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The Art of More: How Mathematics Created Civilization
by Michael BrooksAn illuminating, millennia-spanning history of the impact mathematics has had on the world, and the fascinating people who have mastered its inherent power, from Babylonian tax officials to the Apollo astronauts to the eccentric professor who invented the infrastructure of the online worldCounting is not innate to our nature, and without education humans can rarely count past three—beyond that, it&’s just &“more.&” But once harnessed by our ancestors, the power of numbers allowed humanity to flourish in ways that continue to lead to discoveries and enrich our lives today. Ancient tax collectors used basic numeracy to fuel the growth of early civilization, navigators used clever geometrical tricks to engage in trade and connect people across vast distances, astronomers used logarithms to unlock the secrets of the heavens, and their descendants put them to use to land us on the moon. In every case, mathematics has proved to be a greatly underappreciated engine of human progress. In this captivating, sweeping history, Michael Brooks acts as our guide through the ages. He makes the case that mathematics was one of the foundational innovations that catapulted humanity from a nomadic existence to civilization, and that it has since then been instrumental in every great leap of humankind. Here are ancient Egyptian priests, Babylonian bureaucrats, medieval architects, dueling Swiss brothers, and renaissance painters. Their stories clearly demonstrate that the invention of mathematics was every bit as important to the human species as was the discovery of fire. From first page to last, The Art of More brings mathematics back into the heart of what it means to be human.
The Art Of Probability: For Scientists And Engineers
by Richard W. HammingOffering accessible and nuanced coverage, Richard W. Hamming discusses theories of probability with unique clarity and depth. Topics covered include the basic philosophical assumptions, the nature of stochastic methods, and Shannon entropy. One of the best introductions to the topic, The Art of Probability is filled with unique insights and tricks worth knowing.
The Art of Problem Posing
by Stephen I. Brown Marion I. WalterThe new edition of this classic book describes and provides a myriad of examples of the relationships between problem posing and problem solving, and explores the educational potential of integrating these two activities in classrooms at all levels. The Art of Problem Posing, Third Edition encourages readers to shift their thinking about problem posing (such as where problems come from, what to do with them, and the like) from the "other" to themselves and offers a broader conception of what can be done with problems. Special features include: an exploration of the logical relationship between problem posing and problem solving; sketches, drawings, and diagrams that illustrate the schemes proposed; and a special section on writing in mathematics.In the updated third edition, the authors specifically:*address the role of problem posing in the NCTM Standards;*elaborate on the concept of student as author and critic;*include discussion of computer applications to illustrate the potential of technology to enhance problem posing in the classroom;*expand the section on diversity/multiculturalism; and*broaden discussion of writing as a classroom enterprise.This book offers present and future teachers at the middle school, secondary school, and higher education levels ideas to enrich their teaching and suggestions for how to incorporate problem posing into a standard mathematics curriculum.
The Art of Progressive Censoring
by N. Balakrishnan Erhard CramerThis book offers a thorough and updated guide to the theory and methods of progressive censoring, an area that has experienced tremendous growth over the last decade. The theory has developed quite nicely in some special cases having practical applications to reliability and quality. The Art of Progressive Censoring is a valuable reference for graduate students, researchers, and practitioners in applied statistics, quality control, life testing, and reliability. With its accessible style and concrete examples, the work may also be used as a textbook in an advanced undergraduate or a beginning graduate course on censoring or progressive censoring, as well as a supplementary textbook for a course on ordered data.
