To miss out on mathematics is to live without experiencing some of humanity's most beautiful ideas.In this profound book, written for a wide audience but especially for those disenchanted by their past experiences, and award-winning mathematician and educator weaves parables, puzzles, and personal reflections to show how mathematics meets basic human desires - such as for play, beauty, freedom, justice, and love - and cultivates virtues essential for human flourishing.These desires and virtues, and the stories told here, reveal how mathematics is intimately tied to being human. Some lessons emerge from those who have struggled, including philosopher Simone Weil, whose own mathematical contributions were overshadowed by her brother's and Christopher Jackson, who discovered mathematics as an inmate in a federal prison.Christopher's letters to the author appear throughout the book and show how this intellectual pursuit can - and must - be open to all.PLEASE NOTE: If purchasing this title in the Audible version, the accompanying PDF will be available in your Audible Library along with the audio.RUNNING TIME ⇒ 6hrs. and 52mins.©2020 Francis Edward Su (P)2020 Tantor

     In our world today we hear a lot about self-love; a lot about embracing who you are now. But if you really love yourself and your body, you wouldn't act like you have a spare. It is never too late to love yourself enough to be healthy. WARNING IF YOU ARE SENSITIVE, DO NOT BUY THIS BOOK. It's not for you. This book is for people with thick skin who believe good health is more important than polite presentation. So if you care about getting healthy, staying fit, and doing it in a sustainable way - then consider this book your drill instructor (harsh language and all). ABOUT THE AUTHOR Alan Roberts is the founder of Every Damn Day Fitness and Co-Founder of the Damn Collective with his wife Crystal. Together, they have helped thousands of people increase the quality of their lives by coaching them to healthier habits, wisdom which they accrued through trial and error in their own lives. Originally from Pittsburgh, PA, Alan now resides in sunny, south west Florida.

    

    Switching from thin tailed to fat tailed distributions requires more than "changing the color of the dress." Traditional asymptotics deal mainly with either n=1 or n=∞, and the real world is in between, under the "laws of the medium numbers"-which vary widely across specific distributions. Both the law of large numbers and the generalized central limit mechanisms operate in highly idiosyncratic ways outside the standard Gaussian or Levy-Stable basins of convergence. A few examples: - The sample mean is rarely in line with the population mean, with effect on "na�ve empiricism," but can be sometimes be estimated via parametric methods. - The "empirical distribution" is rarely empirical. - Parameter uncertainty has compounding effects on statistical metrics. - Dimension reduction (principal components) fails. - Inequality estimators (Gini or quantile contributions) are not additive and produce wrong results. - Many "biases" found in psychology become entirely rational under more sophisticated probability distributions. - Most of the failures of financial economics, econometrics, and behavioral economics can be attributed to using the wrong distributions. This book, the first volume of the Technical Incerto, weaves a narrative around published journal articles.

    These topics are traditionally taught in disparate courses, making it hard for data science or computer science students, or professionals, to efficiently learn the mathematics. This self-contained textbook bridges the gap between mathematical and machine learning texts, introducing the mathematical concepts with a minimum of prerequisites. It uses these concepts to derive four central machine learning methods: linear regression, principal component analysis, Gaussian mixture models and support vector machines. For students and others with a mathematical background, these derivations provide a starting point to machine learning texts. For those learning the mathematics for the first time, the methods help build intuition and practical experience with applying mathematical concepts. Every chapter includes worked examples and exercises to test understanding. Programming tutorials are offered on the book's web site.

    They have the curiosity to notice relationships, the confidence to ask why, and the knowledge to understand the answer. They are the lucky ones. Many others just "do" maths. They look at a question, think about how to answer it, answer it, and then move on.In this book, Craig Barton, maths teacher and best-selling author of How I wish I'd taught maths, offers an approach to help all our students think mathematically. It requires the careful sequencing of questions and examples, the role of the teacher, and the mathematical behaviour of our students. It has transformed his teaching.Drawing upon research into the Self-Explanation Effect, the Hypercorrection Effect and Variation Theory, together with two years of developing this approach with teachers and students around the world, Craig describes exactly what this looks like in the classroom. But be warned: not everyone agrees. Indeed, it is this very approach that led to Craig being labelled as "the most dangerous and clueless man in maths education."If that is not a recommendation to keep reading, we don't know what is.

