Validated Numerics

A Short Introduction to Rigorous Computations

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Author: Warwick Tucker

Publisher: Princeton University Press

ISBN: 9781400838974

Category: Mathematics

Page: 152

View: 5760

This textbook provides a comprehensive introduction to the theory and practice of validated numerics, an emerging new field that combines the strengths of scientific computing and pure mathematics. In numerous fields ranging from pharmaceutics and engineering to weather prediction and robotics, fast and precise computations are essential. Based on the theory of set-valued analysis, a new suite of numerical methods is developed, producing efficient and reliable solvers for numerous problems in nonlinear analysis. Validated numerics yields rigorous computations that can find all possible solutions to a problem while taking into account all possible sources of error--fast, and with guaranteed accuracy. Validated Numerics offers a self-contained primer on the subject, guiding readers from the basics to more advanced concepts and techniques. This book is an essential resource for those entering this fast-developing field, and it is also the ideal textbook for graduate students and advanced undergraduates needing an accessible introduction to the subject. Validated Numerics features many examples, exercises, and computer labs using MATLAB/C++, as well as detailed appendixes and an extensive bibliography for further reading. Provides a comprehensive, self-contained introduction to validated numerics Requires no advanced mathematics or programming skills Features many examples, exercises, and computer labs Includes code snippets that illustrate implementation Suitable as a textbook for graduate students and advanced undergraduates

The Princeton Companion to Applied Mathematics

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Author: Nicholas J. Higham

Publisher: Princeton University Press

ISBN: 1400874475

Category: Mathematics

Page: 1016

View: 2194

This is the most authoritative and accessible single-volume reference book on applied mathematics. Featuring numerous entries by leading experts and organized thematically, it introduces readers to applied mathematics and its uses; explains key concepts; describes important equations, laws, and functions; looks at exciting areas of research; covers modeling and simulation; explores areas of application; and more. Modeled on the popular Princeton Companion to Mathematics, this volume is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book on applied mathematics. Features nearly 200 entries organized thematically and written by an international team of distinguished contributors Presents the major ideas and branches of applied mathematics in a clear and accessible way Explains important mathematical concepts, methods, equations, and applications Introduces the language of applied mathematics and the goals of applied mathematical research Gives a wide range of examples of mathematical modeling Covers continuum mechanics, dynamical systems, numerical analysis, discrete and combinatorial mathematics, mathematical physics, and much more Explores the connections between applied mathematics and other disciplines Includes suggestions for further reading, cross-references, and a comprehensive index

Interactive Theorem Proving

7th International Conference, ITP 2016, Nancy, France, August 22-25, 2016, Proceedings

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Author: Jasmin Christian Blanchette,Stephan Merz

Publisher: Springer

ISBN: 3319431447

Category: Mathematics

Page: 502

View: 8610

This book constitutes the refereed proceedings of the 7th International Conference on Interactive Theorem Proving, ITP 2016, held in Nancy, France, in August 2016. The 27 full papers and 5 short papers presented were carefully reviewed and selected from 55 submissions. The topics range from theoretical foundations to implementation aspects and applications in program verification, security and formalization of mathematical theories.

Numerical Software Verification

10th International Workshop, NSV 2017, Heidelberg, Germany, July 22-23, 2017, Proceedings

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Author: Alessandro Abate,Sylvie Boldo

Publisher: Springer

ISBN: 3319635018

Category: Computers

Page: 115

View: 3971

This book constitutes the proceedings of the 10th International Workshop on Numerical Software Verification, NSV 2017, held in Heidelberg, Germany, in July 2017 - colocated with the International Workshop on Formal Methods for Rigorous Systems Engineering of Cyber-Physical Systems, RISE4CPS 2017, a one-time, invited-only event.The 3 full papers presented together with 3 short papers, 2 keynote abstracts and 4 invited abstracts were carefully reviewed and selected from numerous submissions.The NSV 2017 workshop is dedicated to the development of logical and mathematical techniques for the reasoning about programmability and reliability.