The Art of Proving Binomial Identities (Discrete Mathematics and Its Applications)
by Michael Z. SpiveyThe Art of Proving Binomial Identities accomplishes two goals: (1) It provides a unified treatment of the binomial coefficients, and (2) Brings together much of the undergraduate mathematics curriculum via one theme (the binomial coefficients). The binomial coefficients arise in a variety of areas of mathematics: combinatorics, of course, but also basic algebra (binomial theorem), infinite series (Newton’s binomial series), differentiation (Leibniz’s generalized product rule), special functions (the beta and gamma functions), probability, statistics, number theory, finite difference calculus, algorithm analysis, and even statistical mechanics. The book is very suitable for advanced undergraduates or beginning graduate students and includes various exercises asking them to prove identities. Students will find that the text and notes at the end of the chapters encourages them to look at binomial coefficients from different angles. With this learning experience, students will be able to understand binomial coefficients in a new way. Features: Provides a unified treatment of many of the techniques for proving binomial coefficient identities. Ties together several of the courses in the undergraduate mathematics curriculum via a single theme. A textbook for a capstone or senior seminar course in mathematics. Contains several results by the author on proof techniques for binomial coefficients that are not well-known. Ideal for self-study, it contains a large number of exercises at the end of each chapter, with hints or solutions for every exercise at the end of the book.
The Art of Quantitative Finance Vol.2: Volatilities, Stochastic Analysis and Valuation Tools (Springer Texts in Business and Economics)
by Gerhard LarcherThis textbook provides the necessary techniques from financial mathematics and stochastic analysis for the valuation of more complex financial products and strategies. The author discusses how to make use of mathematical methods to analyse volatilities in capital markets. Furthermore, he illustrates how to apply and extend the Black-Scholes theory to several fields in finance. In the final section of the book, the author introduces the readers to the fundamentals of stochastic analysis and presents examples of applications. This book builds on the previous volume of the author’s trilogy on quantitative finance. The aim of the second volume is to present and discuss more complex and advanced techniques of modern financial mathematics in a way that is intuitive and easy to follow. As in the previous volume, the author provides financial mathematicians with insights into practical requirements when applying financial mathematical techniques in the real world.
The Art of Quantitative Finance Vol. 3: Risk, Optimal Portfolios, and Case Studies (Springer Texts in Business and Economics)
by Gerhard LarcherThe textbook discusses risk management in capital markets and presents various techniques of portfolio optimization. Special attention is given to risk measurement and credit risk management. Furthermore, the author discusses optimal investment problems and presents various examples. In the last section, the book includes numerous case studies based on the author’s own work as a fund manager, court-appointed expert and consultant in the field of quantitative finance. This book is the third volume of the quantitative finance trilogy by the author and builds on the theoretical groundwork introduced in the previous books. The volume presents real-life examples of the successful application of the introduced techniques and methods in financial services and capital markets.
The Art of R Programming: A Tour of Statistical Software Design
by Norman MatloffR is the world's most popular language for developing statistical software: Archaeologists use it to track the spread of ancient civilizations, drug companies use it to discover which medications are safe and effective, and actuaries use it to assess financial risks and keep economies running smoothly.The Art of R Programming takes you on a guided tour of software development with R, from basic types and data structures to advanced topics like closures, recursion, and anonymous functions. No statistical knowledge is required, and your programming skills can range from hobbyist to pro.Along the way, you'll learn about functional and object-oriented programming, running mathematical simulations, and rearranging complex data into simpler, more useful formats. You'll also learn to:–Create artful graphs to visualize complex data sets and functions–Write more efficient code using parallel R and vectorization–Interface R with C/C++ and Python for increased speed or functionality–Find new R packages for text analysis, image manipulation, and more–Squash annoying bugs with advanced debugging techniquesWhether you're designing aircraft, forecasting the weather, or you just need to tame your data, The Art of R Programming is your guide to harnessing the power of statistical computing.