    I loved it." – Rory Sutherland, Ogilvy's Vice Chairman“So insightful with common sense applications of Complexity and the ability to communicate clearly!!” – Bob Klapetzky.“A SUPERB book […] by one of the profound thinkers in our field [behavioral economics].” – Michal G. BartlettWhat's ergodicity, and why it matters?"The Most Important Property to Understand in Probability, in Life, in Anything." – Nassim Nicholas Taleb on ergodicity."I think the most under-rated idea is ergodicity." – David Perell, author.Is ergodicity the most important concept in decision-making and behavioral sciences? (Yes.)Is it relevant for you in your daily life? (Yes.)Is it possible to explain it so simply that a grandma or a high-schooler can understand it? (Yes.)Even if they know nothing about maths? (Yes.)That's because ergodicity is an important idea with so many practical applications. Sadly, most books describe it in a very technical way, making it inaccessible to most people.In this short book, 6-times author Luca Dellanna describes ergodicity as simply as possible. You will read stories about how not knowing about it destroyed his cousin’s career as a skier, or how misunderstanding it caused additional deaths during the pandemic. You will learn how to spot situations in which ergodicity matters and the three strategies to react appropriately.Who is this book for?This book is for readers interested in growing themselves, their career, or their business, and who want to learn about ergodicity and its practical applications without having to understand its mathematical foundation. No mathematical knowledge is required, only a high-school level understanding of English.Readers who want to master the theory and mathematical foundation of ergodicity are better off reading a more formal manuscript. This book is not a substitute for it, but a complement.About the authorLuca Dellanna is the author of 6 books. He is a researcher in complexity science and emergent behaviors, and an operational excellence consultant. He spoke at Nudgestock and regularly teaches risk management in masters.His personal website is Luca-Dellanna.com and his Twitter is @DellAnnaLuca.

    This means that some students hardly talk at all. Yet, talking and writing about in-process and unfinished ideas are vital to learning mathematics. How can we meet this challenge? Amanda (Mandy) Jansen and her collaborating teachers have developed a breakthrough approach: expand the idea of 'rough drafts' to the mathematics classroom. In Rough Draft Math, Mandy shares the power of infusing math class with the spirit of revision so that students feel comfortable thinking aloud as they talk to learn through problem-solving rather than talking only to perform right answers. In the process, a class of students becomes a community of mathematical thinkers, and teachers gain access into their students’ ideas and understandings. Inside you’ll find the following:an exploration of what the idea of revision could mean for math teaching and learningclassroom vignettes to see rough draft math in actionspecific teaching techniques to encourage and practice rough draft thinkingvoices of teachers and students in rough draft classroomsMandy’s reflections about her own teaching as a work in progressIn Rough Draft Math, Mandy shows how to create a classroom culture in which your students will feel more comfortable expressing their partial understandings and in-process thinking, and then continually revising that thinking as they build deep, conceptual understanding of mathematics.

    

    Further digging leads Blum to Kay Westfield, a charming bank executive who once witnessed a bizarre explosion on Feldmann's experimental farm.As Blum and Westfield begin to unravel the labyrinth of funding behind the professor's research center, a picture emerges of a monstrous plot by a shadowy international think tank to infect millions of people.Meanwhile, Feldmann's assistant, a math prodigy with past ties to a violent, white-supremacist movement is busy optimizing the virus's distribution--fulfilling the Pangaea Solution.

    

    

    Real statistical problems, however, are complex and subtle. This is not a book about the theory of regression. It is about using regression to solve real problems of comparison, estimation, prediction, and causal inference. Unlike other books, it focuses on practical issues such as sample size and missing data and a wide range of goals and techniques. It jumps right in to methods and computer code you can use immediately. Real examples, real stories from the authors' experience demonstrate what regression can do and its limitations, with practical advice for understanding assumptions and implementing methods for experiments and observational studies. They make a smooth transition to logistic regression and GLM. The emphasis is on computation in R and Stan rather than derivations, with code available online. Graphics and presentation aid understanding of the models and model fitting.

