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The wavelet transform can be seen as a synthesis of ideas that have emerged since the 1960s in mathematics, physics, and electrical engineering. The basic idea is to use a family of "building blocks" to represent in an efficient way the object at hand, be it a function, an operator, a signal, or an image. The building blocks themselves come in different "sizes" which can describe different features with different resolutions. The papers in this book attempt to give some theoretical and technical shape to this intuitive picture of wavelets and their uses. The papers collected here were prepared for an AMS Short Course on Wavelets and Applications, held at the Joint Mathematics Meetings in San Antonio in January 1993. Here readers will find general background on wavelets as well as more detailed views of specific techniques and applications. With contributions by some of the top experts in the field, this book provides an excellent introduction to this important and growing area of research.
This book introduces readers to key ideas and applications of computational algebraic geometry. Beginning with the discovery of Gröbner bases and fueled by the advent of modern computers and the rediscovery of resultants, computational algebraic geometry has grown rapidly in importance. The fact that "crunching equations" is now as easy as "crunching numbers" has had a profound impact in recent years. At the same time, the mathematics used in computational algebraic geometry is unusually elegant and accessible, which makes the subject easy to learn and easy to apply. This book begins with an introduction to Gröbner bases and resultants, then discusses some of the more recent methods for solving systems of polynomial equations. A sampler of possible applications follows, including computer-aided geometric design, complex information systems, integer programming, and algebraic coding theory. The lectures in the book assume no previous acquaintance with the material.
This book presents written versions of the eight lectures given during the AMS Short Course held at the Joint Mathematics Meetings in Washington, D.C. The objective of this course was to share with the scientific community the many exciting mathematical challenges arising from the new field of quantum computation and quantum information science. The course was geared toward demonstrating the great breadth and depth of this mathematically rich research field. Interrelationships with existing mathematical research areas were emphasized as much as possible. Moreover, the course was designed so that participants with little background in quantum mechanics would, upon completion, be prepared to begin reading the research literature on quantum computation and quantum information science. Based on audience feedback and questions, the written versions of the lectures have been greatly expanded, and supplementary material has been added. The book features an overview of relevant parts of quantum mechanics with an introduction to quantum computation, including many potential quantum mechanical computing devices; introduction to quantum algorithms and quantum complexity theory; in-depth discussion on quantum error correcting codes and quantum cryptography; and finally, exploration into dive...
The foundation for the subject of mathematical finance was laid nearly 100 years ago by Bachelier in his fundamental work, Théorie de la spéculation. In this work, he provided the first treatment of Brownian motion. Since then, the research of Markowitz, and then of Black, Merton, Scholes, and Samuelson brought remarkable and important strides in the field. A few years later, Harrison and Kreps demonstrated the fundamental role of martingales and stochastic analysis in constructing and understanding models for financial markets. The connection opened the door for a flood of mathematical developments and growth. Concurrently with these mathematical advances, markets have grown, and developments in both academia and industry continue to expand. This lively activity inspired an AMS Short Course at the Joint Mathematics Meetings in San Diego (CA). The present volume includes the written results of that course. Articles are featured by an impressive list of recognized researchers and practitioners. Their contributions present deep results, pose challenging questions, and suggest directions for future research. This collection offers compelling introductory articles on this new, exciting, and rapidly growing field.
Flatland, Edwin Abbott Abbott's story of a two-dimensional universe, as told by one of its inhabitants who is introduced to the mysteries of three-dimensional space, has enjoyed an enduring popularity from the time of its publication in 1884. This fully annotated edition enables the modern-day reader to understand and appreciate the many "dimensions" of this classic satire. Mathematical notes and illustrations enhance the usefulness of Flatland as an elementary introduction to higher-dimensional geometry. Historical notes show connections to late-Victorian England and to classical Greece. Citations from Abbott's other writings as well as the works of Plato and Aristotle serve to interpret the text. Commentary on language and literary style includes numerous definitions of obscure words. An appendix gives a comprehensive account of the life and work of Flatland's remarkable author.
This book provides a stimulating presentation of the history of Greek mathematics, with special emphasis on the Alexandrian school. Beginning with number systems of the ancients and Egyptian influences on Greek mathematics, the book traces the development up to Pappus and Proclus in the fourth century A.D. This is a standard work on the history of Greek mathematics, with special emphasis on the Alexandrian school of mathematics.
Since their emergence in 1917, tomography and inverse problems remain active and important fields that combine pure and applied mathematics and provide strong interplay between diverse mathematical problems and applications. The applied side is best known for medical and scientific use, in particular, medical imaging, radiotherapy, and industrial non-destructive testing. Doctors use tomography to see the internal structure of the body or to find functional information, such as metabolic processes, noninvasively. Scientists discover defects in objects, the topography of the ocean floor, and geological information using X-rays, geophysical measurements, sonar, or other data. This volume, based on the lectures in the Short Course The Radon Transform and Applications to Inverse Problems at the American Mathematical Society meeting in Atlanta, GA, January 3-4, 2005, brings together articles on mathematical aspects of tomography and related inverse problems. The articles cover introductory material, theoretical problems, and practical issues in 3-D tomography, impedance imaging, local tomography, wavelet methods, regularization and approximate inverse, sampling, and emission tomography. All contributions are written for a general audience, and the authors have included references for f...
The modern subject of mathematical finance has undergone considerable development, both in theory and practice, since the seminal work of Black and Scholes appeared a third of a century ago. This book is intended as an introduction to some elements of the theory that will enable students and researchers to go on to read more advanced texts and research papers. The book begins with the development of the basic ideas of hedging and pricing of European and American derivatives in the discrete (i.e., discrete time and discrete state) setting of binomial tree models. Then a general discrete finite market model is introduced, and the fundamental theorems of asset pricing are proved in this setting. Tools from probability such as conditional expectation, filtration, (super)martingale, equivalent martingale measure, and martingale representation are all used first in this simple discrete framework. This provides a bridge to the continuous (time and state) setting, which requires the additional concepts of Brownian motion and stochastic calculus. The simplest model in the continuous setting is the famous Black-Scholes model, for which pricing and hedging of European and American derivatives are developed. The book concludes with a description of the fundamental theorems for a continuous m...
Where can you hear an old man in a nursing home tell of how he disproved Goldbach's Conjecture as part of an undergraduate research project? Get inside the mind of James Clerk Maxwell as he discovers electro-magnetic waves? Witness the 19th century's greatest mathematician finally get the credit she was denied by sexism and murder? In Reality Conditions, a collection of short stories spanning a variety of genres, you can share in these and other fictional mathematical experiences. Each story is a mathematical journey designed to entertain, educate and tantalize. There is something here for everyone: humor, drama, the little details to the big picture, science fiction to true histories. Through these stories, those with little mathematical background will encounter some of the most interesting parts of the field of mathematics for the first time. Even professional mathematicians will be captivated by ideas that take us to the limits of knowledge, addressing the questions of how mathematics is related to the human mind and how it is related to reality. The book is perfect for leisure reading. Join one of the leading experts in the area of mathematical fiction as he takes us on a whirlwind tour of mathematics, both real and imaginary.
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
American Mathematical Society Short
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