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    These methods are effective in estimating click-through rates on ads, success rates of experiments, and other situations common in modern data science. You'll learn both the theory and the practice behind empirical Bayes, including computing credible intervals, performing Bayesian A/B testing, and fitting mixture models. Each example is accompanied with visualizations to demonstrate the mathematical concepts, as well as R code that can be adapted to analyze your own data.

    Essentially, you make an initial guess, and then get more data to improve it. Bayes Theorem, or Bayes Rule, has a ton of real world applications, from estimating your risk of a heart attack to making recommendations on Netflix But It Isn't That Complicated This book is a short introduction to Bayes Theorem. It is only 15 pages long, and is intended to show you how Bayes Theorem works as quickly as possible. The examples are intentionally kept simple to focus solely on Bayes Theorem without requiring that the reader know complicated probability distributions. If you want to learn the basics of Bayes Theorem as quickly as possible, with some easy to duplicate examples, this is a good book for you.

    They make web searches better, organize photos, and are even used in speech translation. Heck, they can even generate encryption. At the same time, they are also mysterious and mind-bending: how exactly do they accomplish these things ? What goes on inside a neural network? On a high level, a network learns just like we do, through trial and error. This is true regardless if the network is supervised, unsupervised, or semi-supervised. Once we dig a bit deeper though, we discover that a handful of mathematical functions play a major role in the trial and error process. It also becomes clear that a grasp of the underlying mathematics helps clarify how a network learns. In the following chapters we will unpack the mathematics that drive a neural network. To do this, we will use a feedforward network as our model and follow input as it moves through the network.

    Understanding why what you're doing works is the part that often stumps students and teachers alike. Does math feels like a collection of random rules and steps that somehow lead you to an answer? Don't worry, you're not alone. Ask yourself: why do we have odd and even numbers? Why do two negative numbers multiply to make a positive? Why do fraction operations work? What is cosine and where does it come from? Yes, but why? answers all of your questions, and sheds light on the hidden connections between everything in mathematics at school. Math makes sense. It always has, but until now maybe no-one ever showed you. A must-read for those training to teach primary or secondary mathematics via university-based (PGCE, BEd, BA w/QTS) or school-based (School Direct, SCITT, Teach First) routes and current teachers wishing to deepen their mathematical understanding.

    This extraordinary formula is the basis of eternal existence. It furnishes the building blocks of reality. It not only explains the pre-time, pre-space domain that produces the Big Bang universe, it also solves the intractable problem of Cartesian dualism by showing exactly how mind produces matter. As we demonstrate mathematically, Euler’s Formula is the true basis of Einstein’s special theory of relativity, and the all-important Lorentz transformations. Euler’s Formula reveals the exact difference between Einstein’s relativity and Lorentz’s relativity, and shows how they can be reconciled via a higher level of theory. Reality is nothing like what it seems. It is not religious, it is not philosophical, and it is not scientific. Do you want to know how deep the rabbit hole goes? Are you ready for the ride of your life? Are you ready to discover the true secrets of reality?

    What Is The Binomial Distribution? The binomial distribution is one of the key ideas in statistics.  It calculates the probability of getting a certain number of an outcome, for instance you can use it to calculate the probability of rolling five 6's out of 20 dice rolled.  The binomial distribution finds applications in things such as predicting outcomes from elections, in gambling, and even on the game "Plinko" on the television game show "The Price Is Right" How Is The Binomial Theorem Explained In This Book? This book walks through how the binomial distribution works in a step by step fashion, starting with some simple flips of a coin, and building up to examples that have uneven probability, and examples where you need to calculate the binomial coefficient over a range of numbers.  I.e.  to calculate the odds of winning at least 51 hands of blackjack out of 100 played.The first several examples are explained using Pascal's triangle, since it gives a good visualization of the probability of different binomial coefficients.  Later problems give examples using the binomial equation, since it is more versatile. Other Key Topics In This Book Multinomial Equation - If you need to calculate the probability distribution for more than two events, you need the multinomial distribution, not the binomial distribution The Normal Approximation - The binomial distribution is great, but sometimes you need an answer with less calculation.  This shows how to get a very good answer using the normal curve, provided you have a sufficient number of events

