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In Pursuit of the Traveling Salesman travels to the very threshold of our understanding about the nature of complexity, and challenges you yourself to discover the solution to this captivating mathematical problem.

Some images inside the book are unavailable due to digital copyright restrictions.

Social Media is huge - Nothing in the history of the world has brought people together and changed the face of business like social media has.

Reach out to the world and get them to like you.

This highly versatile text provides mathematical background used in a wide variety of disciplines, including mathematics and mathematics education, computer science, biology, chemistry, engineering, communications, and business.

Some of the major features and strengths of this textbook

More than 1,600 exercises, ranging from elementary to challenging, are included with hints/answers to all odd-numbered exercises.

Descriptions of proof techniques are accessible and lively.

Students benefit from the historical discussions throughout the textbook.

Various professionals will find this book immensely useful, whether it be the industrial engineer, the industrial manager, or anyone associated with engineering in a technical or managing role. It will bring about a clear understanding of not only how to implement Six Sigma statistical tools, but also how to do so within the bounds of Lean manufacturing scheme. It will show how Lean Six Sigma can help reinforce the notion of “less is more, while at the same time preserving minimal error rates in final manufactured products.

Reviews the essential statistical tools upon which Six Sigma rests, including normal distribution and mean deviation and the derivation of 1 sigma through six sigmaExplains essential lean tools like Value-Stream Mapping and quality improvement tools like Kaizen techniques within the context of Lean Six Sigma practiceExtended case study to clearly demonstrate how Six Sigma and Lean principles have been actually implemented, reducing production times and costs and creating improved product qualityThe second edition adds a discussion of vector auto-regressive, structural vector auto-regressive, and structural vector error-correction models. To analyze the interactions between the investigated variables, further impulse response function and forecast error variance decompositions are introduced as well as forecasting. The author explains how these model types relate to each other.

"Seamless R and C++ integration with Rcpp" is simply a wonderful book. For anyone who uses C/C++ and R, it is an indispensable resource. The writing is outstanding. A huge bonus is the section on applications. This section covers the matrix packages Armadillo and Eigen and the GNU Scientific Library as well as RInside which enables you to use R inside C++. These applications are what most of us need to know to really do scientific programming with R and C++. I love this book. -- Robert McCulloch, University of Chicago Booth School of Business

Rcpp is now considered an essential package for anybody doing serious computational research using R. Dirk's book is an excellent companion and takes the reader from a gentle introduction to more advanced applications via numerous examples and efficiency enhancing gems. The book is packed with all you might have ever wanted to know about Rcpp, its cousins (RcppArmadillo, RcppEigen .etc.), modules, package development and sugar. Overall, this book is a must-have on your shelf. -- Sanjog Misra, UCLA Anderson School of Management

The Rcpp package represents a major leap forward for scientific computations with R. With very few lines of C++ code, one has R's data structures readily at hand for further computations in C++. Hence, high-level numerical programming can be made in C++ almost as easily as in R, but often with a substantial speed gain. Dirk is a crucial person in these developments, and his book takes the reader from the first fragile steps on to using the full Rcpp machinery. A very recommended book! -- Søren Højsgaard, Department of Mathematical Sciences, Aalborg University, Denmark

"Seamless R and C ++ Integration with Rcpp" provides the first comprehensive introduction to Rcpp. Rcpp has become the most widely-used language extension for R, and is deployed by over one-hundred different CRAN and BioConductor packages. Rcpp permits users to pass scalars, vectors, matrices, list or entire R objects back and forth between R and C++ with ease. This brings the depth of the R analysis framework together with the power, speed, and efficiency of C++.

Dirk Eddelbuettel has been a contributor to CRAN for over a decade and maintains around twenty packages. He is the Debian/Ubuntu maintainer for R and other quantitative software, edits the CRAN Task Views for Finance and High-Performance Computing, is a co-founder of the annual R/Finance conference, and an editor of the Journal of Statistical Software. He holds a Ph.D. in Mathematical Economics from EHESS (Paris), and works in Chicago as a Senior Quantitative Analyst.

The 21 self-contained chapters in this volume are devoted to the examination of modern trends and open problems in the field of optimization. This book will be a valuable tool not only to specialists interested in the technical detail and various applications presented, but also to researchers interested in building upon the book’s theoretical results.

