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Katherine Johnson: teacher, mathematician, trailblazer. Award-winning children's author, Leila Rasheed, explores the life of the inspirational NASA mathematician made famous by the film Hidden Voices - Katherine Johnson. A Life Story: This gripping series throws the reader directly into the lives of modern society's most influential figures. With striking black-and-white illustration along with timelines and never-heard-before facts. Also in the series: Stephen Hawking: A Life Story Rosalind Franklin: A Life Story Alan Turing: A Life Story
Mathematical modelling and simulation is an increasingly powerful area of mathematics and computer science, which in recent years has been fuelled by the unprecedented access to larger than ever stores of data. These techniques have an increasing number of applications in the professional and political spheres, and people try to predict the results of certain courses of action as accurately as possible. Computing Possible Futures explores the use of models on everyday phenomena such as waiting in lines and driving a car, before expanding the model's complexity to look at how large-scale computational models can help imagine big scale <"what-if>" scenarios like the effect self-driving cars on the US economy. The successes and failures of complex real world problems are examined, and it is shown how few, if any, failures are due to model errors or computational difficulties. It is also shown how real life decision makers have addressed important problems and used their model-based understanding of possible futures to inform these decisions. Written in an entertaining and accessible way, Computing Possible Futures will help those concerned about the futurity of their decisions to understand what fundamentally needs to be done, why it needs to be done, and how to do it.
This revised and enlarged sixth edition of Proofs from THE BOOK features an entirely new chapter on Van der Waerden's permanent conjecture, as well as additional, highly original and delightful proofs in other chapters. From the citation on the occasion of the 2018 "Steele Prize for Mathematical Exposition" "... It is almost impossible to write a mathematics book that can be read and enjoyed by people of all levels and backgrounds, yet Aigner and Ziegler accomplish this feat of exposition with virtuoso style. [...] This book does an invaluable service to mathematics, by illustrating for non-mathematicians what it is that mathematicians mean when they speak about beauty." From the Reviews "... Inside PFTB (Proofs from The Book) is indeed a glimpse of mathematical heaven, where clever insights and beautiful ideas combine in astonishing and glorious ways. There is vast wealth within its pages, one gem after another. ... Aigner and Ziegler... write: "... all we offer is the examples that we have selected, hoping that our readers will share our enthusiasm about brilliant ideas, clever insights and wonderful observations." I do. ... " Notices of the AMS, August 1999 "... This book is a pleasure to hold and to look at: ample margins, nice photos, instructive pictures and beautiful drawings ... It is a pleasure to read as well: the style is clear and entertaining, the level is close to elementary, the necessary background is given separately and the proofs are brilliant. ..." LMS Newsletter, January 1999 "Martin Aigner and Gunter Ziegler succeeded admirably in putting together a broad collection of theorems and their proofs that would undoubtedly be in the Book of Erdoes. The theorems are so fundamental, their proofs so elegant and the remaining open questions so intriguing that every mathematician, regardless of speciality, can benefit from reading this book. ... " SIGACT News, December 2011
This comprehensive text provides a modern and technically precise exposition of the fundamental theory and applications of temporal logics in computer science. Part I presents the basics of discrete transition systems, including constructions and behavioural equivalences. Part II examines the most important temporal logics for transition systems and Part III looks at their expressiveness and complexity. Finally, Part IV describes the main computational methods and decision procedures for model checking and model building - based on tableaux, automata and games - and discusses their relationships. The book contains a wealth of examples and exercises, as well as an extensive annotated bibliography. Thus, the book is not only a solid professional reference for researchers in the field but also a comprehensive graduate textbook that can be used for self-study as well as for teaching courses.
Do you want reliable code for the latest methods in scientific computing? This CD-ROM contains all the source code from the new, and all previous, editions and language versions of Numerical Recipes. Included are: Numerical Recipes, Third Edition: complete source code in C++, with many brand-new routines Numerical Recipes, Second Edition: complete source code in C, Fortran 77, and Fortran 90 Numerical Recipes, First Edition: complete source code in Pascal and BASIC plus third-party ports of the code to Modula 2 and Common Lisp The CDROM also features an archive of difficult-to-find historical materials, including Baker's C Tools and More C Tools, Lau's Numerical Library in C for Scientists and Engineers, the influential NUMAL Algol 60 library from the Mathematisch Centrum in Amsterdam, and more than 250 MB of physically generated and multiply encrypted random bytes. Compatible with all computers and operating systems, the CDROM includes a Personal Single-User License that allows an individual to use the copyrighted code on any number of computers (no more than one at a time). For support or more general license information visit at www.nr.com.