The Art of Randomness: Randomized Algorithms in the Real World
by Ronald T. KneuselHarness the power of randomness (and Python code) to solve real-world problems in fun, hands-on experiments—from simulating evolution to encrypting messages to making machine-learning algorithms!The Art of Randomness is a hands-on guide to mastering the many ways you can use randomized algorithms to solve real programming and scientific problems. You&’ll learn how to use randomness to run simulations, hide information, design experiments, and even create art and music. All you need is some Python, basic high school math, and a roll of the dice.Author Ronald T. Kneusel focuses on helping you build your intuition so that you&’ll know when and how to use random processes to get things done. You&’ll develop a randomness engine (a Python class that supplies random values from your chosen source), then explore how to leverage randomness to:Simulate Darwinian evolution and optimize with swarm-based search algorithmsDesign scientific experiments to produce more meaningful results by making them truly randomImplement machine learning algorithms like neural networks and random forestsUse Markov Chain Monte Carlo methods to sample from complex distributionsHide information in audio files and images, generate art, and create musicReconstruct original signals and images from only randomly sampled dataScientific anecdotes and code examples throughout illustrate how randomness plays into areas like optimization, machine learning, and audio signals. End-of-chapter exercises encourage further exploration.Whether you&’re a programmer, scientist, engineer, mathematician, or artist, you&’ll find The Art of Randomness to be your ticket to discovering the hidden power of applied randomness and the ways it can transform your approach to solving problems, from the technical to the artistic.
The Art of Science
by Rossella Lupacchini Annarita AngeliniIn addition to linear perspective, complex numbers and probability were notable discoveries of the Renaissance. While the power of perspective, which transformed Renaissance art, was quickly recognized, the scientific establishment treated both complex numbers and probability with much suspicion. It was only in the twentieth century that quantum theory showed how probability might be molded from complex numbers and defined the notion of "complex probability amplitude". From a theoretical point of view, however, the space opened to painting by linear perspective and that opened to science by complex numbers share significant characteristics. The Art of Science explores this shared field with the purpose of extending Leonardo's vision of painting to issues of mathematics and encouraging the reader to see science as an art. The intention is to restore a visual dimension to mathematical sciences - an element dulled, if not obscured, by historians, philosophers, and scientists themselves.
The Art of Statistics: How to Learn from Data
by David SpiegelhalterThe definitive guide to statistical thinkingStatistics 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.
The Art of Strategy: A Game Theorist's Guide to Success in Business and Life
by Barry J. Nalebuff Avinash K. Dixit"I am hard pressed to think of another book that can match the combination of practical insights and reading enjoyment."--Steven Levitt Game theory means rigorous strategic thinking. It's the art of anticipating your opponent's next moves, knowing full well that your rival is trying to do the same thing to you. Though parts of game theory involve simple common sense, much is counterintuitive, and it can only be mastered by developing a new way of seeing the world. Using a diverse array of rich case studies--from pop culture, TV, movies, sports, politics, and history--the authors show how nearly every business and personal interaction has a game-theory component to it. Mastering game theory will make you more successful in business and life, and this lively book is the key to that mastery.
Artful Math Activity Book
by Clarissa GrandiThe wonderful thing about mathematical art is that the most beautiful geometric patterns can be produced without needing to be able to draw, or be ‘good at art'. Mathematical art is accessible to learners of all ages: its algorithmic nature means that it simply requires the ability to follow instructions carefully and to use a pencil and ruler accurately. It is engaging, enriching, thoroughly enjoyable and is a great leveller in the classroom. Learners who may not normally shine in mathematics lessons will take your breath away with their creativity. Those who struggle with their mathematics will experience the joy of success through their mathematical art-making. The six Artful Maths activities in this book are hands-on tasks that will develop important skills such as hand-eye co-ordination, manual dexterity and design thinking, which is a valuable form of problem-solving. Decisions need to be made about placement, size and colour, all of which entail thinking about measurements, proportions and symmetry. They can be undertaken alone or witha teacher to draw out the mathematics underlying the patterns and to practice key content in the school curriculum. For ages 9 to 16+. Contents: Curves of Pursuit, Mazes and Labyrinths,Impossible Objects, Epicycloids,,Perfect Proportions, Parabolic Curves.
