book is to present these fascinating mathematical problems in a new and engaging way and illustrate the connections between integrals, sums, and series, many of which involve zeta functions, harmonic series, polylogarithms, and various other special functions and constants. Throughout the book, the reader will find both classical and new problems, with numerous original problems and solutions coming from the personal research of the author. Where classical problems are concerned, such as those given in Olympiads or proposed by famous mathematicians like Ramanujan, the author has come up with new, surprising or unconventional ways of obtaining the desired results. The book begins with a lively foreword by renowned author Paul Nahin and is accessible to those with a good knowledge of calculus from undergraduate students to researchers, and will appeal to all mathematical puzzlers who love a good integral or series.

    Walk in the shoes of teachers as they engage in the countless micro-decisions required to balance strategies, tasks, and assessments, demonstrating that it's not only what works, but when. A decision-making matrix and grade-leveled examples help you leverage the most effective teaching practices at the most effective time to meet the surface, deep, and transfer learning needs of every student.

    Simply choose from the hundreds of great ideas in this book and get going, with no extra time wasted! From activities on addition and subtraction to fractions and decimals, Classroom-Ready Number Talks for Kindergarten, First and Second Grade Teachers includes: Grade-level specific strategies Number talk how-tos Visual and numerical examples Scaffolding suggestions Common core alignments Questions to build understanding Reduce time spent lesson planning and preparing materials and enjoy more time engaging your students in learning important math concepts! These ready-to-use number talks are sure to foster a fresh and exciting learning environment in your classroom, as well as help your students increase their comprehension of numbers and mathematical principles.

    The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.

    It's the science of the future that proves the shocking truth that the world is not material but a collective dream, that so-called “matter” is an illusion, and the ultimate reality is a domain of pure mind. This is not a belief but a deductive, mathematical certainty. Ontological Mathematics was originally leaked to the public via a controversial hidden society operating under various pseudonyms. Since then, it has taken the world by storm. Ontological mathematics isn’t any one person’s idea. It’s a new way of thinking that is championed by the greatest thinkers of the age. Nearly 100 books have been written about it by various authors and independent ontological mathematics research groups are appearing around the world. Ontological mathematics and Hyperianism is a global phenomenon. We have made the groundbreaking knowledge of our system available to all by introducing the reader to the foundational concepts of ontological mathematics in an accessible way. This text assumes the reader has only minimal philosophical knowledge, and it is written in such a way that anyone can begin learning the mathematics of our system. Imagine living in a time and place where the Earth is believed to be flat and humans created by a god. Now imagine you discover a book containing many astounding facts of science such as the spheroidal shape of the Earth and evolution. How exciting would that be? As you read the book, your entire perspective of reality would change. Your world would never be the same. This is such a book. You currently exist in a time and place where existence is viewed as material. This book reveals that the world is in fact a shared dream. Ontological mathematics is the study of the mathematical wave nature of existence. This is not a reality of matter, rather, it’s a reality mind, of thought. And what is thought? Thoughts are mathematical sinusoidal waves. So ontological mathematics is the study of the mathematical waveforms of mind that make up all of existence and your very being. The spacetime world isn’t a material reality at all. It’s the Holos, which is a mathematical Fourier projection from a frequency singularity known as the Source. When properly understood and integrated, the information within this text will change your existence forever and elevate you to a new level of consciousness. This is the science of the future that one day soon will be taught in every school throughout the world. You are a Mind. Existence is Thought. The World is a Dream. The Science of the Future is Here.