Principles of Modeling

Essays Dedicated to Edward A. Lee on the Occasion of His 60th Birthday

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Author: Marten Lohstroh,Patricia Derler,Marjan Sirjani

Publisher: Springer

ISBN: 3319952463

Category: Computer simulation

Page: 539

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Introduction to Interval Analysis

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Author: Ramon E. Moore,R. Baker Kearfott,Michael J. Cloud

Publisher: SIAM

ISBN: 089871771X

Category: Interval analysis (Mathematics)

Page: 223

View: 1518

An update on the author's previous books, this introduction to interval analysis provides an introduction to INTLAB, a high-quality, comprehensive MATLAB toolbox for interval computations, making this the first interval analysis book that does with INTLAB what general numerical analysis texts do with MATLAB.

Introduction to Information Retrieval

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Author: Christopher D. Manning,Prabhakar Raghavan,Hinrich Schütze

Publisher: Cambridge University Press

ISBN: 1139472100

Category: Computers

Page: N.A

View: 1234

Class-tested and coherent, this textbook teaches classical and web information retrieval, including web search and the related areas of text classification and text clustering from basic concepts. It gives an up-to-date treatment of all aspects of the design and implementation of systems for gathering, indexing, and searching documents; methods for evaluating systems; and an introduction to the use of machine learning methods on text collections. All the important ideas are explained using examples and figures, making it perfect for introductory courses in information retrieval for advanced undergraduates and graduate students in computer science. Based on feedback from extensive classroom experience, the book has been carefully structured in order to make teaching more natural and effective. Slides and additional exercises (with solutions for lecturers) are also available through the book's supporting website to help course instructors prepare their lectures.

An Introduction to Statistical Learning

with Applications in R

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Author: Gareth James,Daniela Witten,Trevor Hastie,Robert Tibshirani

Publisher: Springer Science & Business Media

ISBN: 1461471389

Category: Mathematics

Page: 426

View: 8280

An Introduction to Statistical Learning provides an accessible overview of the field of statistical learning, an essential toolset for making sense of the vast and complex data sets that have emerged in fields ranging from biology to finance to marketing to astrophysics in the past twenty years. This book presents some of the most important modeling and prediction techniques, along with relevant applications. Topics include linear regression, classification, resampling methods, shrinkage approaches, tree-based methods, support vector machines, clustering, and more. Color graphics and real-world examples are used to illustrate the methods presented. Since the goal of this textbook is to facilitate the use of these statistical learning techniques by practitioners in science, industry, and other fields, each chapter contains a tutorial on implementing the analyses and methods presented in R, an extremely popular open source statistical software platform. Two of the authors co-wrote The Elements of Statistical Learning (Hastie, Tibshirani and Friedman, 2nd edition 2009), a popular reference book for statistics and machine learning researchers. An Introduction to Statistical Learning covers many of the same topics, but at a level accessible to a much broader audience. This book is targeted at statisticians and non-statisticians alike who wish to use cutting-edge statistical learning techniques to analyze their data. The text assumes only a previous course in linear regression and no knowledge of matrix algebra.

The Math Book

From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics

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Author: Clifford A. Pickover

Publisher: Sterling Publishing Company, Inc.

ISBN: 9781402757969

Category: Mathematics

Page: 527

View: 509

This book covers 250 milestones in mathematical history, beginning millions of years ago with ancient "ant odometers" and moving through time to our modern-day quest for new dimensions.

Eloquent JavaScript, 2nd Ed.