    Campbell, Mathematics Magazine How can a shape have more than one dimension but fewer than two? What is the best way to elect public officials when more than two candidates are vying for the office? Is it possible for a highly accurate medical test to give mostly incorrect results? Can you tile your floor with regular pentagons? How can you use only the first digit of sales numbers to determine if your accountant is lying? Can mathematics give insights into free will?   Edward Scheinerman, an accomplished mathematician and enthusiastic educator, answers all these questions and more in this book, a collection of mathematical masterworks. In bite-sized chapters that require only high school algebra, he invites readers to try their hands at solving mathematical puzzles and provides an engaging and friendly tour of numbers, shapes, and uncertainty. The result is an unforgettable introduction to the fundamentals and pleasures of thinking mathematically.

    Blending classic wisdom with over 100 pop culture references--music, television and film--Singh whimsically switches the lens in this book from the traditional society teaching math to a new and bold math teaching society. Written with charming buoyancy and intimacy, he takes us on an emotional and surprising journey through the deepest goldmine of mathematics--our personal happiness.--Dan Finkel, Founder of Math for Love, Creator of Prime Climb and Tiny Polka Dot, TEDx Speaker: Five Principles of Extraordinary Math Teaching

    Perhaps at school you liked mathematics for a while but were then put off because you missed a key idea and kept getting stuck. Perhaps you always liked mathematics but gave it up because your main interest was music or languages or science or philosophy. Or perhaps you studied mathematics to advanced levels, but have now forgotten most of what you once knew. Whichever is the case, this book isfor you. It aims to build on what you know, revisiting basic ideas with a focus on meaning. Each chapter starts with an idea from school mathematics - often primary school mathematics - and gradually builds up a network of links to more advanced material. It explores fundamental ideas in depth,using insights from research in mathematics education and psychology to explain why people often get confused, and how to overcome that confusion. For nervous readers, it will build confidence by clarifying basic ideas. For more experienced readers, it will highlight new connections to more advanced material. Throughout, the book explains how mathematicians think, and how ordinary people can understand and enjoy mathematical ideas and arguments. If you would like to be better informed aboutthe intrinsic elegance of mathematics, this engaging guide is the place to start.

    Cheese consumption, margarine and drowning by falling out of fishing boats. This book has got it all. A roller coaster of a book in 8 witty chapters, this might just be the most entertaining statistics book you’ll read this year. Did you know that pirates caused global warming, and that a statistical lie gave rise to one of the fastest growing religions on the planet? Probably not – you might have missed the memo that day. Did you also know that organic food is the real cause of autism, and that Mexican lemons are a major cause of deaths on American roads? They’re true, honest – and this book has got the stats to prove it. In this eye-opening book, award winning statistician and author Lee Baker uncovers the key tricks of the trade used by politicians, corporations and other statistical conmen to deceive, hoodwink and otherwise dupe the unwary. Like how the ex-Chancellor of the Exchequer attempted to persuade us that 5 lots of 10 make 150, or how the President of the United States tried to convince us that 420,000 is a larger number than 782,000. Nice try boys, but we were awake that day! In his trademark sardonic style, the author reveals the secrets of how the statistical hustlers manipulate and misrepresent data for political or commercial gain – and often get away with it. Written as a layman’s guide to lying, cheating and deceiving with data and statistics, there’s not a dull page in sight! Discover the exciting world of statistical cheating and persuasive misdirection. Get this book, TODAY!

    It consists of 169 pages. The language and method used in presenting the ideas and techniques of tensors make it very suitable as a textbook or as a reference for an introductory course on tensor algebra and calculus or as a guide for self-studying and learning. The book contains many exercises. The detailed solutions of all these exercises are available in another book by the author (Solutions of Exercises of Tensor Calculus Made Simple).

