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  • Random Matrices and Non-Commutative Probability

    par Arup Bose ...
    This is an introductory book on Non-Commutative Probability or Free Probability and Large Dimensional Random Matrices. Basic concepts of free probability are introduced by analogy with classical probability in a lucid and quick manner. It then develops the results on the convergence of large dimensional random matrices, with a special focus on the interesting connections to free probability. The ... En savoir plus

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  • Random Circulant Matrices

    Circulant matrices have been around for a long time and have been extensively used in many scientific areas. This book studies the properties of the eigenvalues for various types of circulant matrices, such as the usual circulant, the reverse circulant, and the k-circulant when the dimension of the matrices grow and the entries are random.In particular, the behavior of the spectral distribution, ... En savoir plus

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  • Large Covariance and Autocovariance Matrices

    Collections series Chapman & Hall/CRC Monographs on Statistics and Applied Probability
    Large Covariance and Autocovariance Matrices brings together a collection of recent results on sample covariance and autocovariance matrices in high-dimensional models and novel ideas on how to use them for statistical inference in one or more high-dimensional time series models. The prerequisites include knowledge of elementary multivariate analysis, basic time series analysis and basic results ... En savoir plus

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  • Patterned Random Matrices

    par Arup Bose ...
    Large dimensional random matrices (LDRM) with specific patterns arise in econometrics, computer science, mathematics, physics, and statistics. This book provides an easy initiation to LDRM. Through a unified approach, we investigate the existence and properties of the limiting spectral distribution (LSD) of different patterned random matrices as the dimension grows. The main ingredients are the ... En savoir plus

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  • A Little Book of Martingales

    Collections series Mathematics and Statistics (R0)
    This concise textbook, fashioned along the syllabus for master’s and Ph.D. programmes, covers basic results on discrete-time martingales and applications. It includes additional interesting and useful topics, providing the ability to move beyond. Adequate details are provided with exercises within the text and at the end of chapters. Basic results include Doob’s optional sampling theorem, Wald ... En savoir plus

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    Collections series Chapman & Hall/CRC Monographs and Research Notes in Mathematics
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  • Abstract Algebra

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    Collections series Mathematics and Statistics (R0)
    This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences.Applications include:Identification numbers and modular ... En savoir plus

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  • Schaum's Outline of Abstract Algebra

    Tough Test Questions? Missed Lectures? Not Rnough Time?Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get ... En savoir plus

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  • Introduction to Lattices and Order

    This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept ... En savoir plus

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  • Computational Aspects of Modular Forms and Galois Representations

    How One Can Compute in Polynomial Time the Value of Ramanujan's Tau at a Prime

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    Modular forms are tremendously important in various areas of mathematics, from number theory and algebraic geometry to combinatorics and lattices. Their Fourier coefficients, with Ramanujan's tau-function as a typical example, have deep arithmetic significance. Prior to this book, the fastest known algorithms for computing these Fourier coefficients took exponential time, except in some special ... En savoir plus

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    Collections Livre 3 - Ltcc Advanced Mathematics Series
    This book leads readers from a basic foundation to an advanced level understanding of algebra, logic and combinatorics. Perfect for graduate or PhD mathematical-science students looking for help in understanding the fundamentals of the topic, it also explores more specific areas such as invariant theory of finite groups, model theory, and enumerative combinatorics.Algebra, Logic and Combinatorics ... En savoir plus

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  • Mathematical Tools for Data Mining

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