The Second Edition is completely revised and provides additional review material on linear algebra as well as complete coverage of elementary linear programming. Other topics covered include: the Duality Theorem; transportation problems; the assignment problem; and the maximal flow problem. New figures and exercises are provided and the authors have updated all computer applications.

More review material on linear algebraElementary linear programming covered more efficientlyPresentation improved, especially for the duality theorem, transportation problems, the assignment problem, and the maximal flow problemNew figures and exercisesComputer applications updatedNew guide to inexpensive linear programming software for personal computersCovering all the mathematical techniques required to resolve geometric problems and design computer programs for computer graphic applications, each chapter explores a specific mathematical topic prior to moving forward into the more advanced areas of matrix transforms, 3D curves and surface patches. Problem-solving techniques using vector analysis and geometric algebra are also discussed.

All the key areas are covered including: Numbers, Algebra, Trigonometry, Coordinate geometry, Transforms, Vectors, Curves and surfaces, Barycentric coordinates, Analytic geometry.

Plus – and unusually in a student textbook – a chapter on geometric algebra is included.

The author presents the first extended treatment of MM algorithms, which are ideal for high-dimensional optimization problems in data mining, imaging, and genomics; derives numerous algorithms from a broad diversity of application areas, with a particular emphasis on statistics, biology, and data mining; and summarizes a large amount of literature that has not reached book form before.

It covers the topics traditionally treated in a first course, but also highlights new and emerging themes. Chapters are broken down into `lecture' sized pieces, motivated and illustrated by numerous theoretical and computational examples.

Over 200 exercises are provided and these are starred according to their degree of difficulty. Solutions to all exercises are available to authorized instructors.

The book covers key foundation topics:

o Taylor series methods

o Runge--Kutta methods

o Linear multistep methods

o Convergence

o Stability

and a range of modern themes:

o Adaptive stepsize selection

o Long term dynamics

o Modified equations

o Geometric integration

o Stochastic differential equations

The prerequisite of a basic university-level calculus class is assumed, although appropriate background results are also summarized in appendices. A dedicated website for the book containing extra information can be found via www.springer.com

The extensively revised second edition provides further clarification of matters that typically give rise to difficulty in the classroom and restructures the chapters on logic to emphasize the role of consequence relations and higher-level rules, as well as including more exercises and solutions.

Topics and features: teaches finite mathematics as a language for thinking, as much as knowledge and skills to be acquired; uses an intuitive approach with a focus on examples for all general concepts; brings out the interplay between the qualitative and the quantitative in all areas covered, particularly in the treatment of recursion and induction; balances carefully the abstract and concrete, principles and proofs, specific facts and general perspectives; includes highlight boxes that raise common queries and clear away confusions; provides numerous exercises, with selected solutions, to test and deepen the reader’s understanding.

This clearly-written text/reference is a must-read for first-year undergraduate students of computing. Assuming only minimal mathematical background, it is ideal for both the classroom and independent study.

The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine.

What else is new?

New chapters on measurement and analytic graph theory

Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.

Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth

Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition

Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader

Gross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

The book begins by tracing the development of cryptology from that of an arcane practice used, for example, to conceal alchemic recipes, to the modern scientific method that is studied and employed today. The remainder of the book explores the modern aspects and applications of cryptography, covering symmetric- and public-key cryptography, cryptographic protocols, key management, message authentication, e-mail and Internet security, and advanced applications such as wireless security, smart cards, biometrics, and quantum cryptography. The author also includes non-cryptographic security issues and a chapter devoted to information theory and coding. Nearly 200 diagrams, examples, figures, and tables along with abundant references and exercises complement the discussion.

Written by leading authority and best-selling author on the subject Richard A. Mollin, Codes: The Guide to Secrecy from Ancient to Modern Times is the essential reference for anyone interested in this exciting and fascinating field, from novice to veteran practitioner.

This concise and easy-to-read textbook/reference presents an algorithmic approach to mathematical analysis, with a focus on modelling and on the applications of analysis. Fully integrating mathematical software into the text as an important component of analysis, the book makes thorough use of examples and explanations using MATLAB, Maple, and Java applets. Mathematical theory is described alongside the basic concepts and methods of numerical analysis, supported by computer experiments and programming exercises, and an extensive use of figure illustrations.