    The formulation and presentation are largely based on a tensor calculus approach. It can be used as part of a course on tensor calculus as well as a textbook or a reference for an intermediate-level course on differential geometry of curves and surfaces. The book is furnished with extensive sets of exercises and many cross references, which are hyperlinked, to facilitate linking related concepts and sections. The book also contains a considerable number of 2D and 3D graphic illustrations to help the readers and users to visualize the ideas and understand the abstract concepts. We also provided an introductory chapter where the main concepts and techniques needed to understand the offered materials of differential geometry are outlined to make the book fairly self-contained and reduce the need for external references.

    Its exposition reflects the most recent scholarship in mathematics and its history. Almost 500 sharp illustrations accompany elegant proofs, from prime decomposition through quadratic reciprocity. Geometric and dynamical arguments provide new insights, and allow for a rigorous approach with less algebraic manipulation. The final chapters contain an extended treatment of binary quadratic forms, using Conway's topograph to solve quadratic Diophantine equations (e.g., Pell's equation) and to study reduction and the finiteness of class numbers. Data visualizations introduce the reader to open questions and cutting-edge results in analytic number theory such as the Riemann hypothesis, boundedness of prime gaps, and the class number 1 problem. Accompanying each chapter, historical notes curate primary sources and secondary scholarship to trace the development of number theory within and outside the Western tradition. Requiring only high school algebra and geometry, this text is recommended for a first course in elementary number theory. It is also suitable for mathematicians seeking a fresh perspective on an ancient subject.

    The book is based upon the Singapore Primary Mathematics curriculum, as well as the International Math curriculum. More than twenty topics are covered and explained step by step through visual representation to convey mathematical concepts. It has been specially developed for: - Students who have been diagnosed with Dyscalculia; other terms may include Mathematics Learning Disability, or Mathematics Disorder - Students who have been diagnosed with Dyslexia; as according to research more than fifty percent of those experience difficulties with mathematics. Some students may have Dyslexia and Dyscalculia as co-existing disorders - Students diagnosed with ADHD; as they may struggle with mathematics. Some students may have ADHD and Dyscalculia as co-existing disorders. - Students who have difficulties in learning Mathematics - Slow learners - Teens/Adults who have severe Math Difficulties or Dyscalculia Students will gain more confidence in mathematics, become more independent and produce better results. This book will provide them with an opportunity to experience success and maintain a positive attitude towards math. It is suitable to be used in combination with Educational Therapy or remedial intervention in Math that students with dyscalculia or Math difficulties need. An assessment conducted by a psychologist is essential and early interventions are most effective.

    Instead, the twins enter the world of the Lily Maidens, an organization of women who travel through legends and time in pursuit of knowledge. But dark forces are uniting against the Kingdom; Merlin, the Black Pig, and a vast army of men and mythological beasts are marching for Camelot's gate. Only the magic of science, mathematics, and poetry can preserve honor's code and defend the Kingdom against the impending onslaught of evil.

    Unlike the previous book which is largely based on a Cartesian approach, the formulation in the present book is based on a general coordinate system. The book is furnished with an index as well as detailed sets of exercises to provide useful revision and practice. To facilitate linking related concepts and sections, cross referencing is used extensively throughout the book. The book also contains a number of graphic illustrations to help the readers to visualize the ideas and understand the subtle concepts. The book can be used as a text for an introductory or an intermediate level course on tensor calculus.

    SAME CONTENTS AS IN US EDITION - ISBN - 9788120353350 - Printed in Asia - - Note: It is Alternate Edition , Not US Edition and does NOT carry any CD or CODE unless specified above

    Short, engaging, interactive lessons that guide your young student to a solid understanding of addition and subtraction through 100.

