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This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

Computer science. --- Computer science --- Mathematical analysis. --- Analysis (Mathematics). --- Computer Science. --- Mathematics of Computing. --- Analysis. --- Mathematics. --- 517.1 Mathematical analysis --- Mathematical analysis --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Informatics --- Mathematics --- Global analysis (Mathematics). --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Computer science—Mathematics.

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This book is a comprehensive, unifying introduction to the field of mathematical analysis and the mathematics of computing. It develops the relevant theory at a modern level and it directly relates modern mathematical ideas to their diverse applications. The authors develop the whole theory. Starting with a simple axiom system for the real numbers, they then lay the foundations, developing the theory, exemplifying where it's applicable, in turn motivating further development of the theory. They progress from sets, structures, and numbers to metric spaces, continuous functions in metric spaces, linear normed spaces and linear mappings; and then differential calculus and its applications, the integral calculus, the gamma function, and linear integral operators. They then present important aspects of approximation theory, including numerical integration. The remaining parts of the book are devoted to ordinary differential equations, the discretization of operator equations, and numerical solutions of ordinary differential equations. This textbook contains many exercises of varying degrees of difficulty, suitable for self-study, and at the end of each chapter the authors present more advanced problems that shed light on interesting features, suitable for classroom seminars or study groups. It will be valuable for undergraduate and graduate students in mathematics, computer science, and related fields such as engineering. This is a rich field that has experienced enormous development in recent decades, and the book will also act as a reference for graduate students and practitioners who require a deeper understanding of the methodologies, techniques, and foundations.

Mathematical analysis --- Mathematics --- Computer science --- Computer. Automation --- analyse (wiskunde) --- computers --- informatica --- externe fixatie (geneeskunde --- wiskunde --- computerkunde

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This book constitutes the refereed proceedings of the 5th International Symposium on Stochastic Algorithms, Foundations and Applications, SAGA 2009, held in Sapporo, Japan, in October 2009. The 15 revised full papers presented together with 2 invited papers were carefully reviewed and selected from 22 submissions. The papers are organized in topical sections on learning, graphs, testing, optimization and caching, as well as stochastic algorithms in bioinformatics.

Algorithms --- Stochastic approximation --- Computer science --- Mathematical Theory --- Computer Science --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Computer science. --- Data structures (Computer science). --- Computers. --- Algorithms. --- Mathematical statistics. --- Probabilities. --- Computer Science. --- Theory of Computation. --- Data Structures. --- Probability Theory and Stochastic Processes. --- Algorithm Analysis and Problem Complexity. --- Computation by Abstract Devices. --- Probability and Statistics in Computer Science. --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Algorism --- Algebra --- Arithmetic --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Cybernetics --- Machine theory --- Calculators --- Cyberspace --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Informatics --- Science --- Statistical methods --- Foundations --- Approximation theory --- Stochastic processes --- Information theory. --- Data structures (Computer scienc. --- Distribution (Probability theory. --- Computer software. --- Distribution functions --- Frequency distribution --- Characteristic functions --- Communication theory --- Communication --- Software, Computer --- Artificial intelligence—Data processing. --- Computer science—Mathematics. --- Data Science. --- Probability Theory.

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This book constitutes the refereed proceedings of the 20th International Conference on Algorithmic Learning Theory, ALT 2009, held in Porto, Portugal, in October 2009, co-located with the 12th International Conference on Discovery Science, DS 2009. The 26 revised full papers presented together with the abstracts of 5 invited talks were carefully reviewed and selected from 60 submissions. The papers are divided into topical sections of papers on online learning, learning graphs, active learning and query learning, statistical learning, inductive inference, and semisupervised and unsupervised learning. The volume also contains abstracts of the invited talks: Sanjoy Dasgupta, The Two Faces of Active Learning; Hector Geffner, Inference and Learning in Planning; Jiawei Han, Mining Heterogeneous; Information Networks By Exploring the Power of Links, Yishay Mansour, Learning and Domain Adaptation; Fernando C.N. Pereira, Learning on the Web.