A Modern Introduction to Programming

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Author: Marijn Haverbeke

Publisher: No Starch Press

ISBN: 1593276613

Category: Computers

Page: 472

View: 6545

JavaScript lies at the heart of almost every modern web application, from social apps to the newest browser-based games. Though simple for beginners to pick up and play with, JavaScript is a flexible, complex language that you can use to build full-scale applications. Eloquent JavaScript, 2nd Edition dives deep into the JavaScript language to show you how to write beautiful, effective code. Author Marijn Haverbeke immerses you in example code from the start, while exercises and full-chapter projects give you hands-on experience with writing your own programs. As you build projects such as an artificial life simulation, a simple programming language, and a paint program, you’ll learn: –The essential elements of programming, including syntax, control, and data –How to organize and clarify your code with object-oriented and functional programming techniques –How to script the browser and make basic web applications –How to use the DOM effectively to interact with browsers –How to harness Node.js to build servers and utilities This edition is thoroughly revised and modernized to reflect the current state of Java­Script and web browsers, with brand-new material, such as a chapter on code performance in Java­Script, and expanded coverage of recursion and closures. All source code is available online in an inter­active sandbox, where you can edit the code, run it, and see its output instantly. Isn’t it time you became fluent in the language of the Web? Includes an exclusive chapter, only available in the No Starch Press edition!

Automatic Differentiation of Algorithms

From Simulation to Optimization

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Author: George Corliss,Christele Faure,Andreas Griewank,Laurent Hascoet,Uwe Naumann

Publisher: Springer Science & Business Media

ISBN: 1461300754

Category: Computers

Page: 432

View: 4446

A survey book focusing on the key relationships and synergies between automatic differentiation (AD) tools and other software tools, such as compilers and parallelizers, as well as their applications. The key objective is to survey the field and present the recent developments. In doing so the topics covered shed light on a variety of perspectives. They reflect the mathematical aspects, such as the differentiation of iterative processes, and the analysis of nonsmooth code. They cover the scientific programming aspects, such as the use of adjoints in optimization and the propagation of rounding errors. They also cover "implementation" problems.

Effective Computation in Physics

Field Guide to Research with Python

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Author: Anthony Scopatz,Kathryn D. Huff

Publisher: "O'Reilly Media, Inc."

ISBN: 1491901586

Category: Science

Page: 552

View: 3069

More physicists today are taking on the role of software developer as part of their research, but software development isn’t always easy or obvious, even for physicists. This practical book teaches essential software development skills to help you automate and accomplish nearly any aspect of research in a physics-based field. Written by two PhDs in nuclear engineering, this book includes practical examples drawn from a working knowledge of physics concepts. You’ll learn how to use the Python programming language to perform everything from collecting and analyzing data to building software and publishing your results. In four parts, this book includes: Getting Started: Jump into Python, the command line, data containers, functions, flow control and logic, and classes and objects Getting It Done: Learn about regular expressions, analysis and visualization, NumPy, storing data in files and HDF5, important data structures in physics, computing in parallel, and deploying software Getting It Right: Build pipelines and software, learn to use local and remote version control, and debug and test your code Getting It Out There: Document your code, process and publish your findings, and collaborate efficiently; dive into software licenses, ownership, and copyright procedures

Introduction to Computational Genomics

A Case Studies Approach

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Author: Nello Cristianini,Matthew W. Hahn

Publisher: Cambridge University Press

ISBN: 1139460153

Category: Computers

Page: N.A

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Where did SARS come from? Have we inherited genes from Neanderthals? How do plants use their internal clock? The genomic revolution in biology enables us to answer such questions. But the revolution would have been impossible without the support of powerful computational and statistical methods that enable us to exploit genomic data. Many universities are introducing courses to train the next generation of bioinformaticians: biologists fluent in mathematics and computer science, and data analysts familiar with biology. This readable and entertaining book, based on successful taught courses, provides a roadmap to navigate entry to this field. It guides the reader through key achievements of bioinformatics, using a hands-on approach. Statistical sequence analysis, sequence alignment, hidden Markov models, gene and motif finding and more, are introduced in a rigorous yet accessible way. A companion website provides the reader with Matlab-related software tools for reproducing the steps demonstrated in the book.

Introduction to Computation and Programming Using Python

With Application to Understanding Data

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Author: John V. Guttag

Publisher: MIT Press

ISBN: 0262529629

Category: Computers

Page: 472

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The new edition of an introductory text that teaches students the art of computational problem solving, covering topics ranging from simple algorithms to information visualization.