    From predator-prey populations in an ecosystem, to hormone regulation within the body, the natural world abounds in dynamical systems that affect us profoundly. Complex feedback relations and counter-intuitive responses are common in nature; this book develops the quantitative skills needed to explore these interactions.Differential equations are the natural mathematical tool for quantifying change, and are the driving force throughout this book. The use of Euler’s method makes nonlinear examples tractable and accessible to a broad spectrum of early-stage undergraduates, thus providing a practical alternative to the procedural approach of a traditional Calculus curriculum. Tools are developed within numerous, relevant examples, with an emphasis on the construction, evaluation, and interpretation of mathematical models throughout. Encountering these concepts in context, students learn not only quantitative techniques, but how to bridge between biological and mathematical ways of thinking.Examples range broadly, exploring the dynamics of neurons and the immune system, through to population dynamics and the Google PageRank algorithm. Each scenario relies only on an interest in the natural world; no biological expertise is assumed of student or instructor. Building on a single prerequisite of Precalculus, the book suits a two-quarter sequence for first or second year undergraduates, and meets the mathematical requirements of medical school entry. The later material provides opportunities for more advanced students in both mathematics and life sciences to revisit theoretical knowledge in a rich, real-world framework. In all cases, the focus is clear: how does the math help us understand the science?

    Through fun activities and illustrations, This Book Thinks You're a Math Genius encourages young readers to engage with new ideas by experimenting and investigating for themselves.This Book Thinks You're a Math Genius explores seven key areas of math: geometry, space and volume, statistics, numbers and number patterns, codes and ciphers, and the concept of infinity. Each spread centers on an open-ended question that introduces a key mathematical concept and suggests activities that engage the child in a fun way. Activities include reading minds with math, having a eureka moment, and playing mathematical guess who. The end of the book includes a section of paper-based crafts.This creative approach, along with Russell's wonderfully humorous hand-drawn illustrations, make math fun and accessible for children.

    The exposition follows the historical development of the concepts of connection and curvature with the goal of explaining the Chern–Weil theory of characteristic classes on a principal bundle. Along the way we encounter some of the high points in the history of differential geometry, for example, Gauss' Theorema Egregium and the Gauss–Bonnet theorem. Exercises throughout the book test the reader’s understanding of the material and sometimes illustrate extensions of the theory. Initially, the prerequisites for the reader include a passing familiarity with manifolds. After the first chapter, it becomes necessary to understand and manipulate differential forms. A knowledge of de Rham cohomology is required for the last third of the text.Prerequisite material is contained in author's text An Introduction to Manifolds, and can be learned in one semester. For the benefit of the reader and to establish common notations, Appendix A recalls the basics of manifold theory. Additionally, in an attempt to make the exposition more self-contained, sections on algebraic constructions such as the tensor product and the exterior power are included.Differential geometry, as its name implies, is the study of geometry using differential calculus. It dates back to Newton and Leibniz in the seventeenth century, but it was not until the nineteenth century, with the work of Gauss on surfaces and Riemann on the curvature tensor, that differential geometry flourished and its modern foundation was laid. Over the past one hundred years, differential geometry has proven indispensable to an understanding of the physical world, in Einstein's general theory of relativity, in the theory of gravitation, in gauge theory, and now in string theory. Differential geometry is also useful in topology, several complex variables, algebraic geometry, complex manifolds, and dynamical systems, among other fields. The field has even found applications to group theory as in Gromov's work and to probability theory as in Diaconis's work. It is not too far-fetched to argue that differential geometry should be in every mathematician's arsenal.

    https://aeon.co/essays/consciousness-...The special trick of consciousness is being able to project action and time into a range of possible futures

    The first dips into the history of quantitative finance and explains its key principles, the second is about the quantitative finance industry today and how it is evolving. Finally, the book will conclude with what should happen, what needs to happen, to prevent future financial disaster.

    Plus along the way you'll discover how social media trends work, why the universe has a favourite number and what this means for you. Mathematics is inescapable. Wherever you go, whatever you do, however you live your life, mathematics plays an important role. From controlling a city’s traffic to finding love, spending money online to building a skyscraper, the mathematics at play in our world is fascinating. Yet despite its ubiquity, for many of us, how the maths of today really works remains complex. ​Mathematician Timothy Revell distills these complexities in this essential guide to modern-day mathematics, exploring questions such as; Could we solve queuing with an equation?  How do algorithms control our news?  What is the secret behind encryption codes?