    

    

    Most of what we see of the subject in school comes from these heavenly origins; 15th century astronomer Regiomontanus called it "the foot of the ladder to the stars."In this Very Short Introduction Glen Van Brummelen shows how trigonometry connects mathematics to science, and has today become an indispensable tool in predicting cyclic patterns like animal populations and ocean tides. Its historical journey through major cultures such as medieval India and the Islamic World has taken it through disciplines such as geography and even religious practice. Trigonometry has also been a major player in the most startling mathematical developments of the modern world. Its interactions with the concept of infinity led to Taylor and Fourier series, some of the most practical tools of modern science. The birth of complex numbers led to a shocking union of exponential and trigonometric functions, creating the most beautiful formulas and powerful modelling tools in science. Finally, as Van Brummelen shows, trigonometry allows us to explore the strange new worlds of non-Euclidean geometries, opening up bizarre possibilities for the shape of space itself. And indeed, one of those new geometries - spherical - takes us full circle back to ancient Greek astronomers and European navigators, who first used it to chart their ways across the heavens and the earth.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.

    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 eighth-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.

    After an introduction to functional programming languages, we present propositional logic, λ-calculus, the Curry-Howard correspondence, first-order logic, Agda, dependent types and homotopy type theory.

    A technical revolution has transformed the field, and extracting meaningful information from large biological data sets is now a central methodological challenge. Algebraic topology is a well-established branch of pure mathematics that studies qualitative descriptors of the shape of geometric objects. It aims to reduce comparisons of shape to a comparison of algebraic invariants, such as numbers, which are typically easier to work with. Topological data analysis is a rapidly developing subfield that leverages the tools of algebraic topology to provide robust multiscale analysis of data sets. This book introduces the central ideas and techniques of topological data analysis and its specific applications to biology, including the evolution of viruses, bacteria and humans, genomics of cancer, and single cell characterization of developmental processes. Bridging two disciplines, the book is for researchers and graduate students in genomics and evolutionary biology as well as mathematicians interested in applied topology.

    The author, a leading research mathematician, presents a series of engaging and compelling mathematical statements with interesting elementary proofs. These proofs capture a wide range of topics, including number theory, combinatorics, graph theory, the theory of games, geometry, infinity, order theory, and real analysis. The goal is to show students and aspiring mathematicians how to write proofs with elegance and precision.

    Nowadays, our lives are run by algorithms. They determine what news we see. They influence which products we buy. They suggest our dating partners. They may even be determining the outcome ofnational elections. They are creating, and destroying, entire industries. Despite mounting concerns, few know what algorithms are, how they work, or who created them.Poems that Solve Puzzles tells the story of algorithms from their ancient origins to the present day and beyond. The book introduces readers to the inventors and inspirational events behind the genesis of the world's most important algorithms. Professor Chris Bleakley recounts tales of ancient lostinscriptions, Victorian steam-driven contraptions, top secret military projects, penniless academics, hippy dreamers, tech billionaires, superhuman artificial intelligences, cryptocurrencies, and quantum computing. Along the way, the book explains, with the aid of clear examples and illustrations, how the most influential algorithms work.Compelling and impactful, Poems that Solve Puzzles tells the story of how algorithms came to revolutionise our world.

    Secure success2. Run routines3. Nudge norms4. Build belonging5. Boost buy-inPRAISE FOR THE HIGH IMPACT TEACHING SERIES"If you have a spare half-hour or so, you could read Memorable Teaching from cover to cover. I doubt you'll find an education book with more useful insights per minute of reading time." - Dylan Wiliam, Emeritus Professor of Educational Assessment, UCL"How to improve your teaching by planning better. Things that make teachers' lives simpler like that are few and far between." - Doug Lemov, Author of Teach Like a Champion"I can't remember when I have ever read a book that takes such complex ideas and communicates them with sophistication and simplicity." - Oliver Caviglioli, Founder and author of HOW2s"The book packs an awful lot of useful material into a short, easy to read format and as such is something that all teachers should add to their collections." - Josh Goodrich, Head of CPD at Oasis Southbank"A truly excellent book which sets out the science behind learning with remarkable clarity." - Mark Enser, Head of Geography at Heathfield Community College

