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Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration

Indispensable for students, invaluable for researchers, this comprehensive treatment of contemporary quasi-Monte Carlo methods, digital nets and sequences, and discrepancy theory starts from scratch with detailed explanations of the basic concepts and then advances to current methods used in research. As deterministic versions of the Monte...

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...
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
...

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...

Partial Differential Equations 2: Functional Analytic Methods (Universitext)
Partial Differential Equations 2: Functional Analytic Methods (Universitext)
This comprehensive two-volume textbook presents the whole area of Partial Differential Equations - of the elliptic, parabolic, and hyperbolic type - in two and several variables. Special emphasis is put on the connection of PDEs and complex variable methods.

In this second volume the following topics are treated: Solvability of...

The Philosophy of Mathematical Practice
The Philosophy of Mathematical Practice
Contemporary philosophy of mathematics offers us an embarrassment of riches. Among the major areas of work one could list developments of the classical foundational programs, analytic approaches to epistemology and ontology of mathematics, and developments at the intersection of history and philosophy of mathematics. But anyone familiar with...
Interpolation and Approximation (Dover Books on Mathematics)
Interpolation and Approximation (Dover Books on Mathematics)

Interpolation and approximation offer important applications in computer science and elsewhere. This intermediate-level survey abounds in useful examples of related subjects, starting with remainder theory, convergence theorems, and uniform and best approximation. Other topics include least square approximation, Hilbert space, orthogonal...

Euclidean & Non-Euclidean Geometries: Development and History
Euclidean & Non-Euclidean Geometries: Development and History

This is the definitive presentation of the history, development and philosophical significance of non-Euclidean geometry as well as of the rigorous foundations for it and for elementary Euclidean geometry, essentially according to Hilbert. Appropriate for liberal arts students, prospective high school teachers, math. majors, and even bright high...

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...

Coherent States in Quantum Physics
Coherent States in Quantum Physics

This self-contained introduction discusses the evolution of the notion of coherent states, from the early works of Schr?dinger to the most recent advances, including signal analysis. An integrated and modern approach to the utility of coherent states in many different branches of physics, it strikes a balance between mathematical and physical...

The History of Approximation Theory: From Euler to Bernstein
The History of Approximation Theory: From Euler to Bernstein

The problem of approximating a given quantity is one of the oldest challenges faced by mathematicians. Its increasing importance in contemporary mathematics has created an entirely new area known as Approximation Theory. The modern theory was initially developed along two divergent schools of thought: the Eastern or Russian group, employing...

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