Topics and features: thoroughly describes the essential concepts of analysis, covering real and complex numbers, trigonometry, sequences and series, functions, derivatives and antiderivatives, definite integrals and double integrals, and curves; provides summaries and exercises in each chapter, as well as computer experiments; discusses important applications and advanced topics, such as fractals and L-systems, numerical integration, linear regression, and differential equations; presents tools from vector and matrix algebra in the appendices, together with further information on continuity; includes definitions, propositions and examples throughout the text, together with a list of relevant textbooks and references for further reading; supplementary software can be downloaded from the book’s webpage at www.springer.com.

This textbook is essential for undergraduate students in Computer Science. Written to specifically address the needs of computer scientists and researchers, it will also serve professionals looking to bolster their knowledge in such fundamentals extremely well.

Research on distributions associated with sorting algorithms has grown dramatically over the last few decades, spawning many exact and limiting distributions of complexity measures for many sorting algorithms. Yet much of this information has been scattered in disparate and highly specialized sources throughout the literature. In Sorting: A Distribution Theory, leading authority Hosam Mahmoud compiles, consolidates, and clarifies the large volume of available research, providing a much-needed, comprehensive treatment of the entire emerging distributional theory of sorting.

Mahmoud carefully constructs a logical framework for the analysis of all standard sorting algorithms, focusing on the development of the probability distributions associated with the algorithms, as well as other issues in probability theory such as measures of concentration and rates of convergence. With an emphasis on narrative rather than technical explanations, this exceptionally well-written book makes new results easily accessible to a broad spectrum of readers, including computer professionals, scientists, mathematicians, and engineers. Sorting: A Distribution Theory:

* Contains introductory material on complete and partial sorting

* Explains insertion sort, quick sort, and merge sort, among other methods

* Offers verbal descriptions of the mechanics of the algorithms as well as the necessary code

* Illustrates the distribution theory of sorting using a broad array of both classical and modern techniques

* Features a variety of end-of-chapter exercises

This major new edition features many topics not covered in the original, including graphical models, random forests, ensemble methods, least angle regression & path algorithms for the lasso, non-negative matrix factorization, and spectral clustering. There is also a chapter on methods for ``wide'' data (p bigger than n), including multiple testing and false discovery rates.

Trevor Hastie, Robert Tibshirani, and Jerome Friedman are professors of statistics at Stanford University. They are prominent researchers in this area: Hastie and Tibshirani developed generalized additive models and wrote a popular book of that title. Hastie co-developed much of the statistical modeling software and environment in R/S-PLUS and invented principal curves and surfaces. Tibshirani proposed the lasso and is co-author of the very successful An Introduction to the Bootstrap. Friedman is the co-inventor of many data-mining tools including CART, MARS, projection pursuit and gradient boosting.

At first glance, this riddle may seem impossible to solve: how can all of the necessary information be transmitted by the prisoners using only a single light bulb? There is indeed a solution, however, and it can be found by reasoning about knowledge.

This book provides a guided tour through eleven classic logic puzzles that are engaging and challenging and often surprising in their solutions. These riddles revolve around the characters’ declarations of knowledge, ignorance, and the appearance that they are contradicting themselves in some way. Each chapter focuses on one puzzle, which the authors break down in order to guide the reader toward the solution.

For general readers and students with little technical knowledge of mathematics, One Hundred Prisoners and a Light Bulb will be an accessible and fun introduction to epistemic logic. Additionally, more advanced students and their teachers will find it to be a valuable reference text for introductory course work and further study.

The new edition of this classic book gives all the major concepts, techniques and applications of sparse representation, reflecting the key role the subject plays in today's signal processing. The book clearly presents the standard representations with Fourier, wavelet and time-frequency transforms, and the construction of orthogonal bases with fast algorithms. The central concept of sparsity is explained and applied to signal compression, noise reduction, and inverse problems, while coverage is given to sparse representations in redundant dictionaries, super-resolution and compressive sensing applications.

Features:

* Balances presentation of the mathematics with applications to signal processing

* Algorithms and numerical examples are implemented in WaveLab, a MATLAB toolbox

New in this edition

* Sparse signal representations in dictionaries

* Compressive sensing, super-resolution and source separation

* Geometric image processing with curvelets and bandlets

* Wavelets for computer graphics with lifting on surfaces

* Time-frequency audio processing and denoising

* Image compression with JPEG-2000

* New and updated exercises

A Wavelet Tour of Signal Processing: The Sparse Way, Third Edition, is an invaluable resource for researchers and R&D engineers wishing to apply the theory in fields such as image processing, video processing and compression, bio-sensing, medical imaging, machine vision and communications engineering.

