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Mathematics --- Mathématiques --- Popular works. --- Ouvrages de vulgarisation --- Mathématiques --- Arithmetic --- Arithmétique --- History --- Histoire. --- Philosophie --- Philosophy --- Philosophy. --- Mathematics - Popular works --- Calcul --- Mathematiques --- Theorie des nombres --- Histoire

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In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab­ stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor­ ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num­ bers have shown up in other areas of mathematics, and even in physics.

p-adic numbers --- Numbers, p-adic --- Number theory --- p-adic analysis --- P-adic numbers. --- p-adic numbers. --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Theorie des nombres --- P-adiques

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The main purpose of this book is to give an overview of the developments during the last 20 years in the theory of uniformly distributed sequences. The authors focus on various aspects such as special sequences, metric theory, geometric concepts of discrepancy, irregularities of distribution, continuous uniform distribution and uniform distribution in discrete spaces. Specific applications are presented in detail: numerical integration, spherical designs, random number generation and mathematical finance. Furthermore over 1000 references are collected and discussed. While written in the style of a research monograph, the book is readable with basic knowledge in analysis, number theory and measure theory.

Mathematical analysis --- Distribution [Rectangular ] (Probability theory) --- Distribution [Uniform ] (Probability theory) --- Distribution uniforme (Théorie des probabilités) --- Mathematical sequences --- Numerical sequences --- Numerieke reeksen --- Rectangular distribution (Probability theory) --- Reeksen (Wiskunde) --- Sequences (Mathematics) --- Suites (Mathématiques) --- Suites numériques --- Uniform distribution (Probability theory) --- Uniforme verdeling (Theorie van de probabiliteiten) --- Verdeling [Uniforme ] (Theorie van de probabiliteiten) --- Wiskundige reeksen --- Applied Mathematics --- Mathematical Theory --- Engineering & Applied Sciences --- Mathematics --- Physical Sciences & Mathematics --- Number theory. --- Number Theory. --- Number study --- Numbers, Theory of --- Algebra --- Distribution, Rectangular (Probability theory) --- Distribution, Uniform (Probability theory) --- Probabilities --- Theorie des nombres --- Theorie probabiliste