    So goes the legend of the tricky knot of Gordius, king of Phrygia.Many had tried; many had failed, but Alexander the Great simplycut the knot with his sword. He went on to conquer most of Asia,eventually reaching as far east as Northern India.Cut the Knot is a book of probability riddles curated to challenge the mind andexpand mathematical and logical thinking skills. First housed on cut-the-knot.org,these puzzles and their solutions represent the efforts of great minds around theworld. Follow along as Alexander Bogomolny presents these selected riddles bytopical progression. Try them for yourself before reading their solutions. Just like itwas for Alexander the Great, the non-trivial, unexpected solution might be exactlythe one you need.

    James Stewart's Calculus series is the top-seller in the world because of its problem-solving focus, mathematical precision and accuracy, and outstanding examples and problem sets. Selected and mentored by Stewart, coauthors Daniel Clegg and Saleem Watson continue his legacy, and their careful refinements retain Stewart's clarity of exposition and make the 9th Edition an even more usable learning tool. The accompanying WebAssign includes helpful learning support and new resources like Explore It interactive learning modules. Showing that Calculus is both practical and beautiful, the Stewart approach and WebAssign resources enhance understanding and build confidence for millions of students worldwide.

    Games like Sudoku and Mastermind are fun and engrossing recreational activities, but they also share deep foundations in mathematical logic and are worthy of serious intellectual inquiry. Games for Your Mind explores the history and future of logic puzzles while enabling you to test your skill against a variety of puzzles yourself.In this informative and entertaining book, Jason Rosenhouse begins by introducing readers to logic and logic puzzles and goes on to reveal the rich history of these puzzles. He shows how Carroll's puzzles presented Aristotelian logic as a game for children, yet also informed his scholarly work on logic. He reveals how another pioneer of logic puzzles, Raymond Smullyan, drew on classic puzzles about liars and truthtellers to illustrate Kurt G�del's theorems and illuminate profound questions in mathematical logic. Rosenhouse then presents a new vision for the future of logic puzzles based on nonclassical logic, which is used today in computer science and automated reasoning to manipulate large and sometimes contradictory sets of data.Featuring a wealth of sample puzzles ranging from simple to extremely challenging, this lively and engaging book brings together many of the most ingenious puzzles ever devised, including the Hardest Logic Puzzle Ever, metapuzzles, paradoxes, and the logic puzzles in detective stories.

    But it is also completely mad. Although the theory quite obviously works, it leaves us chasing ghosts and phantoms; particles that are waves and waves that are particles; cats that are at once both alive and dead; lots of seemingly spooky goings-on; and a desperate desire to lie down quietly in a darkened room. The Quantum Cookbook explains why this is. It provides a unique bridge between popular exposition and formal textbook presentation, written for curious readers with some background in physics and sufficient mathematical capability. It aims not to teach readers how to do quantum mechanics but rather helps them to understand how to think about quantum mechanics. Each derivation is presented as a 'recipe' with listed ingredients, including standard results from the mathematician's toolkit, set out in a series of easy-to-follow steps. The recipes have been written sympathetically, for readers who - like the author - will often struggle to follow the logic of a derivation which misses out steps that are 'obvious', or which use techniques that readers are assumed to know.

    Many graduate students are familiar with the ideas of point-set topology and they are ready to learn something new about them. Teaching the subject using category theory--a contemporary branch of mathematics that provides a way to represent abstract concepts--both deepens students' understanding of elementary topology and lays a solid foundation for future work in advanced topics.After presenting the basics of both category theory and topology, the book covers the universal properties of familiar constructions and three main topological properties--connectedness, Hausdorff, and compactness. It presents a fine-grained approach to convergence of sequences and filters; explores categorical limits and colimits, with examples; looks in detail at adjunctions in topology, particularly in mapping spaces; and examines additional adjunctions, presenting ideas from homotopy theory, the fundamental groupoid, and the Seifert van Kampen theorem. End-of-chapter exercises allow students to apply what they have learned. The book expertly guides students of topology through the important transition from undergraduate student with a solid background in analysis or point-set topology to graduate student preparing to work on contemporary problems in mathematics.