Stephane Mallat is Professor in Applied Mathematics at École Polytechnique, Paris, France. From 1986 to 1996 he was a Professor at the Courant Institute of Mathematical Sciences at New York University, and between 2001 and 2007, he co-founded and became CEO of an image processing semiconductor company.Includes all the latest developments since the book was published in 1999, including its

application to JPEG 2000 and MPEG-4

Algorithms and numerical examples are implemented in Wavelab, a MATLAB toolbox

Balances presentation of the mathematics with applications to signal processing

This hands-on textbook/reference presents a comprehensive review of key distributed graph algorithms for computer network applications, with a particular emphasis on practical implementation. Each chapter opens with a concise introduction to a specific problem, supporting the theory with numerous examples, before providing a list of relevant algorithms. These algorithms are described in detail from conceptual basis to pseudocode, complete with graph templates for the stepwise implementation of the algorithm, followed by its analysis. The chapters then conclude with summarizing notes and programming exercises.

Topics and features: introduces a range of fundamental graph algorithms, covering spanning trees, graph traversal algorithms, routing algorithms, and self-stabilization; reviews graph-theoretical distributed approximation algorithms with applications in ad hoc wireless networks; describes in detail the implementation of each algorithm, with extensive use of supporting examples, and discusses their concrete network applications; examines key graph-theoretical algorithm concepts, such as dominating sets, and parameters for mobility and energy levels of nodes in wireless ad hoc networks, and provides a contemporary survey of each topic; presents a simple simulator, developed to run distributed algorithms; provides practical exercises at the end of each chapter.

This classroom-tested and easy-to-follow textbook is essential reading for all graduate students and researchers interested in discrete mathematics, algorithms and computer networks.

Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved.

Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

There is a selected solutions manual for instructors for the new edition.

Discrete mathematics has the answer to these—and many other—questions of picking, choosing, and shuffling. T. S. Michael's gem of a book brings this vital but tough-to-teach subject to life using examples from real life and popular culture. Each chapter uses one problem—such as slicing a pizza—to detail key concepts about counting numbers and arranging finite sets. Michael takes a different perspective in tackling each of eight problems and explains them in differing degrees of generality, showing in the process how the same mathematical concepts appear in varied guises and contexts. In doing so, he imparts a broader understanding of the ideas underlying discrete mathematics and helps readers appreciate and understand mathematical thinking and discovery.

This book explains the basic concepts of discrete mathematics and demonstrates how to apply them in largely nontechnical language. The explanations and formulas can be grasped with a basic understanding of linear equations.

The Fortran 2003 Handbook is the definitive and comprehensive guide to Fortran 2003, the latest standard version of Fortran. This all-inclusive volume offers a reader-friendly, easy-to-follow and informal description of Fortran 2003, and has been developed to provide not only a readable explanation of features, but also some rationale for the inclusion of features and their use. Experienced Fortran 95 programmers will be able to use this volume to assimilate quickly those features in Fortran 2003 that are not in Fortran 95 (Fortran 2003 contains all of the features of Fortran 95).

Features and benefits:

• The complete syntax of Fortran 2003 is supplied.

• Each of the intrinsic standard procedures is described in detail.

• There is a complete listing of the new, obsolescent, and deleted features.

• Numerous examples are given throughout, providing insights into intended uses and interactions of the features.

• IEEE module procedures are covered thoroughly.

• Chapters begin with a summary of the main terms and concepts described.

• Models provide the reader with insight into the language.

Key Topics:

• Fortran Concepts and Terms

• Language Elements and Source Form

• Data Types

• Block Constructs and Execution Control

• I/O Processing and Editing

• Interoperability with C

• Standard Intrinsic Procedures

This highly versatile and authoritative handbook is intended for anyone who wants a comprehensive survey of Fortran 2003, including those familiar with programming language concepts but unfamiliar with Fortran. It offers a practical description of Fortran 2003 for professionals developing sophisticated application and commercial software in Fortran, as well as developers of Fortran compilers.

All authors have been heavily involved in the development of Fortran standards. They have served on national and international Fortran standard development committees, and include a chair, convenors and editors of the Fortran 90, 95, and 2003 standards. In addition, Walt Brainerd is the owner of The Fortran Company, Tucson, AZ, USA.