    

    With important practical applications to computer science and industry, computational complexity theory has evolved into a highly interdisciplinary field, with strong links to most mathematical areas and to a growing number of scientific endeavors.Avi Wigderson takes a sweeping survey of complexity theory, emphasizing the field’s insights and challenges. He explains the ideas and motivations leading to key models, notions, and results. In particular, he looks at algorithms and complexity, computations and proofs, randomness and interaction, quantum and arithmetic computation, and cryptography and learning, all as parts of a cohesive whole with numerous cross-influences. Wigderson illustrates the immense breadth of the field, its beauty and richness, and its diverse and growing interactions with other areas of mathematics. He ends with a comprehensive look at the theory of computation, its methodology and aspirations, and the unique and fundamental ways in which it has shaped and will further shape science, technology, and society. For further reading, an extensive bibliography is provided for all topics covered.Mathematics and Computation is useful for undergraduate and graduate students in mathematics, computer science, and related fields, as well as researchers and teachers in these fields. Many parts require little background, and serve as an invitation to newcomers seeking an introduction to the theory of computation. Comprehensive coverage of computational complexity theory, and beyond High-level, intuitive exposition, which brings conceptual clarity to this central and dynamic scientific discipline Historical accounts of the evolution and motivations of central concepts and models A broad view of the theory of computation's influence on science, technology, and society Extensive bibliography

    This book presents computer programming as a key method for solving mathematical problems. This second edition of the well-received book has been extensively revised: All code is now written in Python version 3.6 (no longer version 2.7). In addition, the two first chapters of the previous edition have been extended and split up into five new chapters, thus expanding the introduction to programming from 50 to 150 pages. Throughout the book, the explanations provided are now more detailed, previous examples have been modified, and new sections, examples and exercises have been added. Also, a number of small errors have been corrected. The book was inspired by the Springer book TCSE 6: A Primer on Scientific Programming with Python (by Langtangen), but the style employed is more accessible and concise, in keeping with the needs of engineering students. The book outlines the shortest possible path from no previous experience with programming to a set of skills that allows students to write simple programs for solving common mathematical problems with numerical methods in the context of engineering and science courses. The emphasis is on generic algorithms, clean program design, the use of functions, and automatic tests for verification.

    Norman Matloff is a professor of computer science at the University of California, Davis, and was formerly a statistics professor there. He is on the editorial boards of the Journal of Statistical Software and The R Journal. His book Statistical Regression and Classification: From Linear Models to Machine Learning was the recipient of the Ziegel Award for the best book reviewed in Technometrics in 2017. He is a recipient of his university's Distinguished Teaching Award.

    At its heart is a method of statistical inference in which Bayes' theorem is used to update the probability for a hypothesis as more evidence or information becomes available. It is an approach that is ideally suited to making initial assessments based on incomplete or imperfect information; as that information is gathered and disseminated, the Bayesian approach corrects or replaces the assumptions and alters its decision-making accordingly to generate a new set of probabilities. As new data/evidence becomes available the probability for a particular hypothesis can therefore be steadily refined and revised. It is very well-suited to the scientific method in general and is widely used across the social, biological, medical, and physical sciences. Key to this book's novel and informal perspective is its unique pedagogy, a question and answer approach that utilizes accessible language, humor, plentiful illustrations, and frequent reference to on-line resources.Bayesian Statistics for Beginners is an introductory textbook suitable for senior undergraduate and graduate students, professional researchers, and practitioners seeking to improve their understanding of the Bayesian statistical techniques they routinely use for data analysis in the life and medical sciences, psychology, public health, business, and other fields.

     Filled with lots of helpful graphics and more than 200 exercises and mini-projects, this book unlocks the door to interesting-and lucrative!-careers in some of today's hottest programming fields. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications.

    It has been written in a teach yourself style strictly following a student-friendly approach, and is essentially meant to serve as a tutor at home.

    Advanced Calculus Explored helps build a stronger, more intuitive understanding of calculus that will serve the reader in advanced mathematics and science courses.Learn the tools you need for success.Read this book and unlock the benefits today!

      Why is a rainbow curved? Why aren’t left-handers extinct? How is a sunflower like a synchronized swimmer? Why is e a magic number?   The answer to these questions and more is contained within one simple word: math. Because math is all about patterns, and our universe is extraordinarily patterned.   With enthusiasm, humor, and heart, Eddie Woo shows how card tricks, conspiracy theories, teacups, killer butterflies, music, lightning, and so much more illuminate the spellbinding world of numbers that surrounds us.