Artful Math Teacher Book
by Clarissa GrandiBook contains teacher notes, and access to downloadable templates and Powerpoint lesson plans. The wonderful thing about mathematical art is that the most beautiful geometric patterns can be produced without needing to be able to draw, or be ‘good at art'. Mathematical art is accessible to learners of all ages: its algorithmic nature means that it simply requires the ability to follow instructions carefully and to use a pencil and ruler accurately. It is engaging, enriching, thoroughly enjoyable and is a great leveller in the classroom. Learners who may not normally shine in mathematics lessons will take your breath away with their creativity. Those who struggle with their mathematics will experience the joy of success through their mathematical art-making. The six Artful Maths activities in this book are hands-on tasks that will develop important skills such as hand-eye co-ordination, manual dexterity and design thinking, which is a valuable form of problem-solving. Decisions need to be made about placement, size and colour, all of which entail thinking about measurements, proportions and symmetry. They can be undertaken alone or with a teacher to draw out the mathematics underlying the patterns and to practice key content in the school curriculum. For ages 9 to 16+. Contents: Curves of Pursuit, Mazes and Labyrinths, Impossible Objects, Epicycloids,,Perfect Proportions, Parabolic Curves.
Arthur's Invariant Trace Formula and Comparison of Inner Forms
by Yuval Z. FlickerThis monograph provides an accessible and comprehensive introduction to James Arthur's invariant trace formula, a crucial tool in the theory of automorphic representations. It synthesizes two decades of Arthur's research and writing into one volume, treating a highly detailed and often difficult subject in a clearer and more uniform manner without sacrificing any technical details. The book begins with a brief overview of Arthur's work and a proof of the correspondence between GL(n) and its inner forms in general. Subsequent chapters develop the invariant trace formula in a form fit for applications, starting with Arthur's proof of the basic, non-invariant trace formula, followed by a study of the non-invariance of the terms in the basic trace formula, and, finally, an in-depth look at the development of the invariant formula. The final chapter illustrates the use of the formula by comparing it for G' = GL(n) and its inner form G Arthur's Invariant Trace Formula and Comparison of Inner Forms will appeal to advanced graduate students, researchers, and others interested in automorphic forms and trace formulae. Additionally, it can be used as a supplemental text in graduate courses on representation theory.
Artificial Adaptive Systems Using Auto Contractive Maps: Theory, Applications And Extensions (Studies In Systems, Decision And Control #131)
by Paolo Massimo Buscema Weldon A. Lodwick Giulia Massini Marco Breda Francis Newman Masoud Asadi-ZeydabadiDescribes a newer approach to artificial adaptive systems, the auto contractive map.<P><P> This book offers an introduction to artificial adaptive systems and a general model of the relationships between the data and algorithms used to analyze them. It subsequently describes artificial neural networks as a subclass of artificial adaptive systems, and reports on the backpropagation algorithm, while also identifying an important connection between supervised and unsupervised artificial neural networks. <P> The book’s primary focus is on the auto contractive map, an unsupervised artificial neural network employing a fixed point method versus traditional energy minimization. This is a powerful tool for understanding, associating and transforming data, as demonstrated in the numerous examples presented here. A supervised version of the auto contracting map is also introduced as an outstanding method for recognizing digits and defects. In closing, the book walks the readers through the theory and examples of how the auto contracting map can be used in conjunction with another artificial neural network, the “spin-net,” as a dynamic form of auto-associative memory.
Artificial Economics and Self Organization: Agent-Based Approaches to Economics and Social Systems (Lecture Notes in Economics and Mathematical Systems #669)
by Stephan Leitner Friederike WallThis volume presents recent advances in the dynamic field of Artificial Economics and its various applications. Artificial Economics provides a structured approach to model and investigate economic and social systems. In particular, this approach is based on the use of agent-based simulations and further computational techniques. The main aim is to analyze the outcomes at the overall systems' level as results from the agents' behavior at the micro-level. These emergent characteristics of complex economic and social systems can neither be foreseen nor are they intended. The emergence rather makes these systems function. Artificial Economics especially facilitates the investigation of this emergent systems' behavior.