The first book to present the common mathematical foundations of big data analysis across a range of applications and technologies. Today, the volume, velocity, and variety of data are increasing rapidly across a range of fields, including Internet search, healthcare, finance, social media, wireless devices, and cybersecurity. Indeed, these data are growing at a rate beyond our capacity to analyze them. The tools-including spreadsheets, databases, matrices, and graphs-developed to address this challenge all reflect the need to store and operate on data as whole sets rather than as individual elements. This book presents the common mathematical foundations of these data sets that apply across many applications and technologies. Associative arrays unify and simplify data, allowing readers to look past the differences among the various tools and leverage their mathematical similarities in order to solve the hardest big data challenges. The book first introduces the concept of the associative array in practical terms, presents the associative array manipulation system D4M (Dynamic Distributed Dimensional Data Model), and describes the application of associative arrays to graph analysis and machine learning. It provides a mathematically rigorous definition of associative arrays and describes the properties of associative arrays that arise from this definition. Finally, the book shows how concepts of linearity can be extended to encompass associative arrays. Mathematics of Big Data can be used as a textbook or reference by engineers, scientists, mathematicians, computer scientists, and software engineers who analyze big data.
If you struggle with binary multiplication, or Big O Notation, this is the book for you. This textbook companion will help improve your essential maths skills for computer science, whichever awarding body specification you're following. You can use it throughout your course, whenever you feel you need some extra help. - Develop your understanding of both maths and computer science with all worked examples and questions within a computer science context - Improve your confidence with a step-by-step approach to every maths skill - Measure your progress with guided and non-guided questions to see how you're improving - Understand where you're going wrong with full worked solutions to every question - Feel confident in expert guidance from experienced teachers and examiners Victoria Ellis and Gavin Craddock, reviewed by Dr Kathleen Maitland, Senior Lecturer in Computing and Director of the SAS Student Academy at Birmingham City University
Discrete Mathematics for Computing presents the essential mathematics needed for the study of computing and information systems. The subject is covered in a gentle and informal style, but without compromising the need for correct methodology. It is perfect for students with a limited background in mathematics. This new edition includes: * An expanded section on encryption * Additional examples of the ways in which theory can be applied to problems in computing * Many more exercises covering a range of levels, from the basic to the more advanced This book is ideal for students taking a one-semester introductory course in discrete mathematics - particularly for first year undergraduates studying Computing and Information Systems. PETER GROSSMAN has worked in both academic and industrial roles as a mathematician and computing professional. As a lecturer in mathematics, he was responsible for coordinating and developing mathematics courses for Computing students. He has also applied his skills in areas as diverse as calculator design, irrigation systems and underground mine layouts. He lives and works in Melbourne, Australia.
This book presents a collection of 36 pieces of scientific work in
the areas of complexity theory and foundations of cryptography: 20
research contributions, 13 survey articles, and 3 programmatic and
reflective viewpoint statements. These so far formally unpublished
pieces were written by Oded Goldreich, some in collaboration with
Each chapter of this book covers specific topics in statistical analysis, such as robust alternatives to t-tests or how to develop a questionnaire. They also address particular questions on these topics, which are commonly asked by human-computer interaction (HCI) researchers when planning or completing the analysis of their data. The book presents the current best practice in statistics, drawing on the state-of-the-art literature that is rarely presented in HCI. This is achieved by providing strong arguments that support good statistical analysis without relying on mathematical explanations. It additionally offers some philosophical underpinnings for statistics, so that readers can see how statistics fit with experimental design and the fundamental goal of discovering new HCI knowledge.
The genesis of the digital idea and why it transformed civilization A few short decades ago, we were informed by the smooth signals of analog television and radio; we communicated using our analog telephones; and we even computed with analog computers. Today our world is digital, built with zeros and ones. Why did this revolution occur? The Discrete Charm of the Machine explains, in an engaging and accessible manner, the varied physical and logical reasons behind this radical transformation. The spark of individual genius shines through this story of innovation: the stored program of Jacquard (TM)s loom; Charles Babbage (TM)s logical branching; Alan Turing (TM)s brilliant abstraction of the discrete machine; Harry Nyquist (TM)s foundation for digital signal processing; Claude Shannon (TM)s breakthrough insights into the meaning of information and bandwidth; and Richard Feynman (TM)s prescient proposals for nanotechnology and quantum computing. Ken Steiglitz follows the progression of these ideas in the building of our digital world, from the internet and artificial intelligence to the edge of the unknown. Are questions like the famous traveling salesman problem truly beyond the reach of ordinary digital computers? Can quantum computers transcend these barriers? Does a mysterious magical power reside in the analog mechanisms of the brain? Steiglitz concludes by confronting the moral and aesthetic questions raised by the development of artificial intelligence and autonomous robots. The Discrete Charm of the Machine examines why our information technology, the lifeblood of our civilization, became digital, and challenges us to think about where its future trajectory may lead.
