An Introduction to Kolmogorov Complexity and Its Applications (Texts in Computer Science)

“The book is outstanding and admirable in many respects. ... is necessary reading for all kinds of readers from undergraduate students to top authorities in the field.” Journal of Symbolic Logic Written by two experts in the field, this is the only comprehensive and unified treatment of the central ideas and applications of Kolmogorov complexity. The book presents a thorough treatment of the subject with a wide range of illustrative applications. Such applications include the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and the thermodynamics of computing. It will be ideal for advanced undergraduate students, graduate students, and researchers in computer science, mathematics, cognitive sciences, philosophy, artificial intelligence, statistics, and physics. The book is self-contained in that it contains the basic requirements from mathematics and computer science. Included are also numerous problem sets, comments, source references, and hints to solutions of problems. New topics in this edition include Omega numbers, Kolmogorov–Loveland randomness, universal learning, communication complexity, Kolmogorov's random graphs, time-limited universal distribution, Shannon information and others.

An Introduction to Kolmogorov Complexity and Its Applications

LI, Ming

Vitányi, Paul

Reference

Springer-Nature New York Inc

Providing a broad but in-depth introduction to neural network and machine learning in a statistical framework, this book provides a single, comprehensive resource for study and further research. All the major popular neural network models and statistical learning approaches are covered with examples and exercises in every chapter to develop a practical working understanding of the content.
Each of the twenty-five chapters includes state-of-the-art descriptions and important research results on the respective topics. The broad coverage includes the multilayer perceptron, the Hopfield network, associative memory models, clustering models and algorithms, the radial basis function network, recurrent neural networks, principal component analysis, nonnegative matrix factorization, independent component analysis, discriminant analysis, support vector machines, kernel methods, reinforcement learning, probabilistic and Bayesian networks, data fusion and ensemble learning, fuzzy sets and logic, neurofuzzy models, hardware implementations, and some machine learning topics. Applications to biometric/bioinformatics and data mining are also included.
Focusing on the prominent accomplishments and their practical aspects, academic and technical staff, graduate students and researchers will find that this provides a solid foundation and encompassing reference for the fields of neural networks, pattern recognition, signal processing, machine learning, computational intelligence, and data mining.

Neural Networks and Statistical Learning

Computers & Technology

Du, Ke-Lin

Swamy, M.N.S.

Computer Science

This book explains the principal techniques of data mining, for classification, association rule mining and clustering. Each topic is clearly explained and illustrated by detailed examples, with a focus on algorithms rather than mathematical formalism.

Principles of Data Mining (Undergraduate Topics in Computer Science)

Bramer, Max

John Vinceexplains a wide range of mathematical techniques and problem-solving strategies associated with computer games, computer animation, virtual reality, CAD and other areas of computer graphics in this completely revised and expanded fifth edition.
The first five chapters cover a general introduction, number sets, algebra, trigonometry and coordinate systems, which are employed in the following chapters on vectors, matrix algebra, transforms, interpolation, curves and patches, analytic geometry and barycentric coordinates. Following this, the reader is introduced to the relatively new topic of geometric algebra, followed by two chapters that introduce differential and integral calculus. Finally, there is a chapter on worked examples.
Mathematics for Computer Graphics covers all of the key areas of the subject, including:· Number sets· Algebra
· Trigonometry
· Coordinate systems· Determinants· Vectors· Quaternions
· Matrix algebra
· Geometric transforms· Interpolation· Curves and surfaces
· Analytic geometry
· Barycentric coordinates
· Geometric algebra· Differential calculus· Integral calculus
This fifth edition contains over 120 worked examples and over 320 colour illustrations, which are central to the author’s descriptive writing style. Mathematics for Computer Graphics provides a sound understanding of the mathematics required for computer graphics, giving a fascinating insight into the design of computer graphics software and setting the scene for further reading of more advanced books and technical research papers.

Mathematics for Computer Graphics (Undergraduate Topics in Computer Science)

John A. Vince

This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students.The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography.NEW to the second edition:• Doubles the tutorial material and exercises over the first edition
• Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video• Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them• Includes several NEW "war stories" relating experiences from real-world applications
• Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java

The Algorithm Design Manual

Skiena, Steve S.

In this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers. John Vince describes a range of mathematical topics to provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author’s visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications.\nThis second edition includes new, full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will help consolidate the understanding of abstract mathematical concepts. 
Whether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.\nFrom the Back Cover\nIn this second edition of Foundation Mathematics for Computer Science, John Vince has reviewed and edited the original book and written new chapters on combinatorics, probability, modular arithmetic and complex numbers. These subjects complement the existing chapters on number systems, algebra, logic, trigonometry, coordinate systems, determinants, vectors, matrices, geometric matrix transforms, differential and integral calculus. During this journey, the author touches upon more esoteric topics such as quaternions, octonions, Grassmann algebra, Barrycentric coordinates, transfinite sets and prime numbers. John Vince describes a range of mathematical topics to provide a solid foundation for an undergraduate course in computer science, starting with a review of number systems and their relevance to digital computers, and finishing with differential and integral calculus. Readers will find that the author’s visual approach will greatly improve their understanding as to why certain mathematical structures exist, together with how they are used in real-world applications.\nThis second edition includes new, full-colour illustrations to clarify the mathematical descriptions, and in some cases, equations are also coloured to reveal vital algebraic patterns. The numerous worked examples will help consolidate the understanding of abstract mathematical concepts.\nWhether you intend to pursue a career in programming, scientific visualisation, artificial intelligence, systems design, or real-time computing, you should find the author’s literary style refreshingly lucid and engaging, and prepare you for more advanced texts.

