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  • Concentration Inequalities for Sums and Martingales

    Series series Mathematics and Statistics (R0)
    The purpose of this book is to provide an overview of historical and recent results on concentration inequalities for sums of independent random variables and for martingales.The first chapter is devoted to classical asymptotic results in probability such as the strong law of large numbers and the central limit theorem. Our goal is to show that it is really interesting to make use of concentration ... Read more

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    Cures Many Mathematical Ills

    by Paul J. Nahin ...
    Series series Princeton Science Library
    In the mid-eighteenth century, Swiss-born mathematician Leonhard Euler developed a formula so innovative and complex that it continues to inspire research, discussion, and even the occasional limerick. Dr. Euler's Fabulous Formula shares the fascinating story of this groundbreaking formula—long regarded as the gold standard for mathematical beauty—and shows why it still lies at the heart of ... Read more

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  • Meta Math!

    The Quest for Omega

    Gregory Chaitin, one of the world’s foremost mathematicians, leads us on a spellbinding journey, illuminating the process by which he arrived at his groundbreaking theory.Chaitin’s revolutionary discovery, the Omega number, is an exquisitely complex representation of unknowability in mathematics. His investigations shed light on what we can ultimately know about the universe and the very nature of ... Read more

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  • A Course in Mathematical Analysis: Volume 1, Foundations and Elementary Real Analysis

    The three volumes of A Course in Mathematical Analysis provide a full and detailed account of all those elements of real and complex analysis that an undergraduate mathematics student can expect to encounter in their first two or three years of study. Containing hundreds of exercises, examples and applications, these books will become an invaluable resource for both students and instructors. This ... Read more

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  • Fractals in Probability and Analysis

    Series Book 162 - Cambridge Studies in Advanced Mathematics
    This is a mathematically rigorous introduction to fractals which emphasizes examples and fundamental ideas. Building up from basic techniques of geometric measure theory and probability, central topics such as Hausdorff dimension, self-similar sets and Brownian motion are introduced, as are more specialized topics, including Kakeya sets, capacity, percolation on trees and the traveling salesman ... Read more

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  • On the Teaching of Linear Algebra

    Edited by J.-L. Dorier ...
    Series Book 23 - Mathematics Education Library
    To a large extent, it lies, no doubt, in what is presented in this work under the title of ‘meta lever‘, a method which it is certainly interesting to develop and further refine. There exists in mathematics courses a strange prudery which forbids one to ask questions such as, ‹‹ Why are we doing this? », ‹‹ At what is the objective aimed? », whereas it is usually easy to reply to such questions, ... Read more

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  • Pseudodifferential Equations Over Non-Archimedean Spaces

    Series series Mathematics and Statistics (R0)
    Focusing on p-adic and adelic analogues of pseudodifferential equations, this monograph presents a very general theory of parabolic-type equations and their Markov processes motivated by their connection with models of complex hierarchic systems. The Gelfand-Shilov method for constructing fundamental solutions using local zeta functions is developed in a p-adic setting and several particular ... Read more

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  • Probability on Compact Lie Groups

    Series Book 70 - Probability Theory and Stochastic Modelling
    Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an ... Read more

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  • The Real and the Complex: A History of Analysis in the 19th Century

    by Jeremy Gray ...
    Series series Mathematics and Statistics (R0)
    This book contains a history of real and complex analysis in the nineteenth century, from the work of Lagrange and Fourier to the origins of set theory and the modern foundations of analysis. It studies the works of many contributors including Gauss, Cauchy, Riemann, and Weierstrass.This book is unique owing to the treatment of real and complex analysis as overlapping, inter-related subjects, in ... Read more

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  • Extensions of Positive Definite Functions

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    Series series Mathematics and Statistics (R0)
    This monograph deals with the mathematics of extending given partial data-sets obtained from experiments;Experimentalists frequently gather spectral data when the observed data is limited, e.g., by the precision of instruments; or by other limiting external factors. Here the limited information is a restriction, and the extensions take the form of full positive definite function on some prescribed ... Read more

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  • Hidden Harmony—Geometric Fantasies

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    Series series Mathematics and Statistics (R0)
    This book is a history of complex function theory from its origins to 1914, when the essential features of the modern theory were in place. It is the first history of mathematics devoted to complex function theory, and it draws on a wide range of published and unpublished sources. In addition to an extensive and detailed coverage of the three founders of the subject – Cauchy, Riemann, and ... Read more

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  • A First Course in Analysis

    Series series Cambridge Mathematical Textbooks
    This rigorous textbook is intended for a year-long analysis or advanced calculus course for advanced undergraduate or beginning graduate students. Starting with detailed, slow-paced proofs that allow students to acquire facility in reading and writing proofs, it clearly and concisely explains the basics of differentiation and integration of functions of one and several variables, and covers the ... Read more

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