    

    

    Built around the central framework of the General Linear Model (GLM), Statistics for the Social Sciences teaches students how different statistical methods are interrelated to one another. With the GLM as a basis, students with varying levels of background are better equipped to interpret statistics and learn more advanced methods in their later courses. Russell T. Warne makes statistics relevant to students' varying majors by using fascinating real-life examples from the social sciences. Students who use this book will benefit from clear explanations, warnings against common erroneous beliefs about statistics, and the latest developments in the philosophy, reporting and practice of statistics in the social sciences. The textbook is packed with helpful pedagogical features including learning goals, guided practice and reflection questions.

    But don't statistics lie?Well, no--people lie, and sometimes they use statistical language to do it. Knowing when you're being hoodwinked requires a degree of statistical literacy, but most people don't learn how to interpret statistical claims unless they take a formal course that trains them in the mathematical techniques of statistical analysis.This book won't turn you into a statistician--that would require a much longer and more technical discussion--but it will give you the tools to understand statistical claims and avoid common pitfalls associated with translating statistical information from the language of mathematics to plain English.

    

    Unlike many of the traditional academic works on the topic, this book was written for practitioners. Accordingly, it especially addresses: the construction of finite difference schemes, formulation and implementation of algorithms, verification of implementations, analyses of physical behavior as implied by the numerical solutions, and how to apply the methods and software to solve problems in the fields of physics and biology.

    It is intended to be the first in an occasional series of volumes of CMI lectures. Although not explicitly linked, the topics inthis inaugural volume have a common flavour and a common appeal to all who are interested in recent developments in geometry. They are intended to be accessible to all who work in this general area, regardless of their own particular research interests.

    Except for a small number of exercises inthe first few sections, we provide solutions of the (228) odd-numbered problemsappearing in first part of the book (Topology). The primary targets of this manual are thestudents of topology. This set is not disjoint from the set of instructors of topologycourses, who may also find this manual useful as a source of examples, exam problems, etc.

    

    She recalls conversations, collaborations and even arguments shared with many great scientists, including her experiences with Albert Einstein. She also describes some of her numerous trips around the world, spurred by a passion for travel, beauty and mathematics. At once reflective, enlightening and bittersweet, this book allows readers a look into the life and thought processes of an esteemed female academic.Contents: PrologueAncestorsGood Daddy, Aunt Mary, Mame and TontonMy ParentsChildhood and AdolescenceYouth 1940–1944Disaster 1944–1946Life in MontaigneA New Life, AmericaMarseille 1953–1955Transitions 1957–1964First Years in Antony 1965–1968After the Reform 1968–1979Academician 1979Life Continues 1979–1990Retirement 1990–2003A I'I.H.E.S 2003–?Far Away TravelsOur House in DammartinEpilogueReadership: The general public, academics and students with a specific interest in the life of Yvonne Choquet–Bruhat and/or a general interest in the life of an accomplished mathematician and theoretical physicist. Keywords: Autobiography;Yvonne Choquet-Bruhat;Mathematics;Physics;General Relativity;Einstein;Field Equations;Research;TravelReview:0

    For most students, in addition to learning new material about real numbers, topology, and sequences, they are also learning to read and write rigorous proofs for the first time. The Real Analysis Lifesaver is an innovative guide that helps students through their first real analysis course while giving them the solid foundation they need for further study in proof-based math.Rather than presenting polished proofs with no explanation of how they were devised, The Real Analysis Lifesaver takes a two-step approach, first showing students how to work backwards to solve the crux of the problem, then showing them how to write it up formally. It takes the time to provide plenty of examples as well as guided fill in the blanks exercises to solidify understanding.Newcomers to real analysis can feel like they are drowning in new symbols, concepts, and an entirely new way of thinking about math. Inspired by the popular Calculus Lifesaver, this book is refreshingly straightforward and full of clear explanations, pictures, and humor. It is the lifesaver that every drowning student needs.The essential "lifesaver" companion for any course in real analysisClear, humorous, and easy-to-read styleTeaches students not just what the proofs are, but how to do them--in more than 40 worked-out examplesEvery new definition is accompanied by examples and important clarificationsFeatures more than 20 "fill in the blanks" exercises to help internalize proof techniquesTried and tested in the classroom

    The Handbook has been developed, improved and refined over more than a half decade in a research university setting and is used in an accredited PhD level training program. The contents of this book have provided the analytical foundation to hundreds of students, many of whom have become full time bioinformaticians and work at the most innovative companies in the world.