The first part provides an introduction to basic procedures for handling and operating with text strings. Then, it reviews major mathematical modeling approaches. Statistical and geometrical models are also described along with main dimensionality reduction methods. Finally, it presents some specific applications such as document clustering, classification, search and terminology extraction.

All descriptions presented are supported with practical examples that are fully reproducible. Further reading, as well as additional exercises and projects, are proposed at the end of each chapter for those readers interested in conducting further experimentation.

The Handbook of Applied Cryptography provides a treatment that is multifunctional:

It serves as an introduction to the more practical aspects of both conventional and public-key cryptography

It is a valuable source of the latest techniques and algorithms for the serious practitioner

It provides an integrated treatment of the field, while still presenting each major topic as a self-contained unit

It provides a mathematical treatment to accompany practical discussions

It contains enough abstraction to be a valuable reference for theoreticians while containing enough detail to actually allow implementation of the algorithms discussed

Now in its third printing, this is the definitive cryptography reference that the novice as well as experienced developers, designers, researchers, engineers, computer scientists, and mathematicians alike will use.

The common approach to presenting mathematical concepts and operators is to define them in terms of properties they satisfy, and then based on these definitions develop ways of computing the result of applying the operators and prove them correct. This book is mainly written for computer science students, so here the author takes a different approach: he starts by defining ways of calculating the results of applying the operators and then proves that they satisfy various properties. After justifying his underlying approach the author offers detailed chapters covering propositional logic, predicate calculus, sets, relations, discrete structures, structured types, numbers, and reasoning about programs.

The book contains chapter and section summaries, detailed proofs and many end-of-section exercises -- key to the learning process. The book is suitable for undergraduate and graduate students, and although the treatment focuses on areas with frequent applications in computer science, the book is also suitable for students of mathematics and engineering.The 54 revised full papers presented in this volume were carefully reviewed and selected from 148 submissions.

The Algorithms and Data Structures Symposium - WADS (formerly Workshop on Algorithms And Data Structures), which alternates with the Scandinavian Workshop on Algorithm Theory, is intended as a forum for researchers in the area of design and analysis of algorithms and data structures. WADS includes papers presenting original research on algorithms and data structures in all areas, including bioinformatics, combinatorics, computational geometry, databases, graphics, and parallel and distributed computing.

The glossary defines over 50 R terms using SAS/SPSS jargon and again using R jargon. The table of contents and the index allow you to find equivalent R functions by looking up both SAS statements and SPSS commands. When finished, you will be able to import data, manage and transform it, create publication quality graphics, and perform basic statistical analyses.

This new edition has updated programming, an expanded index, and even more statistical methods covered in over 25 new sections.

Key features:

* Begins with a brief survey of basic notions in algebraic and differential geometry, Lie groups and Lie algebras

* Examines how, in a new chapter, Clifford algebra is relevant to robot kinematics and Euclidean geometry in 3D

* Introduces mathematical concepts and methods using examples from robotics

* Solves substantial problems in the design and control of robots via new methods

* Provides solutions to well-known enumerative problems in robot kinematics using intersection theory on the group of rigid body motions

* Extends dynamics, in another new chapter, to robots with end-effector constraints, which lead to equations of motion for parallel manipulators

Geometric Fundamentals of Robotics serves a wide audience of graduate students as well as researchers in a variety of areas, notably mechanical engineering, computer science, and applied mathematics. It is also an invaluable reference text.

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From a Review of the First Edition:

"The majority of textbooks dealing with this subject cover various topics in kinematics, dynamics, control, sensing, and planning for robot manipulators. The distinguishing feature of this book is that it introduces mathematical tools, especially geometric ones, for solving problems in robotics. In particular, Lie groups and allied algebraic and geometric concepts are presented in a comprehensive manner to an audience interested in robotics. The aim of the author is to show the power and elegance of these methods as they apply to problems in robotics."

--MathSciNet

This biography attempts to shed light on all facets of Zermelo's life and achievements. Personal and scientific aspects are kept separate as far as coherence allows, in order to enable the reader to follow the one or the other of these threads. The description of his personality owes much to conversations with his late wife Gertrud. The presentation of his work explores motivations, aims, acceptance, and influence. Selected proofs and information gleaned from unpublished notes and letters add to the analysis.

All facts presented are documented by appropriate sources. The biography contains more than 40 photos and facsimiles, most of them provided by Gertrud Zermelo and published here for the first time.