Finite-state methods are the most efficient mechanisms for analysing textual and symbolic data, providing elegant solutions for an immense number of practical problems in computational linguistics and computer science. This book for graduate students and researchers gives a complete coverage of the field, starting from a conceptual introduction and building to advanced topics and applications. The central finite-state technologies are introduced with mathematical rigour, ranging from simple finite-state automata to transducers and bimachines as 'input-output' devices. Special attention is given to the rich possibilities of simplifying, transforming and combining finite-state devices. All algorithms presented are accompanied by full correctness proofs and executable source code in a new programming language, C(M), which focuses on transparency of steps and simplicity of code. Thus, by enabling readers to obtain a deep formal understanding of the subject and to put finite-state methods to real use, this book closes the gap between theory and practice.
Arguably the strongest addition to numerical finance of the past decade, Algorithmic Adjoint Differentiation (AAD) is the technology implemented in modern financial software to produce thousands of accurate risk sensitivities, within seconds, on light hardware. AAD recently became a centerpiece of modern financial systems and a key skill for all quantitative analysts, developers, risk professionals or anyone involved with derivatives. It is increasingly taught in Masters and PhD programs in finance. Danske Bank's wide scale implementation of AAD in its production and regulatory systems won the In-House System of the Year 2015 Risk award. The Modern Computational Finance books, written by three of the very people who designed Danske Bank's systems, offer a unique insight into the modern implementation of financial models. The volumes combine financial modelling, mathematics and programming to resolve real life financial problems and produce effective derivatives software. This volume is a complete, self-contained learning reference for AAD, and its application in finance. AAD is explained in deep detail throughout chapters that gently lead readers from the theoretical foundations to the most delicate areas of an efficient implementation, such as memory management, parallel implementation and acceleration with expression templates. The book comes with professional source code in C++, including an efficient, up to date implementation of AAD and a generic parallel simulation library. Modern C++, high performance parallel programming and interfacing C++ with Excel are also covered. The book builds the code step-by-step, while the code illustrates the concepts and notions developed in the book.
Haskell is a purely functional language that allows programmers to rapidly develop clear, concise, and correct software. The language has grown in popularity in recent years, both in teaching and in industry. This book is based on the author's experience of teaching Haskell for more than twenty years. All concepts are explained from first principles and no programming experience is required, making this book accessible to a broad spectrum of readers. While Part I focuses on basic concepts, Part II introduces the reader to more advanced topics. This new edition has been extensively updated and expanded to include recent and more advanced features of Haskell, new examples and exercises, selected solutions, and freely downloadable lecture slides and example code. The presentation is clean and simple, while also being fully compliant with the latest version of the language, including recent changes concerning applicative, monadic, foldable, and traversable types.
Geometric and topological inference deals with the retrieval of information about a geometric object using only a finite set of possibly noisy sample points. It has connections to manifold learning and provides the mathematical and algorithmic foundations of the rapidly evolving field of topological data analysis. Building on a rigorous treatment of simplicial complexes and distance functions, this self-contained book covers key aspects of the field, from data representation and combinatorial questions to manifold reconstruction and persistent homology. It can serve as a textbook for graduate students or researchers in mathematics, computer science and engineering interested in a geometric approach to data science.