    In addition, all the proofwriting skills that are essential for advanced study in mathematics are covered and reviewed extensively. Set Theory for Beginners is perfect for professors teaching an undergraduate course or basic graduate course in set theory high school teachers working with advanced math students students wishing to see the type of mathematics they would be exposed to as a math major. The material in this pure math book includes: 16 lessons consisting of basic to intermediate topics in set theory and mathematical logic. A problem set after each lesson arranged by difficulty level. A complete solution guide is included as a downloadable PDF file. Set Theory Book Table Of Contents (Selected) Here's a selection from the table of contents:Introduction Lesson 1 - SetsLesson 2 - SubsetsLesson 3 - Operations on SetsLesson 4 - RelationsLesson 5 - Equivalence Relations and PartitionsLesson 6 - FunctionsLesson 7 - EquinumerosityLesson 8 - Induction and Recursion on NLesson 9 - Propositional LogicLesson 10 - First-order LogicLesson 11 - Axiomatic Set TheoryLesson 12 - OrdinalsLesson 13 - CardinalsLesson 14 - Martin's AxiomLesson 15 - The Field of Real NumbersLesson 16 - Clubs and Stationary Sets

    This book is a perfect gift for your kids (secondary school and beyond) for improving their Cognitive abilities. Read further below to know the real benefits of reading each chapters in Logitica. Logitica created by an author, who memorized first 1500 digits of Pi (π) and now is ranked among the top 150 on the Pi World Ranking List. LOGITICA stimulates brainpower and can be considered "The Brain Behind the Brain."Pages: 300+ pages.Improve your critical thinking and problem solving skills by tackling a wide variety of problems that LOGITICA presents.This book contains 13 unique chapters as listed below: Chapter 1: Number Box...... Logic, ReasoningChapter 2: Number Cross...... Logic, ReasoningChapter 3: Number Sequence....... Logic, ReasoningChapter 4: Marbles in a Box....... Simple EquationsChapter 5: Brick Wall....... Simple EquationsChapter 6: Average Cell....... Simple Equations, Arithmetic MeanChapter 7: Mixed Arithmetic Cell....... Simple EquationsChapter 8: Wisgo Number Tile....... Logic, Stimulating both sides of the brainChapter 9: Number Pyramid....... Pascal's Triangle, Simple EquationsChapter 10: Average Number Pyramid....... Pascal's Triangle, Arithmetic MeanChapter 11: I/O Arithmetic Box....... Reverse Step, Logic/MathChapter 12: Lost Ant....... Vector / Scalar, Quadratic EquationsChapter 13: Lock and Key....... Logic, Strategy, Worst-Case ScenarioAbout AuthorNeelabh Kumar is a thinker.- Having memorized the first 1500 digits of Pi (π) using sequential memory recollection, he is ranked among the top 150 on the Pi World Ranking List. - Creator behind Wisgo Logitica, which stimulates both sides of the brain.- One of the Wisgo Logiticas Kumar created has a patent filing in Hong Kong.- Creator of Logitica- After earning a Masters Degree from one of the most prestigious universities in India (IIT), Kumar is now employed in Hong Kong at a large financial firm, while also creating and designing a new Logitica, with more to come.KEYWORDS Problem Solving, Logic, Analytical Thinking, Critical Thinking, ReasoningPreface In today's competitive environment everyone must strive to reach his or her full potential if they want success. Students and professionals alike can do this by working to improve their brainpower. If you plan on developing the next big app or embarking on a professional career in almost any field, you will need highly developed logical and analytical thinking skills. Why not start with LOGITICA: The Brain Behind the Brain?

    This introduction focuses purely on modern classical field theory, helping graduates and researchers build an understanding of classical field theory methods before embarking on future studies in quantum field theory. It describes various classical methods for fields with negligible quantum effects, for instance electromagnetism and gravitational fields. It focuses on solutions that take advantage of classical field theory methods as opposed to applications or geometric properties. Other fields covered includes fermionic fields, scalar fields and Chern-Simons fields. Methods such as symmetries, global and local methods, Noether theorem and energy momentum tensor are also discussed, as well as important solutions of the classical equations, in particular soliton solutions.