Computer algorithms --- Machine learning --- Computer Science --- Mechanical Engineering - General --- Mechanical Engineering --- Engineering & Applied Sciences --- Information Technology --- Artificial Intelligence --- Computer science. --- Computer programming. --- Data mining. --- Information storage and retrieval. --- Artificial intelligence. --- Computational linguistics. --- Pattern recognition. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Programming Techniques. --- Data Mining and Knowledge Discovery. --- Language Translation and Linguistics. --- Pattern Recognition. --- Information Storage and Retrieval. --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Automatic language processing --- Language and languages --- Language data processing --- Linguistics --- Natural language processing (Linguistics) --- Applied linguistics --- Cross-language information retrieval --- Mathematical linguistics --- Multilingual computing --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Machine theory --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Algorithmic knowledge discovery --- Factual data analysis --- KDD (Information retrieval) --- Knowledge discovery in data --- Knowledge discovery in databases --- Mining, Data --- Database searching --- Computers --- Electronic computer programming --- Electronic digital computers --- Programming (Electronic computers) --- Coding theory --- Informatics --- Science --- Data processing --- Programming --- Natural language processing (Computer science). --- Optical pattern recognition. --- Information storage and retrieva. --- Artificial Intelligence. --- Natural Language Processing (NLP). --- NLP (Computer science) --- Artificial intelligence --- Human-computer interaction --- Semantic computing --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Information storage and retrieval systems. --- Automatic data storage --- Automatic information retrieval --- Automation in documentation --- Computer-based information systems --- Data processing systems --- Data storage and retrieval systems --- Discovery systems, Information --- Information discovery systems --- Information processing systems --- Information retrieval systems --- Machine data storage and retrieval --- Mechanized information storage and retrieval systems --- Computer systems --- Electronic information resources --- Data libraries --- Digital libraries --- Information organization --- Information retrieval

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This book constitutes the proceedings of the 24th International Conference on Algorithmic Learning Theory, ALT 2013, held in Singapore in October 2013, and co-located with the 16th International Conference on Discovery Science, DS 2013. The 23 papers presented in this volume were carefully reviewed and selected from 39 submissions. In addition the book contains 3 full papers of invited talks. The papers are organized in topical sections named: online learning, inductive inference and grammatical inference, teaching and learning from queries, bandit theory, statistical learning theory, Bayesian/stochastic learning, and unsupervised/semi-supervised learning.

Mechanical Engineering --- Engineering & Applied Sciences --- Computer Science --- Mechanical Engineering - General --- Computer science. --- Computers. --- Algorithms. --- Computer logic. --- Mathematical logic. --- Artificial intelligence. --- Pattern recognition. --- Computer Science. --- Artificial Intelligence (incl. Robotics). --- Mathematical Logic and Formal Languages. --- Algorithm Analysis and Problem Complexity. --- Computation by Abstract Devices. --- Logics and Meanings of Programs. --- Pattern Recognition. --- Computer algorithms --- Machine learning --- Computer software. --- Logic design. --- Optical pattern recognition. --- Artificial Intelligence. --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Design, Logic --- Design of logic systems --- Digital electronics --- Electronic circuit design --- Logic circuits --- Machine theory --- Switching theory --- Software, Computer --- Computer systems --- Informatics --- Science --- AI (Artificial intelligence) --- Artificial thinking --- Electronic brains --- Intellectronics --- Intelligence, Artificial --- Intelligent machines --- Machine intelligence --- Thinking, Artificial --- Bionics --- Cognitive science --- Digital computer simulation --- Electronic data processing --- Logic machines --- Self-organizing systems --- Simulation methods --- Fifth generation computers --- Neural computers --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Computer science logic --- Logic, Symbolic and mathematical --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Cybernetics --- Calculators --- Cyberspace --- Algorism --- Algebra --- Arithmetic --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Mathematics --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Foundations