Statistical methods are a key part of of data science, yet very few data scientists have any formal statistics training. Courses and books on basic statistics rarely cover the topic from a data science perspective. This practical guide explains how to apply various statistical methods to data science, tells you how to avoid their misuse, and gives you advice on what's important and what's not. Many data science resources incorporate statistical methods but lack a deeper statistical perspective. If you're familiar with the R programming language, and have some exposure to statistics, this quick reference bridges the gap in an accessible, readable format. With this book, you'll learn: Why exploratory data analysis is a key preliminary step in data science How random sampling can reduce bias and yield a higher quality dataset, even with big data How the principles of experimental design yield definitive answers to questions How to use regression to estimate outcomes and detect anomalies Key classification techniques for predicting which categories a record belongs to Statistical machine learning methods that "learn" from data Unsupervised learning methods for extracting meaning from unlabeled data
This thoroughly updated new edition presents state-of-the-art sparse and multiscale image and signal processing. It covers linear multiscale geometric transforms, such as wavelet, ridgelet, or curvelet transforms, and non-linear multiscale transforms based on the median and mathematical morphology operators. Along with an up-to-the-minute description of required computation, it covers the latest results in inverse problem solving and regularization, sparse signal decomposition, blind source separation, in-painting, and compressed sensing. New chapters and sections cover multiscale geometric transforms for three-dimensional data (data cubes), data on the sphere (geo-located data), dictionary learning, and nonnegative matrix factorization. The authors wed theory and practice in examining applications in areas such as astronomy, including recent results from the European Space Agency's Herschel mission, biology, fusion physics, cold dark matter simulation, medical MRI, digital media, and forensics. MATLAB (R) and IDL code, available online at www.SparseSignalRecipes.info, accompany these methods and all applications.
Mathematical and numerical modelling of the human cardiovascular system has attracted remarkable research interest due to its intrinsic mathematical difficulty and the increasing impact of cardiovascular diseases worldwide. This book addresses the two principal components of the cardiovascular system: arterial circulation and heart function. It systematically describes all aspects of the problem, stating the basic physical principles, analysing the associated mathematical models that comprise PDE and ODE systems, reviewing sound and efficient numerical methods for their approximation, and simulating both benchmark problems and clinically inspired problems. Mathematical modelling itself imposes tremendous challenges, due to the amazing complexity of the cardiovascular system and the need for computational methods that are stable, reliable and efficient. The final part is devoted to control and inverse problems, including parameter estimation, uncertainty quantification and the development of reduced-order models that are important when solving problems with high complexity, which would otherwise be out of reach.
Examine business problems and use a practical analytical approach to solve them by implementing predictive models and machine learning techniques using SAS and the R analytical language. This book is ideal for those who are well-versed in writing code and have a basic understanding of statistics, but have limited experience in implementing predictive models and machine learning techniques for analyzing real world data. The most challenging part of solving industrial business problems is the practical and hands-on knowledge of building and deploying advanced predictive models and machine learning algorithms. Applied Analytics through Case Studies Using SAS and R is your answer to solving these business problems by sharpening your analytical skills. What You'll Learn Understand analytics and basic data concepts Use an analytical approach to solve Industrial business problems Build predictive model with machine learning techniques Create and apply analytical strategies Who This Book Is For Data scientists, developers, statisticians, engineers, and research students with a great theoretical understanding of data and statistics who would like to enhance their skills by getting practical exposure in data modeling.
This book covers local search for combinatorial optimization and its extension to mixed-variable optimization. Although not yet understood from the theoretical point of view, local search is the paradigm of choice for tackling large-scale real-life optimization problems. Today's end-users demand interactivity with decision support systems. For optimization software, this means obtaining good-quality solutions quickly. Fast iterative improvement methods, like local search, are suited to satisfying such needs. Here the authors show local search in a new light, in particular presenting a new kind of mathematical programming solver, namely LocalSolver, based on neighborhood search.
First, an iconoclast methodology is presented to design and engineer local search algorithms. The authors' concern about industrializing local search approaches is of particular interest for practitioners. This methodology is applied to solve two industrial problems with high economic stakes. Software based on local search induces extra costs in development and maintenance in comparison with the direct use of mixed-integer linear programming solvers. The authors then move on to present the LocalSolver project whose goal is to offer the power of local search through a model-and-run solver for large-scale 0-1 nonlinear programming. They conclude by presenting their ongoing and future work on LocalSolver toward a full mathematical programming solver based on local search.