Introduction to Numerical Analysis

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Author: Arnold Neumaier

Publisher: Cambridge University Press

ISBN: 9780521336109

Category: Mathematics

Page: 356

View: 5795

This 2001 textbook provides an introduction to constructive methods that provide accurate approximations to the solution of numerical problems using MATLAB.

Essential Bioinformatics

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Author: Jin Xiong

Publisher: Cambridge University Press

ISBN: 113945062X

Category: Science

Page: N.A

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Essential Bioinformatics is a concise yet comprehensive textbook of bioinformatics, which provides a broad introduction to the entire field. Written specifically for a life science audience, the basics of bioinformatics are explained, followed by discussions of the state-of-the-art computational tools available to solve biological research problems. All key areas of bioinformatics are covered including biological databases, sequence alignment, genes and promoter prediction, molecular phylogenetics, structural bioinformatics, genomics and proteomics. The book emphasizes how computational methods work and compares the strengths and weaknesses of different methods. This balanced yet easily accessible text will be invaluable to students who do not have sophisticated computational backgrounds. Technical details of computational algorithms are explained with a minimum use of mathematical formulae; graphical illustrations are used in their place to aid understanding. The effective synthesis of existing literature as well as in-depth and up-to-date coverage of all key topics in bioinformatics make this an ideal textbook for all bioinformatics courses taken by life science students and for researchers wishing to develop their knowledge of bioinformatics to facilitate their own research.

Modern Mathematical Tools and Techniques in Capturing Complexity

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Author: Leandro Pardo,Narayanaswamy Balakrishnan,Maria Angeles Gil

Publisher: Springer Science & Business Media

ISBN: 3642208525

Category: Technology & Engineering

Page: 514

View: 6659

Real-life problems are often quite complicated in form and nature and, for centuries, many different mathematical concepts, ideas and tools have been developed to formulate these problems theoretically and then to solve them either exactly or approximately. This book aims to gather a collection of papers dealing with several different problems arising from many disciplines and some modern mathematical approaches to handle them. In this respect, the book offers a wide overview on many of the current trends in Mathematics as valuable formal techniques in capturing and exploiting the complexity involved in real-world situations. Several researchers, colleagues, friends and students of Professor María Luisa Menéndez have contributed to this volume to pay tribute to her and to recognize the diverse contributions she had made to the fields of Mathematics and Statistics and to the profession in general. She had a sweet and strong personality, and instilled great values and work ethics in her students through her dedication to teaching and research. Even though the academic community lost her prematurely, she would continue to provide inspiration to many students and researchers worldwide through her published work.

Optimization in Practice with MATLAB

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Author: Achille Messac

Publisher: Cambridge University Press

ISBN: 1107109183

Category: Mathematics

Page: 494

View: 4604

This textbook is designed for students and industry practitioners for a first course in optimization integrating MATLAB® software.

One-Dimensional Dynamics

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Author: Welington de Melo,Sebastian van Strien

Publisher: Springer Science & Business Media

ISBN: 3642780431

Category: Mathematics

Page: 606

View: 2615

One-dimensional dynamics has developed in the last decades into a subject in its own right. Yet, many recent results are inaccessible and have never been brought together. For this reason, we have tried to give a unified ac count of the subject and complete proofs of many results. To show what results one might expect, the first chapter deals with the theory of circle diffeomorphisms. The remainder of the book is an attempt to develop the analogous theory in the non-invertible case, despite the intrinsic additional difficulties. In this way, we have tried to show that there is a unified theory in one-dimensional dynamics. By reading one or more of the chapters, the reader can quickly reach the frontier of research. Let us quickly summarize the book. The first chapter deals with circle diffeomorphisms and contains a complete proof of the theorem on the smooth linearizability of circle diffeomorphisms due to M. Herman, J.-C. Yoccoz and others. Chapter II treats the kneading theory of Milnor and Thurstonj also included are an exposition on Hofbauer's tower construction and a result on fuB multimodal families (this last result solves a question posed by J. Milnor).