Foundation Mathematics for Computer Science: A Visual Approach

Vince, John

Many believe mathematics is only about calculations, formulas, numbers, and strange letters. But mathematics is much more than just crunching numbers or manipulating symbols. Mathematics is about discovering patterns, uncovering hidden structures, finding counterexamples, and thinking logically. Mathematics is a way of thinking. It is an activity that is both highly creative and challenging. This book offers an introduction to mathematical reasoning for beginning university or college students, providing a solid foundation for further study in mathematics, computer science, and related disciplines. Written in a manner that directly conveys the sense of excitement and discovery at the heart of doing science, its 25 short and visually appealing chapters cover the basics of set theory, logic, proof methods, combinatorics, graph theory, and much more. In the book you will, among other things, find answers to: <ul> <li>What is a proof? What is a counterexample?</li> <li>What does it mean to say that something follows logically from a set of premises?</li> <li>What does it mean to abstract over something? </li> <li>How can knowledge and information be represented and used in calculations?</li> <li>What is the connection between Morse code and Fibonacci numbers?</li> <li>Why could it take billions of years to solve Hanoi's Tower?</li> </ul> Logical Methods is especially appropriate for students encountering such concepts for the very first time. Designed to ease the transition to a university or college level study of mathematics or computer science, it also provides an accessible and fascinating gateway to logical thinking for students of all disciplines.

Logical Methods: The Art of Thinking Abstractly and Mathematically

Antonsen, Roger

This book is an introductory text on design science, intended to support both graduate students and researchers in structuring, undertaking and presenting design science work. It builds on established design science methods as well as recent work on presenting design science studies and ethical principles for design science, and also offers novel instruments for visualizing the results, both in the form of process diagrams and through a canvas format. While the book does not presume any prior knowledge of design science, it provides readers with a thorough understanding of the subject and enables them to delve into much deeper detail, thanks to extensive sections on further reading.
Design science in information systems and technology aims to create novel artifacts in the form of models, methods, and systems that support people in developing, using and maintaining IT solutions. This work focuses on design science as applied to information systems and technology, but it also includes examples from, and perspectives of, other fields of human practice.
Chapter 1 provides an overview of design science and outlines its ties with empirical research. Chapter 2 discusses the various types and forms of knowledge that can be used and produced by design science research, while Chapter 3 presents a brief overview of common empirical research strategies and methods. Chapter 4 introduces a methodological framework for supporting researchers in doing design science research as well as in presenting their results. This framework includes five core activities, which are described in detail in Chapters 5 to 9. Chapter 10 discusses how to communicate design science results, while Chapter 11 compares the proposed methodological framework with methods for systems development and shows how they can be combined. Chapter 12 discusses how design science relates to research paradigms, in particular to positivism and interpretivism. Lastly, Chapter 13 discusses ethical issues and principles for design science research.

An Introduction to Design Science

Perjons Erik Johannesson Paul

Erik Perjons

While other textbooks devote their pages to explaining introductory programming concepts, The Python Workbook focuses exclusively on exercises, following the philosophy that computer programming is a skill best learned through experience and practice. Designed to support and encourage hands-on learning about programming, this student-friendly work contains 174 exercises, spanning a variety of academic disciplines and everyday situations. Solutions to selected exercises are also provided, supported by brief annotations that explain the technique used to solve the problem, or highlight specific points of Python syntax. No background knowledge is required to solve the exercises, beyond the material covered in a typical introductory Python programming course. Undergraduate students undergoing their first programming course and wishing to enhance their programming abilities will find the exercises and solutions provided in this book to be ideal for their needs.

The Python Workbook: A Brief Introduction With Exercises and Solutions

Stephenson, Ben

This book offers a concise and gentle introduction to finite element programming in Python based on the popular FEniCS software library. Using a series of examples, including the Poisson equation, the equations of linear elasticity, the incompressible Navier–Stokes equations, and systems of nonlinear advection–diffusion–reaction equations, it guides readers through the essential steps to quickly solving a PDE in FEniCS, such as how to define a finite variational problem, how to set boundary conditions, how to solve linear and nonlinear systems, and how to visualize solutions and structure finite element Python programs. 
This book is open access under a CC BY license.

Solving PDEs in Python: The FEniCS Tutorial I (Simula SpringerBriefs on Computing, 3)

Langtangen, Hans Petter Petter

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