Key features:

* Introductory chapters present the main ideas and topics in graph theory—walks, paths and cycles, radius, diameter, eccentricity, cuts and connectivity, trees

* Subsequent chapters examine specialized topics and applications

* Numerous examples and illustrations

* Comprehensive index and bibliography, with suggested literature for more advanced material

New to the second edition:

* New chapters on labeling and communications networks and small-worlds

* Expanded beginner’s material in the early chapters, including more examples, exercises, hints and solutions to key problems

* Many additional changes, improvements, and corrections throughout resulting from classroom use and feedback

Striking a balance between a theoretical and practical approach with a distinctly applied flavor, this gentle introduction to graph theory consists of carefully chosen topics to develop graph-theoretic reasoning for a mixed audience. Familiarity with the basic concepts of set theory, along with some background in matrices and algebra, and a little mathematical maturity are the only prerequisites.

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From a review of the first edition:

"Altogether the book gives a comprehensive introduction to graphs, their theory and their application...The use of the text is optimized when the exercises are solved. The obtained skills improve understanding of graph theory as well... It is very useful that the solutions of these exercises are collected in an appendix."

—Simulation News Europe

Algorithms exert an extraordinary level of influence on our everyday lives - from dating websites and financial trading floors, through to online retailing and internet searches - Google's search algorithm is now a more closely guarded commercial secret than the recipe for Coca-Cola. Algorithms follow a series of instructions to solve a problem and will include a strategy to produce the best outcome possible from the options and permutations available. Used by scientists for many years and applied in a very specialized way they are now increasingly employed to process the vast amounts of data being generated, in investment banks, in the movie industry where they are used to predict success or failure at the box office and by social scientists and policy makers.

What if everything in life could be reduced to a simple formula? What if numbers were able to tell us which partners we were best matched with – not just in terms of attractiveness, but for a long-term committed marriage? Or if they could say which films would be the biggest hits at the box office, and what changes could be made to those films to make them even more successful? Or even who is likely to commit certain crimes, and when? This may sound like the world of science fiction, but in fact it is just the tip of the iceberg in a world that is increasingly ruled by complex algorithms and neural networks.

In The Formula, Luke Dormehl takes readers inside the world of numbers, asking how we came to believe in the all-conquering power of algorithms; introducing the mathematicians, artificial intelligence experts and Silicon Valley entrepreneurs who are shaping this brave new world, and ultimately asking how we survive in an era where numbers can sometimes seem to create as many problems as they solve.

The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

The author collects the main results in the field in this up-to-date, comprehensive reference volume. He highlights significant achievements in the area, and points to research directions and open problems. The book will be of interest to researchers and graduate students in theoretical computer science and mathematics, in particular those working in algebraic combinatorics and combinatorics on words. It will also be of interest to specialists in other branches of mathematics, theoretical physics, and computational biology.

Leading experts have joined forces for the first time to explain the state of the art in quantum computing, hash-based cryptography, code-based cryptography, lattice-based cryptography, and multivariate cryptography. Mathematical foundations and implementation issues are included.

This book is an essential resource for students and researchers who want to contribute to the field of post-quantum cryptography.

The book will be of interest to musicians and musicologists, particularly those engaged with Indian music.

The second part of the book begins with a consideration of various types of matrices encountered in statistics, such as projection matrices and positive definite matrices, and describes the special properties of those matrices. The second part also describes some of the many applications of matrix theory in statistics, including linear models, multivariate analysis, and stochastic processes. The brief coverage in this part illustrates the matrix theory developed in the first part of the book. The first two parts of the book can be used as the text for a course in matrix algebra for statistics students, or as a supplementary text for various courses in linear models or multivariate statistics.

The third part of this book covers numerical linear algebra. It begins with a discussion of the basics of numerical computations, and then describes accurate and efficient algorithms for factoring matrices, solving linear systems of equations, and extracting eigenvalues and eigenvectors. Although the book is not tied to any particular software system, it describes and gives examples of the use of modern computer software for numerical linear algebra. This part is essentially self-contained, although it assumes some ability to program in Fortran or C and/or the ability to use R/S-Plus or Matlab. This part of the book can be used as the text for a course in statistical computing, or as a supplementary text for various courses that emphasize computations.

The book includes a large number of exercises with some solutions provided in an appendix.

The book contains close to150 figures produced with lattice. Many of the examples emphasize principles of good graphical design; almost all use real data sets that are publicly available in various R packages. All code and figures in the book are also available online, along with supplementary material covering more advanced topics.

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