Artificial Evolution: 15th International Conference, Évolution Artificielle, EA 2022, Exeter, UK, October 31 – November 2, 2022, Revised Selected Papers (Lecture Notes in Computer Science #14091)
by Pierrick Legrand Arnaud Liefooghe Edward Keedwell Julien Lepagnot Lhassane Idoumghar Nicolas Monmarché Evelyne LuttonThis book constitutes the refereed post-conference proceedings of the 15th International Conference, Évolution Artificielle, EA 2022, held in Exeter, UK, during October 31–November 2, 2022.The 15 full papers were carefully reviewed and selected from 18 submissions. The papers cover a wide range of topics in the field of artificial evolution, including, but not limited to: evolutionary computation, evolutionary optimization, coevolution, artificial life, population dynamics, theory, algorithmic and modeling, implementations.
Artificial General Intelligence: 14th International Conference, AGI 2021, Palo Alto, CA, USA, October 15–18, 2021, Proceedings (Lecture Notes in Computer Science #13154)
by Ben Goertzel Alexey Potapov Matthew IkléThis book constitutes the refereed proceedings of the 14th International Conference on Artificial General Intelligence, AGI 2021, held as a hybrid event in San Francisco, CA, USA, in October 2021.The 36 full papers presented in this book were carefully reviewed and selected from 50 submissions. The papers cover topics from foundations of AGI, to AGI approaches and AGI ethics, to the roles of systems biology, goal generation, and learning systems, and so much more.
Artificial General Intelligence: 10th International Conference, AGI 2017, Melbourne, VIC, Australia, August 15-18, 2017, Proceedings (Lecture Notes in Computer Science #10414)
by Tom Everitt, Ben Goertzel and Alexey PotapovThis book constitutes the proceedings of the 10th International Conference on Artificial General Intelligence, AGI 2017, held in Melbourne, VIC, Australia, in August 2017. The 24 regular papers presented in this book together with 1 short paper were carefully reviewed and selected from 35 submissions. They cover topics such as architectures; mathematical foundations; algorithms; safety; understanding; human cognition; and philosophy.
Artificial Intelligence: An Introduction to the Big Ideas and their Development (Chapman & Hall/CRC Mathematics and Artificial Intelligence Series)
by Robert H. Chen Chelsea ChenArtificial Intelligence: An Introduction to Big Ideas and their Development, Second Edition guides readers through the history and development of artificial intelligence (AI), from its early mathematical beginnings through to the exciting possibilities of its potential future applications. To make this journey as accessible as possible, the authors build their narrative around accounts of some of the more popular and well-known demonstrations of artificial intelligence, including Deep Blue, AlphaGo and even Texas Hold’em, followed by their historical background, so that AI can be seen as a natural development of the mathematics and computer science of AI. As the book proceeds, more technical descriptions are presented at a pace that should be suitable for all levels of readers, gradually building a broad and reasonably deep understanding and appreciation for the basic mathematics, physics, and computer science that is rapidly developing artificial intelligence as it is today. Features Only mathematical prerequisite is an elementary knowledge of calculus. Accessible to anyone with an interest in AI and its mathematics and computer science. Suitable as a supplementary reading for a course in AI or the History of Mathematics and Computer Science in regard to artificial intelligence. New to the Second Edition Fully revised and corrected throughout to bring the material up-to-date. Greater technical detail and exploration of basic mathematical concepts, while retaining the simplicity of explanation of the first edition. Entirely new chapters on large language models (LLMs), ChatGPT, and quantum computing.