    Distilled into 1001 bite-sized mini-essays arranged thematically, this unique reference book moves steadily from the basics through to the most advanced of ideas, making it the ideal guide for novices and mathematics enthusiasts. Whether used as a handy reference, an informal self-study course or simply as a gratifying dip-in, this book offers - in one volume - a world of mathematical knowledge for the general reader. Maths 1001 is an incredibly comprehensive guide, spanning all of the key mathematical fields including Numbers, Geometry, Algebra, Analysis, Discrete Mathematics, Logic and the Philosophy of Maths, Applied Mathematics, Statistics and Probability and Puzzles and Mathematical Games. From zero and infinity to relativity and Godel's proof that maths is incomplete, Dr Richard Elwes explains the key concepts of mathematics in the simplest language with a minimum of jargon. Along the way he reveals mathematical secrets such as how to count to 1023 using just 10 fingers and how to make an unbreakable code, as well as answering such questions as: Are imaginary numbers real? How can something be both true and false? Why is it impossible to draw an accurate map of the world? And how do you get your head round the mind-bending Monty Hall problem? Extensive, enlightening and entertaining, this really is the only maths book anyone would ever need to buy.

    It focuses, for example, on Australians' love of sports and gambling, and on Melbourne's iconic, mathematically inspired architecture. Written in a playful and humorous style, the book offers mathematical entertainment as well as a glimpse of Australian culture for the mathematically curious of all ages. This collection of engaging stories was extracted from the Maths Masters column that ran from 2007 to 2014 in Australia's Age newspaper. The maths masters in question are Burkard Polster and Marty Ross, two (immigrant) Aussie mathematicians, who each week would write about math in the news, providing a new look at old favorites, mathematical history, quirks of school mathematics—whatever took their fancy. All articles were written for a very general audience, with the intention of being as inviting as possible and assuming a minimum of mathematical background.

    DLs have recently gained increased importance since they form the logical basis of widely used ontology languages, in particular the web ontology language OWL. Written by four renowned experts, this is the first textbook on description logics. It is suitable for self-study by graduates and as the basis for a university course. Starting from a basic DL, the book introduces the reader to their syntax, semantics, reasoning problems and model theory and discusses the computational complexity of these reasoning problems and algorithms to solve them. It then explores a variety of reasoning techniques, knowledge-based applications and tools and it describes the relationship between DLs and OWL.

    That's where The Probability Lifesaver steps in. Designed to serve as a complete stand-alone introduction to the subject or as a supplement for a course, this accessible and user-friendly study guide helps students comfortably navigate probability's terrain and achieve positive results.The Probability Lifesaver is based on a successful course that Steven Miller has taught at Brown University, Mount Holyoke College, and Williams College. With a relaxed and informal style, Miller presents the math with thorough reviews of prerequisite materials, worked-out problems of varying difficulty, and proofs. He explores a topic first to build intuition, and only after that does he dive into technical details. Coverage of topics is comprehensive, and materials are repeated for reinforcement—both in the guide and on the book's website. An appendix goes over proof techniques, and video lectures of the course are available online. Students using this book should have some familiarity with algebra and precalculus.The Probability Lifesaver not only enables students to survive probability but also to achieve mastery of the subject for use in future courses. A helpful introduction to probability or a perfect supplement for a course Numerous worked-out examples Lectures based on the chapters are available free online Intuition of problems emphasized first, then technical proofs given Appendixes review proof techniques Relaxed, conversational approach

    And the math isn't complex. A twelfth grader could understand it. Yet, the output is more comprehensive than the most complex modern algorithm.For your reading pleasure, the mathematics that support this model are explained in a pleasant, pain-free way, paired with a classroom story.