    Why do computers use so much energy? What are the fundamental physical laws governing the relationship between the precise computation run by a system, whether artificial or natural, and how much energy that computation requires? Can we learn how to improve efficiency in computing by examining how biological computers manage to be so efficient? The time is ripe for a new synthesis of nonequilibrium physics, computer science, and biochemistry.This volume integrates pure and applied concepts from these diverse fields, with the goal of cultivating a modern, nonequilibrium thermodynamics of computation.

    This textbook covers the discrete mathematics that every computer science student needs to learn. Guiding students quickly through thirty-one short chapters that discuss one major topic each, this flexible book can be tailored to fit the syllabi for a variety of courses.Proven in the classroom, Essential Discrete Mathematics for Computer Science aims to teach mathematical reasoning as well as concepts and skills by stressing the art of proof. It is fully illustrated in color, and each chapter includes a concise summary as well as a set of exercises. The text requires only precalculus, and where calculus is needed, a quick summary of the basic facts is provided.Essential Discrete Mathematics for Computer Science is the ideal introductory textbook for standard undergraduate courses, and is also suitable for high school courses, distance education for adult learners, and self-study.The essential introduction to discrete mathematicsFeatures thirty-one short chapters, each suitable for a single class lessonIncludes more than 300 exercisesAlmost every formula and theorem proved in fullBreadth of content makes the book adaptable to a variety of coursesEach chapter includes a concise summarySolutions manual available to instructors

    

    It assumes a background in neither general relativity nor statistical mechanics. The full lecture notes come in around 170 pages. Please do email me if you find any typos or mistakes.

     Spanning 4,000 years of civilisation, The Story of Mathematics describes twenty-four great equations that have shaped science and society – from the elementary (1+1=2) to the sophisticated (the Black-Scholes formula) and from the famous (E=mc2) to the arcane (Hamilton’s quaternion equations). This is a tale of genius, drama and beauty brought vividly to life in a compelling narrative by Dana Mackenzie and at the same time he tells us why these equations have something timeless to say about the universe.

    The book was written specifically for biologists with little or no prior experience of writing code - with the goal of giving them not only a foundation in Python programming, but also the confidence and inspiration to start using Python in their own research.Virtually all of the examples in the book are drawn from across a wide spectrum of life science research, from simple biochemical calculations and sequence analysis, to modeling the dynamic interactions of genes and proteins in cells, or the drift of genes in an evolving population.Best of all, Python for the Life Sciences shows you how to implement all of these projects in Python, one of the most popular programming languages for scientific computing. If you are a life scientist interested in learning Python to jump-start your research, this is the book for you.What You'll Learn Write Python scripts to automate your lab calculationsSearch for important motifs in genome sequencesUse object-oriented programming with PythonStudy mining interaction network data for patternsReview dynamic modeling of biochemical switchesWho This Book Is ForLife scientists with little or no programming experience, including undergraduate and graduate students, postdoctoral researchers in academia and industry, medical professionals, and teachers/lecturers. "A comprehensive introduction to using Python for computational biology... A lovely book with humor and perspective" -- John Novembre, Associate Professor of Human Genetics, University of Chicago and MacArthur Fellow "Fun, entertaining, witty and darn useful. A magical portal to the big data revolution" -- Sandro Santagata, Assistant Professor in Pathology, Harvard Medical School "Alex and Gordon's enthusiasm for Python is contagious" -- Glenys Thomson Professor of Integrative Biology, University of California, Berkeley

    

    Inside, you'll get basic content review for every concept, paired with examples and plenty of practice problems, ample workspace, step-by-step solutions, and thorough explanations for each and every problem.In Pre-Calculus Workbook For Dummies, you'll also get free access to a quiz for every chapter online! With all of the lessons and practice offered, you'll memorize the most frequently used formulas, see how to avoid common mistakes, understand tricky trig proofs, and get the inside scoop on key concepts such as quadratic equations.Get ample review before jumping into a calculus course Supplement your classroom work with easy-to-follow guidance Make complex formulas and concepts more approachable Be prepared to further your mathematics studies Whether you're enrolled in a pre-calculus class or you're looking for a refresher as you prepare for a calculus course, this is the perfect study companion to make it easier.