Artificial Intelligence: An Introduction for the Inquisitive Reader
by Robert H. Chen Chelsea C. ChenArtificial Intelligence: An Introduction for the Inquisitive Reader guides readers through the history and development of AI, from its early mathematical beginnings through to the exciting possibilities of its potential future applications. To make this journey as accessible as possible, the authors build their narrative around accounts of some of the more popular and well-known demonstrations of artificial intelligence including Deep Blue, AlphaGo and even Texas Hold’em, followed by their historical background, so that AI can be seen as a natural development of mathematics and computer science. As the book moves forward, more technical descriptions are presented at a pace that should be suitable for all levels of readers, gradually building a broad and reasonably deep understanding and appreciation for the basic mathematics, physics, and computer science that is rapidly developing artificial intelligence as it is today. Features Only mathematical prerequisite is an elementary knowledge of calculus Accessible to anyone with an interest in AI and its mathematics and computer science Suitable as a supplementary reading for a course in AI or the History of Mathematics and Computer Science in regard to artificial intelligence.
Artificial Intelligence (Studies in Systems, Decision and Control #517)
by Reem Khamis Hamdan Amina BuallayThe impact of artificial intelligence (AI) on business and society has been significant, with the incorporation of AI technologies such as robots, facial recognition, algorithms, and natural language processing into business leading to both corporate benefits and potential challenges for stakeholders. The question of how to engage in responsible business practices in the era of AI is an important one, and there is a need for more research on the relationship between AI and corporate social responsibility (CSR). As AI becomes more prevalent, there is a growing focus on the ethical implications of AI and the potential for AI to perpetuate biases or to displace human workers. CSR initiatives can include considerations of ethical AI in the development and use of AI systems. AI has the potential to solve many global challenges and improve people's lives, but it can also have negative consequences if not developed and used responsibly. CSR initiatives can focus on the social impact of AI,including efforts to ensure that the benefits of AI are distributed fairly and that AI is used for the common good. CSR initiatives often involve engaging with stakeholders, including employees, customers, and communities, to understand their needs and concerns and to ensure that their interests are taken into account. This can include engaging with stakeholders about the use of AI in the organization and its potential impactsThe adoption of AI in business is changing many aspects of doing business in a socially responsible manner, and there is a need to examine the potential unethical behaviors and novel ways of engaging in CSR that may arise. This book aims to focus on AI and CSR, and to advance our understanding of the role of AI in organizations and the literature on CSR by assembling high-quality papers with a strong connection between theory and practice.
Artificial Intelligence: 17th Russian Conference, RCAI 2019, Ulyanovsk, Russia, October 21–25, 2019, Proceedings (Communications in Computer and Information Science #1093)
by Sergei O. Kuznetsov Aleksandr I. PanovThis book constitutes the proceedings of the 17th Russian Conference on Artificial Intelligence, RCAI 2019, held in Ulyanovsk, Russia, in October 2019. The 23 full papers presented along with 7 short papers in this volume were carefully reviewed and selected from 130 submissions. The conference deals with a wide range of topics, including multi-agent systems, intelligent robots and behaviour planning; automated reasoning and data mining; natural language processing and understanding of texts; fuzzy models and soft computing; intelligent systems and applications.
Artificial Intelligence: What Is Behind the Technology of the Future?
by Gerhard Paaß Dirk HeckerArtificial Intelligence (AI) is already present in our daily routines, and in the future, we will encounter it in almost every aspect of life – from analyzing X-rays for medical diagnosis, driving autonomous cars, maintaining complex machinery, to drafting essays on environmental problems and drawing imaginative pictures. The potentials of AI are enormous, while at the same time many myths, uncertainties and challenges circulate that need to be tackled. The English translation of the book “Künstliche Intelligenz – Was steckt hinter der Technologie der Zukunft?” originally published in German (Springer Vieweg, 2020), this book is addressed to the general public, from interested citizens to corporate executives who want to develop a better and deeper understanding of AI technologies and assess their consequences. Mathematical basics, terminology, and methods are explained in understandable language. Adaptations to different media such as images, text, and speech and the corresponding generative models are introduced. A concluding discussion of opportunities and challenges helps readers evaluate new developments, demystify them, and assess their relevance for the future.