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Introduction to Hilbert Spaces with Applications
Introduction to Hilbert Spaces with Applications
The Second Edition if this successful text offers a systematic exposition of the basic ideas and results of Hilbert space theory and functional analysis. It includes a simple introduction to the Lebesgue integral and a new chapter on wavelets. The book provides the reader with revised examples and updated diverse applications to differential and...
Approximation Methods for Polynomial Optimization: Models, Algorithms, and Applications (SpringerBriefs in Optimization)
Approximation Methods for Polynomial Optimization: Models, Algorithms, and Applications (SpringerBriefs in Optimization)
Polynomial optimization, as its name suggests, is used to optimize a generic multivariate polynomial function, subject to some suitable polynomial equality and/or inequality constraints. Such problem formulation dates back to the nineteenth century when the relationship between nonnegative polynomials and sum of squares (SOS) was...
Subsystems of Second Order Arithmetic (Perspectives in Logic)
Subsystems of Second Order Arithmetic (Perspectives in Logic)
Foundations of mathematics is the study of the most basic concepts and logical structure ofmathematics, with an eye to the unity of human knowl- edge. Among the most basic mathematical concepts are: number, shape, set, function, algorithm, mathematical axiom, mathematical definition, and mathematical proof. Typical questions in...
E: The Story of a Number
E: The Story of a Number
Maor attempts to give the irrational number e its rightful standing alongside pi as a fundamental constant in science and nature; he succeeds very well.... Maor writes so that both mathematical newcomers and long-time professionals alike can thoroughly enjoy his book, learn something new, and witness the ubiquity of mathematical ideas in...
Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems (Applied Logic Series)
Analysis and Synthesis of Logics: How to Cut and Paste Reasoning Systems (Applied Logic Series)
Starting with simple examples showing the relevance of cutting and pasting logics, the monograph develops a mathematical theory of combining and decomposing logics, ranging from propositional and first-order based logics to higher-order based logics as well as to non-truth functional logics. The theory covers mechanisms for combining semantic...
Fourier Transform Methods in Finance
Fourier Transform Methods in Finance

In recent years, Fourier transform methods have emerged as one of the major methodologies for the evaluation of derivative contracts, largely due to the need to strike a balance between the extension of existing pricing models beyond the traditional Black-Scholes setting and a need to evaluate prices consistently with the market...

Discrete-Signal Analysis and Design
Discrete-Signal Analysis and Design
A clear, step-by-step approach to practical uses of discrete-signal analysis and design, especially for

communications and radio engineers

This book provides an introduction to discrete-time and discrete-frequency signal processing, which is rapidly becoming an important, modern way to design and analyze electronics projects of all...

Challenges for Computational Intelligence (Studies in Computational Intelligence)
Challenges for Computational Intelligence (Studies in Computational Intelligence)
In the year 1900 at the International Congress of Mathematicians in Paris David Hilbert delivered what is now considered the most important talk ever given in the history of mathematics. In this talk Hilbert outlined his philosophy of mathematics and proposed 23 major problems worth working at in future. Some of these problems were in fact more...
Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever
Great Feuds in Mathematics: Ten of the Liveliest Disputes Ever

Mathematical disputes offer indisputable proof that great mathematical minds are calculating in more ways than one. Fueled by greed, jealousy, ambition, and ego, they have plots worthy of a soap opera, pitting brother against brother, father against son, and student against mentor.

In the sixteenth century, Cardano and Tartaglia battled...

Frontiers of Evolutionary Computation
Frontiers of Evolutionary Computation
This book is a collection of essays, authored by eminent scholars in evolutionary computation (EC), artificial intelligence (AI), operations research, complexity theory and mathematics. Each essay revolves around important, interesting and unresolved questions in the field of evolutionary computation....
Finite Frames: Theory and Applications (Applied and Numerical Harmonic Analysis)
Finite Frames: Theory and Applications (Applied and Numerical Harmonic Analysis)

Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics.  More recently, finite frame theory has grown into an important research topic in its own right, with a myriad...

Probability and Schrodinger's Mechanics
Probability and Schrodinger's Mechanics

The presentation and interpretation of (non-relativistic) quantum mechanics is a very well-worked area of study; there have to be very good reasons for adding to the literature on this subject.

My reasons are (obviously) that I am far from satisfied with much of the published work and find difficulties with some points, in
...

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