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Today, nearly every undergraduate mathematics program requires at least one semester of real analysis. Often, students consider this course to be the most challenging or even intimidating of all their mathematics major requirements. The primary goal of A Problem Book in Real Analysis is to alleviate those concerns by systematically solving the problems related to the core concepts of most analysis courses. In doing so, the authors hope that learning analysis becomes less taxing and more satisfying. The wide variety of exercises presented in this book range from the computational to the more conceptual and varies in difficulty. They cover the following subjects: set theory; real numbers; sequences; limits of the functions; continuity; differentiability; integration; series; metric spaces; sequences; and series of functions and fundamentals of topology. Furthermore, the authors define the concepts and cite the theorems used at the beginning of each chapter. A Problem Book in Real Analysis is not simply a collection of problems; it will stimulate its readers to independent thinking in discovering analysis. Prerequisites for the reader are a robust understanding of calculus and linear algebra.

Functional analysis --- Differential equations --- Mathematical analysis --- Mathematics --- analyse (wiskunde) --- mathematische modellen --- wiskunde

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Analyse (Mathématique) --- Analyse (Wiskunde) --- Analyse mathématique --- Analysis (Mathematics) --- Mathematical analysis --- Wiskundige analyse --- Nonstandard mathematical analysis --- Analyse mathématique non standard --- 517.1 --- #KVIV --- Introduction to analysis --- 517.1 Introduction to analysis --- Analyse mathématique non standard

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Advances in bioinformatics and systems biology require improved computational methods for analyzing data, while progress in molecular biology is in turn influencing the development of computer science methods. This book introduces some key problems in bioinformatics, discusses the models used to formally describe these problems, and analyzes the algorithmic approaches used to solve them. After introducing the basics of molecular biology and algorithmics, Part I explains string algorithms and alignments; Part II details the field of physical mapping and DNA sequencing; and Part III examines the application of algorithmics to the analysis of biological data. Exciting application examples include predicting the spatial structure of proteins, and computing haplotypes from genotype data. This book describes topics in detail and presents formal models in a mathematically precise, yet intuitive manner, with many figures and chapter summaries, detailed derivations, and examples. It is well suited as an introduction into the field of bioinformatics, and will benefit students and lecturers in bioinformatics and algorithmics, while also offering practitioners an update on current research topics.

Biomathematics. Biometry. Biostatistics --- moleculaire biologie --- complexe analyse (wiskunde) --- Programming --- Molecular biology --- Complex analysis --- bio-informatica --- Algorithms. --- Bioinformatics --- Mathematics. --- Informatiques -- bioinformatique = informatics -- biological informatics --- Informatiques -- programmation algorithmique = informatics -- algorithmic programming

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An introduction to a broad range of topics in deep learning, covering mathematical and conceptual background, deep learning techniques used in industry, and research perspectives. Deep learning is a form of machine learning that enables computers to learn from experience and understand the world in terms of a hierarchy of concepts. Because the computer gathers knowledge from experience, there is no need for a human computer operator to formally specify all the knowledge that the computer needs. The hierarchy of concepts allows the computer to learn complicated concepts by building them out of simpler ones; a graph of these hierarchies would be many layers deep. This book introduces a broad range of topics in deep learning. The text offers mathematical and conceptual background, covering relevant concepts in linear algebra, probability theory and information theory, numerical computation, and machine learning. It describes deep learning techniques used by practitioners in industry, including deep feedforward networks, regularization, optimization algorithms, convolutional networks, sequence modeling, and practical methodology; and it surveys such applications as natural language processing, speech recognition, computer vision, online recommendation systems, bioinformatics, and videogames. Finally, the book offers research perspectives, covering such theoretical topics as linear factor models, autoencoders, representation learning, structured probabilistic models, Monte Carlo methods, the partition function, approximate inference, and deep generative models. Deep Learning can be used by undergraduate or graduate students planning careers in either industry or research, and by software engineers who want to begin using deep learning in their products or platforms. A website offers supplementary material for both readers and instructors.

Probability theory --- Information systems --- Artificial intelligence. Robotics. Simulation. Graphics --- Mathematical linguistics --- analyse (wiskunde) --- Machine learning. --- Artificiële intelligentie --- Machine learning --- Learning, Machine --- Artificial intelligence --- Machine theory --- למידה חשובית --- Apprentissage automatique --- Machine Learning --- Apprentissage automatique. --- Transfer Learning --- Learning, Transfer --- Machinaal leren --- 681.3*I2 --- 681.3*I2 Artificial intelligence. AI --- Artificial intelligence. AI --- deep learning --- machine learning --- artificiële intelligentie (AI) --- Informatique --- Intelligence artificielle

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There has been a flurry of activity in recent years in the loosely defined area of holomorphic spaces. This book discusses the most well-known and widely used spaces of holomorphic functions in the unit ball of C^n. Spaces discussed include the Bergman spaces, the Hardy spaces, the Bloch space, BMOA, the Dirichlet space, the Besov spaces, and the Lipschitz spaces. Most proofs in the book are new and simpler than the existing ones in the literature. The central idea in almost all these proofs is based on integral representations of holomorphic functions and elementary properties of the Bergman kernel, the Bergman metric, and the automorphism group. The unit ball was chosen as the setting since most results can be achieved there using straightforward formulas without much fuss. The book can be read comfortably by anyone familiar with single variable complex analysis; no prerequisite on several complex variables is required. The author has included exercises at the end of each chapter that vary greatly in the level of difficulty. Kehe Zhu is Professor of Mathematics at State University of New York at Albany. His previous books include Operator Theory in Function Spaces (Marcel Dekker 1990), Theory of Bergman Spaces, with H. Hedenmalm and B. Korenblum (Springer 2000), and An Introduction to Operator Algebras (CRC Press 1993).

Mathematical analysis --- Analytical spaces --- analyse (wiskunde) --- Holomorphic functions --- Fonctions holomorphes --- EPUB-LIV-FT SPRINGER-B LIVMATHE --- Holomorphic functions. --- Unit ball. --- Differential equations, partial. --- Global analysis (Mathematics). --- Several Complex Variables and Analytic Spaces. --- Analysis. --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Partial differential equations --- Functions of complex variables. --- Mathematical analysis. --- Analysis (Mathematics). --- 517.1 Mathematical analysis --- Complex variables --- Elliptic functions --- Functions of real variables