The book treats two approaches to decision theory: (1) the normative, purporting to determine how a 'perfectly rational' actor ought to choose among available alternatives; (2) the descriptive, based on observations of how people actually choose in real life and in laboratory experiments. The mathematical tools used in the normative approach range from elementary algebra to matrix and differential equations. Sections on different levels can be studied independently. Special emphasis is made on 'offshoots' of both theories to cognitive psychology, theoretical biology, and philosophy.

Updates the 1995 text on the same topic. The 12 contributions cover high-order methods, multiresolution expansion, explicit time-domain solutions of Maxwell's equations via generalized grids, analysis of periodic structures, modeling of antennas, high- speed electronic circuits with active and nonlinear components, physics-based modeling of millimeter-wave devices, and microcavity resonators. The book is intended as a single-source reference on the state of FDTD art for university graduate students and faculty and professional engineers and scientists involved in electromagnetic technology. Appends a list of acronym expansions. Annotation c. by Book News, Inc., Portland, Or.

0 Background.- 1 Fundamental Concepts.- 2 The Degree of a Map.- 3 The Fundamental Group and Covering Spaces.- 4 Manifolds.- 5 Differential Forms and Homology in Euclidean Space.- 6 Homology and Cohomology.- 7 Homotopy Classification of Maps of the Sphere.- 8 Homotopy Groups.- 9 Fibered Spaces.- 10 Fibrations and Homotopy Groups.- 11 Homotopy Theory of Fibrations.- 12 Lie Groups.- 13 Lie Algebras.- 14 Topology of Lie Groups and Homogeneous Manifolds.- 15 Geometry of Gauge Fields.- Index of Notation.

This book indicts liberal arts undergraduate education. In view of rather oft-cited failings and shortcomings of education at all levels, why focus on undergraduate education? The liberal arts colleges are the heart of our entire educational system. Why is undergraduate education poor? The prime culprit is the overemphasis on research. This book discusses this problem in depth, with a focus on mathematics.

Book by Raphael Salem, Lennart Carleson

First published in 1990, this is a reissue of Professor Hilary Putname(tm)s dissertation thesis, written in 1951, which concerns itself with The Meaning of the Concept of Probability in Application to Finite Sequences and the problems of the deductive justification for induction. Written under the direction of Putname(tm)s mentor, Hans Reichenbach, the book considers Reichenbache(tm)s idealization of very long finite sequences as infinite sequences and the bearing this has upon Reichenbache(tm)s pragmatic vindication of induction.

The Description for this book, Exact Sequences in the Algebraic Theory of Surgery. (MN-26): , will be forthcoming.

For more than 30 years, this two-volume set has helped prepare graduate students to use partial differential equations and integral equations to handle significant problems arising in applied mathematics, engineering, and the physical sciences. Originally published in 1967, this graduate-level introduction is devoted to the mathematics needed for the modern approach to boundary value problems using Green's functions and using eigenvalue expansions. Now a part of SIAM's Classics series, these volumes contain a large number of concrete, interesting examples of boundary value problems for partial differential equations that cover a variety of applications that are still relevant today. For example, there is substantial treatment of the Helmholtz equation and scattering theory?subjects that play a central role in contemporary inverse problems in acoustics and electromagnetic theory.

A committed terrorist in Russia, an admired professor in America: the astounding story of Sergei Degaev's double life, told in full detail for the first time Sergei Degaev (1857-1921), a political terrorist in tsarist Russia, disappeared after participating in the assassination of the chief of Russia's security organization in 1883. Those who later knew and admired the quietly brilliant Professor Alexander Pell at the University of South Dakota never guessed this was actually Degaev, who had triple-crossed friends and associates while entangled in the revolutionary movement of his homeland. This book is the first in any language to tell in detail the extraordinary story of one of the world's most intriguing revolutionaries, his role in building and betraying the earliest political terrorist network, and his subsequent conventional academic career in America. The well-known historian Richard Pipes uses previously unexplored Russian archives to draw a brilliant psychological, political, and sociological portrait of Degaev. Pipes pursues his protagonist on a twisting journey of changing loyalties and fateful collaborations within the network that provided the model for all modern terrorist organizations. A cunning conspirator, Degaev went on to reinvent himself in the United States as a beloved mathematics professor. Either of his lives would be considered remarkable; that Degaev lived both is nothing short of amazing.