    Spock? Solve these challenging conundrums and prove it! Mr. Spock is famed throughout the galaxy for his mental prowess and ability to think clearly and unemotionally. Now you can pit yourself against his “highly logical” way of reasoning with this officially licensed puzzle book. The half-human, half-Vulcan has come up with a range of fascinating and highly challenging conundrums that gives solvers a unique opportunity to “mind-meld” with the renowned character!

    Using classical concepts such as Gibbs measures, pressure, free energy, and entropy, the book exposes the main features of the classical description of large systems in equilibrium, in particular the central problem of phase transitions. It treats such important topics as the Peierls argument, the Dobrushin uniqueness, Mermin-Wagner and Lee-Yang theorems, and develops from scratch such workhorses as correlation inequalities, the cluster expansion, Pirogov-Sinai Theory, and reflection positivity. Written as a self-contained course for advanced undergraduate or beginning graduate students, the detailed explanations, large collection of exercises (with solutions), and appendix of mathematical results and concepts also make it a handy reference for researchers in related areas.

    A familiar way of introducing concepts in mathematics rests on so-called definitions by abstraction. An example of this is Hume's Principle, which introduces the concept of number by stating that two concepts have the same number if and only if the objects falling under each one of them can be put in one-one correspondence. This principle is at the core of neo-logicism.In the first two chapters of the book, Mancosu provides a historical analysis of the mathematical uses and foundational discussion of definitions by abstraction up to Frege, Peano, and Russell. Chapter one shows that abstraction principles were quite widespread in the mathematical practice thatpreceded Frege's discussion of them and the second chapter provides the first contextual analysis of Frege's discussion of abstraction principles in section 64 of the Grundlagen. In the second part of the book, Mancosu discusses a novel approach to measuring the size of infinite sets known as thetheory of numerosities and shows how this new development leads to deep mathematical, historical, and philosophical problems. The final chapter of the book explore how this theory of numerosities can be exploited to provide surprisingly novel perspectives on neo-logicism.

    It is unique in its presentation of Shannon's measure of information, and the clear distinction between this concept and the thermodynamic entropy.

    Explore the many pitfalls that non-statisticians—and also statisticians who present statistical reports to non-statisticians—must avoid if statistical results are to be correctly used for evidence-based business decision making.Victoria Cox, senior statistician at the United Kingdom’s Defence Science and Technology Laboratory (Dstl), distills the lessons of her long experience presenting the actionable results of complex statistical studies to users of widely varying statistical sophistication across many disciplines.The author shows how faulty statistical reasoning often undermines the utility of statistical results even among those with advanced technical training. Translating Statistics teaches statistically naive readers enough about statistical questions, methods, models, assumptions, and statements that they will be able to extract the practical message from statistical reports and better constrain what conclusions cannot be made from the results. To non-statisticians with some statistical training, this book offers brush-ups, reminders, and tips for the proper use of statistics and solutions to common errors. To fellow statisticians, the author demonstrates how to present statistical output to non-statisticians to ensure that the statistical results are correctly understood and properly applied to real-world tasks and decisions. The book avoids algebra and proofs, but it does supply code written in R for those readers who are motivated to work out examples.Pointing along the way to instructive examples of statistics gone awry, Translating Statistics walks readers through the typical course of a statistical study, progressing from the experimental design stage through the data collection process, exploratory data analysis, descriptive statistics, uncertainty, hypothesis testing, statistical modelling and multivariate methods, to graphs suitable for final presentation. The steady focus throughout the book is on how to turn the mathematical artefacts and specialist jargon that are second nature to statisticians into plain English for corporate customers and stakeholders. The final chapter neatly summarizes the book’s lessons and insights for accurately communicating statistical reports to the non-statisticians who commission and act on them.Readers will: • Recognize and avoid common errors and misconceptions that cause statistical studies to be misinterpreted and misused by non-statisticians in organizational settings. • Gain a practical understanding of the methods, processes, capabilities, and caveats of statistical studies to improve the application of statistical data to business decisions. • See how to code statistical solutions in R.