    Interactive Data Visualization with Python sharpens your data exploration skills, tells you everything there is to know about interactive data visualization in Python.You'll begin by learning how to draw various plots with Matplotlib and Seaborn, the non-interactive data visualization libraries. You'll study different types of visualizations, compare them, and find out how to select a particular type of visualization to suit your requirements. After you get a hang of the various non-interactive visualization libraries, you'll learn the principles of intuitive and persuasive data visualization, and use Bokeh and Plotly to transform your visuals into strong stories. You'll also gain insight into how interactive data and model visualization can optimize the performance of a regression model.By the end of the course, you'll have a new skill set that'll make you the go-to person for transforming data visualizations into engaging and interesting stories.What you will learnExplore and apply different interactive data visualization techniques Manipulate plotting parameters and styles to create appealing plots Customize data visualization for different audiences Design data visualizations using interactive libraries Use Matplotlib, Seaborn, Altair and Bokeh for drawing appealing plots Customize data visualization for different scenarios Who this book is forThis book intends to provide a solid training ground for Python developers, data analysts and data scientists to enable them to present critical data insights in a way that best captures the user's attention and imagination. It serves as a simple step-by-step guide that demonstrates the different types and components of visualization, the principles, and techniques of effective interactivity, as well as common pitfalls to avoid when creating interactive data visualizations. Students should have an intermediate level of competency in writing Python code, as well as some familiarity with using libraries such as pandas.

    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 kindergarten-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.

    

    But, as Mage Merlin's Unsolved Mathematical Mysteries shows, mathematics is filled with intriguing mysteries that take us to the edge of the unknown. This richly illustrated, story-driven volume presents sixteen of today's greatest unsolved mathematical puzzles, all understandable by anyone with elementary math skills. These intriguing mysteries are presented to readers as puzzles that have time-traveled from Camelot, preserved in the notebook of Merlin, the wise magician in King Arthur's court.Our guide is Mage Maryam (named in honor of the brilliant young mathematician, the late Maryam Mirzakhani), a distant descendant of Merlin. Maryam introduces the mysteries--each of which is presented across two beautifully illustrated pages--and provides mathematical and historical context afterward. We find Merlin confronting mathematical puzzles involving tinker toys (a present for Camelot's princesses from the sorceress Morgana), cake-slicing at a festival, Lancelot's labyrinth, a vault for the Holy Grail, and more. Each mystery is a sword awaiting removal from its stone, capturing the beauty and power of mathematics.

    These books cover the basics of mathematics in a clear and simple format - the style Gelfand was known for internationally. Gelfand prepared these materials so as to be suitable for independent studies, thus allowing students to learn and practice the material at their own pace without a class.Geometry takes a different approach to presenting basic geometry for high-school students and others new to the subject. Rather than following the traditional axiomatic method that emphasizes formulae and logical deduction, it focuses on geometric constructions. Illustrations and problems are abundant throughout, and readers are encouraged to draw figures and "move" them in the plane, allowing them to develop and enhance their geometrical vision, imagination, and creativity. Chapters are structured so that only certain operations and the instruments to perform these operations are available for drawing objects and figures on the plane. This structure corresponds to presenting, sequentially, projective, affine, symplectic, and Euclidean geometries, all the while ensuring students have the necessary tools to follow along. Geometry is suitable for a large audience, which includes not only high school geometry students, but also teachers and anyone else interested in improving their geometrical vision and intuition, skills useful in many professions. Similarly, experienced mathematicians can appreciate the book's unique way of presenting plane geometry in a simple form while adhering to its depth and rigor. "Gelfand was a great mathematician and also a great teacher. The book provides an atypical view of geometry. Gelfand gets to the intuitive core of geometry, to the phenomena of shapes and how they move in the plane, leading us to a better understanding of what coordinate geometry and axiomatic geometry seek to describe." - Mark Saul, PhD, Executive Director, Julia Robinson Mathematics Festival"The subject matter is presented as intuitive, interesting and fun. No previous knowledge of the subject is required. Starting from the simplest concepts and by inculcating in the reader the use of visualization skills, [and] after reading the explanations and working through the examples, you will be able to confidently tackle the interesting problems posed. I highly recommend the book to any person interested in this fascinating branch of mathematics." - Ricardo Gorrin, a student of the Extended Gelfand Correspondence Program in Mathematics (EGCPM)

    He shows that the conceptual landscape includes not only the na�ve and iterative conceptions but also the limitation of size conception, the definite conception, the stratified conception and the graph conception. In addition, he presents a novel, minimalist account of the iterative conception which does not require the existence of a relation of metaphysical dependence between a set and its members. His book will be of interest to researchers and advanced students in logic and the philosophy of mathematics.

