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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 --- Analyse mathématique

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toegepaste wiskunde --- Mathematical analysis --- analyse (wiskunde) --- Integral transforms. --- Transformations intégrales --- Integral transforms --- 517.4 --- transforms --- Laplace transformatie --- Fourier --- #TCPW W3.0 --- #TCPW W3.3 --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Functional determinants. Integral transforms. Operational calculus --- 517.4 Functional determinants. Integral transforms. Operational calculus --- Transformations intégrales

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Engineering mathematics. --- Engineering mathematics --- 51-7 --- Engineering --- Engineering analysis --- Mathematical analysis --- 51-7 Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc. --- Mathematical studies and methods in other sciences. Scientific mathematics. Actuarial mathematics. Biometrics. Econometrics etc --- Mathematics --- Numerical analysis --- wiskunde --- ingenieurswetenschappen --- Probability theory --- Algebra --- Number theory --- Analyse (wiskunde). --- Toegepaste wiskunde. --- mathematics --- computer applications --- Mathematical models --- engineering

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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 --- Aprenentatge profund --- Aprenentatge automàtic