This book offers a gentle introduction to the geometry of numbers from a modern Fourier-analytic point of view. One of the main themes is the transfer of geometric knowledge of a polytope to analytic knowledge of its Fourier transform. The Fourier transform preserves all of the information of a polytope, and turns its geometry into analysis. The ......
This book gives a self-contained introduction to the modern ideas and problems of harmonic analysis. Intended for third- and fourth-year undergraduates, the book only requires basic knowledge of real analysis, and covers necessary background in measure theory, Lebesgue integration and approximation theorems. The book motivates the study of ......
It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. ......
This textbook offers a rigorous mathematical introduction to cellular automata (CA). Numerous colorful graphics illustrate the many intriguing phenomena, inviting undergraduates to step into the rich field of symbolic dynamics. Beginning with a brief history, the first half of the book establishes the mathematical foundations of cellular automata. ......
A Constructive Approach Through Interval Arithmetic
Real Analysis: A Constructive Approach Through Interval Arithmetic presents a careful treatment of calculus and its theoretical underpinnings from the constructivist point of view. This leads to an important and unique feature of this book: All existence proofs are direct, so showing that the numbers or functions in question exist means exactly ......
Although there is no precise definition of a ""fractal"", it is usually understood to be a set whose smaller parts, when magnified, resemble the whole. Self-similar and self-affine sets are those for which this resemblance is precise and given by a contracting similitude or affine transformation. The present book is devoted to this most basic ......
The analysis and interpretation of mathematical models is an essential part of the modern scientific process. Topics in Applied Mathematics and Modeling is designed for a one-semester course in this area aimed at a wide undergraduate audience in the mathematical sciences. The prerequisite for access is exposure to the central ideas of linear ......
The main topic of the book is amenable groups, i.e., groups on which there exist invariant finitely additive measures. It was discovered that the existence or non-existence of amenability is responsible for many interesting phenomena such as, e.g., the Banach-Tarski Paradox about breaking a sphere into two spheres of the same radius. Since then, ......