    From a clear explanation of Heawood’s disproof of Kempe’s argument to novel features like quadrilateral switching, this book by Chris McMullen, Ph.D., is packed with content. It even includes a novel handwaving argument explaining why the four-color theorem is true. What is the four-color theorem? Why is it common to work with graphs instead of maps? What are Kempe chains? What is the problem with Alfred Kempe’s attempted proof? How does Euler’s formula relate the numbers of faces, edges, and vertices? What are Kuratowski’s theorem and Wagner’s theorem? What is the motivation behind triangulation? What is quadrilateral switching? What is vertex splitting? What is the three-edges theorem? Is there an algorithm for four-coloring a map or graph? What is a Hamiltonian cycle? What is a separating triangle? How is the four-color theorem like an ill-conditioned logic puzzle? Why is the four-color theorem true? What makes the four-color theorem so difficult to prove by hand?

    The number of possible patterns that can be identified relative to the number that are genuinely useful has grownexponentially - which means that the chances that a discovered pattern is useful is rapidly approaching zero.Patterns in data are often used as evidence, but how can you tell if that evidence is worth believing? We are hard-wired to notice patterns and to think that the patterns we notice are meaningful. Streaks, clusters, and correlations are the norm, not the exception. Our challenge is to overcome ourinherited inclination to think that all patterns are significant, as in this age of Big Data patterns are inevitable and usually coincidental.Through countless examples, The Phantom Pattern Problem is an engaging read that helps us avoid being duped by data, tricked into worthless investing strategies, or scared out of getting vaccinations.

    

    What began as a modest proposal that a mathematician and an economist write a short paper together blossomed, when Princeton University Press published Theory of Games and Economic Behavior. In it, John von Neumann and Oskar Morgenstern conceived a groundbreaking mathematical theory of economic and social organization, based on a theory of games of strategy. Not only would this revolutionize economics, but the entirely new field of scientific inquiry it yielded--game theory--has since been widely used to analyze a host of real-world phenomena from arms races to optimal policy choices of presidential candidates, from vaccination policy to major league baseball salary negotiations. And it is today established throughout both the social sciences and a wide range of other sciences.

    Each page contains a distinct “cheat sheet,” which tells you the most important facts in bite-size chunks, so you can feel like an expert in minutes! From zero to Riemann Hypothesis, from primes to irrational numbers, and from Pythagoras to John Nash and Roger Penrose—every key figure, theory, or term is expressed in succinct and lively text and graphics. Perfect for the knowledge-hungry and time-poor, this collection of graphics-led lessons makes math interesting and accessible. Everything you need to know—and more!—packed into one convenient volume.

    WOODEN BOOKS US EDITIONS. Small books, BIG ideas. Tiny but packed with information. "Stunning" NEW YORK TIMES. "Fascinating" FINANCIAL TIMES. "Beautiful" LONDON REVIEW OF BOOKS. "Rich and Artful" THE LANCET. "Genuinely mind-expanding" FORTEAN TIMES. "Excellent" NEW SCIENTIST.

    245 CE–early 320s) on the Pythagoreans. He thought the Pythagoreans had treated mathematics as essential for drawing the human soul upwards to higher realms described by Plato, and downwards to understand the physical cosmos, the products of arts and crafts and the order required for an ethical life. His Pythagorean treatises use edited quotation to re-tell the history of philosophy, presenting Plato and Aristotle as passing on the ideas invented by Pythagoras and his early followers. Although his quotations tend to come instead from Plato and later Pythagoreanising Platonists, this re-interpretation had a huge impact on the Neoplatonist commentators in Athens. Iamblichus' cleverness, if not to the same extent his re-interpretation, was appreciated by the commentators in Alexandria.