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Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition
Classical Geometries in Modern Contexts: Geometry of Real Inner Product Spaces Third Edition

The focus of this book and its geometric notions is on real vector spaces X that are finite or infinite inner product spaces of arbitrary dimension greater than or equal to 2. It characterizes both euclidean and hyperbolic geometry with respect to natural properties of (general) translations and general distances of X. Also for these spaces...

Spacetime, Geometry and Gravitation (Progress in Mathematical Physics)
Spacetime, Geometry and Gravitation (Progress in Mathematical Physics)

Teaching Einstein’s general relativity at introductory level poses problems because students cannot begin to appreciate the basics of the theory unless they learn a sufficient amount of Riemannian geometry. Most elementary books take the easy course of telling the students a few working rules stripping the mathematical details to a minimum...

The Math Problems Notebook
The Math Problems Notebook
The Math Problems Notebook is a collection of nontrivial, unconventional problems requiring deep insight and imagination reminiscent of those discussed at Sunday Math Circles. These circles have become a place for disseminating beautiful mathematics at an elementary level for college students who have a common passion for mathematics....
Geometric Problems on Maxima and Minima
Geometric Problems on Maxima and Minima
Questions of maxima and minima have great practical significance, with applications to physics, engineering, and economics; they have also given rise to theoretical advances, notably in calculus and optimization. Indeed, while most texts view the study of extrema within the context of calculus, this carefully constructed problem book takes a...
Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics)
Advanced Calculus: A Differential Forms Approach (Modern Birkhäuser Classics)

In a book written for mathematicians, teachers of mathematics, and highly motivated students, Harold Edwards has taken a bold and unusual approach to the presentation of advanced calculus. He begins with a lucid discussion of differential forms and quickly moves to the fundamental theorems of calculus and Stokes’ theorem. The result is...

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...

Fourier Analysis on Finite Abelian Groups (Applied and Numerical Harmonic Analysis)
Fourier Analysis on Finite Abelian Groups (Applied and Numerical Harmonic Analysis)

Fourier analysis has been the inspiration for a technological wave of advances in fields such as imaging processing, financial modeling, algorithms and sequence design. This unified, self-contained book examines the mathematical tools used for decomposing and analyzing functions, specifically, the application of the [discrete] Fourier transform...

Data Modeling for Metrology and Testing in Measurement Science
Data Modeling for Metrology and Testing in Measurement Science
This book and companion DVD provide a comprehensive set of modeling methods for data and uncertainty analysis, taking readers beyond mainstream methods described in standard texts. The emphasis throughout is on techniques having a broad range of real-world applications in measurement science. Mainstream methods of data modeling and analysis...
Mathematical Olympiad Challenges
Mathematical Olympiad Challenges
This significantly revised and expanded second edition of "Mathematical Olympiad Challenges" is a rich collection of problems put together by two experienced and well-known professors and coaches of the U.S. International Mathematical Olympiad Team. Hundreds of beautiful, challenging, and instructive problems from algebra, geometry,...
Introduction to Probability with Statistical Applications
Introduction to Probability with Statistical Applications
This book provides a calculus-based introduction to probability and statistics. It contains enough material for two semesters but, with judicious selection, it can be used as a textbook for a one-semester course, either in probability and statistics or in probability alone.

Each section contains many examples and exercises and, in the
...
Inequalities: A Mathematical Olympiad Approach
Inequalities: A Mathematical Olympiad Approach

This book is intended for the Mathematical Olympiad students who wish to prepare for the study of inequalities, a topic now of frequent use at various levels of mathematical competitions. In this volume we present both classic inequalities and the more useful inequalities for confronting and solving optimization problems. An important part of...

Elementary Functions: Algorithms and Implementation
Elementary Functions: Algorithms and Implementation
"An important topic, which is on the boundary between numerical analysis and computer science…. I found the book well written and containing much interesting material, most of the time disseminated in specialized papers published in specialized journals difficult to find. Moreover, there are very few books on these topics and they are...
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