Co-authored by four leading scientists from academia and industry, Numerical Recipes Third Edition starts with basic mathematics and computer science and proceeds to complete, working routines. Widely recognized as the most comprehensive, accessible and practical basis for scientific computing, this new edition incorporates more than 400 Numerical Recipes routines, many of them new or upgraded. The executable C++ code, now printed in color for easy reading, adopts an object-oriented style particularly suited to scientific applications. The whole book is presented in the informal, easy-to-read style that made earlier editions so popular. Please visit www.nr.com or www.cambridge.org/us/numericalrecipes for more details. New key features: 2 new chapters, 25 new sections, 25% longer than Second Edition Thorough upgrades throughout the text Over 100 completely new routines and upgrades of many more. New Classification and Inference chapter, including Gaussian mixture models, HMMs, hierarchical clustering, Support Vector MachinesNew Computational Geometry chapter covers KD trees, quad- and octrees, Delaunay triangulation, and algorithms for lines, polygons, triangles, and spheres New sections include interior point methods for linear programming, Monte Carlo Markov Chains, spectral and pseudospectral methods for PDEs, and many new statistical distributions An expanded treatment of ODEs with completely new routines Plus comprehensive coverage of linear algebra, interpolation, special functions, random numbers, nonlinear sets of equations, optimization, eigensystems, Fourier methods and wavelets, statistical tests, ODEs and PDEs, integral equations, and inverse theory And much, much more! Visitthe authors' web site for information about electronic subscriptions www.nr.com/aboutNR3book.html
Modern scientific computational methods are undergoing a transformative change; big data and statistical learning methods now have the potential to outperform the classical first-principles modeling paradigm. This book bridges this transition, connecting the theory of probability, stochastic processes, functional analysis, numerical analysis, and differential geometry. It describes two classes of computational methods to leverage data for modeling dynamical systems. The first is concerned with data fitting algorithms to estimate parameters in parametric models that are postulated on the basis of physical or dynamical laws. The second is on operator estimation, which uses the data to nonparametrically approximate the operator generated by the transition function of the underlying dynamical systems. This self-contained book is suitable for graduate studies in applied mathematics, statistics, and engineering. Carefully chosen elementary examples with supplementary MATLAB (R) codes and appendices covering the relevant prerequisite materials are provided, making it suitable for self-study.
Computation is revolutionizing our world, even the inner world of the 'pure' mathematician. Mathematical methods - especially the notion of proof - that have their roots in classical antiquity have seen a radical transformation since the 1970s, as successive advances have challenged the priority of reason over computation. Like many revolutions, this one comes from within. Computation, calculation, algorithms - all have played an important role in mathematical progress from the beginning - but behind the scenes, their contribution was obscured in the enduring mathematical literature. To understand the future of mathematics, this fascinating book returns to its past, tracing the hidden history that follows the thread of computation. Along the way it invites us to reconsider the dialog between mathematics and the natural sciences, as well as the relationship between mathematics and computer science. It also sheds new light on philosophical concepts, such as the notions of analytic and synthetic judgment. Finally, it brings us to the brink of the new age, in which machine intelligence offers new ways of solving mathematical problems previously inaccessible. This book is the 2007 winner of the Grand Prix de Philosophie de l'Academie Francaise.
Key approaches in the rapidly developing area of sparse modeling, focusing on its application in fields including neuroscience, computational biology, and computer vision. Sparse modeling is a rapidly developing area at the intersection of statistical learning and signal processing, motivated by the age-old statistical problem of selecting a small number of predictive variables in high-dimensional datasets. This collection describes key approaches in sparse modeling, focusing on its applications in fields including neuroscience, computational biology, and computer vision. Sparse modeling methods can improve the interpretability of predictive models and aid efficient recovery of high-dimensional unobserved signals from a limited number of measurements. Yet despite significant advances in the field, a number of open issues remain when sparse modeling meets real-life applications. The book discusses a range of practical applications and state-of-the-art approaches for tackling the challenges presented by these applications. Topics considered include the choice of method in genomics applications; analysis of protein mass-spectrometry data; the stability of sparse models in brain imaging applications; sequential testing approaches; algorithmic aspects of sparse recovery; and learning sparse latent models. Contributors A. Vania Apkarian, Marwan Baliki, Melissa K. Carroll, Guillermo A. Cecchi, Volkan Cevher, Xi Chen, Nathan W. Churchill, Remi Emonet, Rahul Garg, Zoubin Ghahramani, Lars Kai Hansen, Matthias Hein, Katherine Heller, Sina Jafarpour, Seyoung Kim, Mladen Kolar, Anastasios Kyrillidis, Seunghak Lee, Aurelie Lozano, Matthew L. Malloy, Pablo Meyer, Shakir Mohamed, Alexandru Niculescu-Mizil, Robert D. Nowak, Jean-Marc Odobez, Peter M. Rasmussen, Irina Rish, Saharon Rosset, Martin Slawski, Stephen C. Strother, Jagannadan Varadarajan, Eric P. Xing
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