Kurt Godel, the greatest logician of our time, startled the world of mathematics in 1931 with his Theorem of Undecidability, which showed that some statements in mathematics are inherently "undecidable." His work on the completeness of logic, the incompleteness of number theory, and the consistency of the axiom of choice and the continuum theory brought him further worldwide fame. In this introductory volume, Raymond Smullyan, himself a well-known logician, guides the reader through the fascinating world of Godel's incompleteness theorems. The level of presentation is suitable for anyone with a basic acquaintance with mathematical logic. As a clear, concise introduction to a difficult but essential subject, the book will appeal to mathematicians, philosophers, and computer scientists.

This book documents the history of pi from the dawn of mathematical time to the present. The story of pi reflects the most seminal, the most serious, and sometimes the most whimsical aspects of mathematics. Much significant mathematics originates with pi, and many great mathematicians have contributed to this story's unfolding. Mathematicians and historians of mathematics will find this book indispensable. Teachers at every level can find here ample resources for anything from individual talks and student projects to special topics courses.

In Greek and Roman antiquity, philosophy was supreme in the domain of learning. Philosophy was the name for the pursuit of truth about the most fundamental things to be known or understood. It was the most desirable of all the goods of the mind. But today we live in an age dominated by science and technology - an age that has witnessed not only the rise of positivism, but the retreat of academic philosophy to an analysis of language. Professorial philosophy has become as specialized a subject as logic and mathematics. If anyone asks why we should be concerned with the intellectual respectability of philosophy, this book provides the answer.

[Hilbert's] style has not the terseness of many of our modem authors in mathematics, which is based on the assumption that printer's labor and paper are costly but the reader's effort and time are not. H. Weyl [143] The purpose of this book is to describe the classical problems in additive number theory and to introduce the circle method and the sieve method, which are the basic analytical and combinatorial tools used to attack these problems. This book is intended for students who want to lel?Ill additive number theory, not for experts who already know it. For this reason, proofs include many "unnecessary" and "obvious" steps; this is by design. The archetypical theorem in additive number theory is due to Lagrange: Every nonnegative integer is the sum of four squares. In general, the set A of nonnegative integers is called an additive basis of order h if every nonnegative integer can be written as the sum of h not necessarily distinct elements of A. Lagrange 's theorem is the statement that the squares are a basis of order four. The set A is called a basis offinite order if A is a basis of order h for some positive integer h. Additive number theory is in large part the study of bases of finite order. The classical bases are the squares, cubes, and higher powers; the polygonal numbers; and the prime numbers. The classical questions associated with these bases are Waring's problem and the Goldbach conjecture.

In 1942, Lt. Herman H. Goldstine, a former mathematics professor, was stationed at the Moore School of Electrical Engineering at the University of Pennsylvania. It was there that he assisted in the creation of the ENIAC, the first electronic digital computer. The ENIAC was operational in 1945, but plans for a new computer were already underway. The principal source of ideas for the new computer was John von Neumann, who became Goldstine's chief collaborator. Together they developed EDVAC, successor to ENIAC. After World War II, at the Institute for Advanced Study, they built what was to become the prototype of the present-day computer. Herman Goldstine writes as both historian and scientist in this first examination of the development of computing machinery, from the seventeenth century through the early 1950s. His personal involvement lends a special authenticity to his narrative, as he sprinkles anecdotes and stories liberally through his text.

While Eugenio Calabi is best known for his contributions to the theory of Calabi-Yau manifolds, this Steele-Prize-winning geometer’s fundamental contributions to mathematics have been far broader and more diverse than might be guessed from this one aspect of his work. His works have deep influence and lasting impact in global differential geometry, mathematical physics and beyond. By bringing together 47 of Calabi’s important articles in a single volume, this book provides a comprehensive overview of his mathematical oeuvre, and includes papers on complex manifolds, algebraic geometry, Kähler metrics, affine geometry, partial differential equations, several complex variables, group actions and topology. The volume also includes essays on Calabi’s mathematics by several of his mathematical admirers, including S.K. Donaldson, B. Lawson and S.-T. Yau, Marcel Berger; and Jean Pierre Bourguignon. This book is intended for mathematicians and graduate students around the world. Calabi’svisionary contributions will certainly continue to shape the course of this subject far into the future.

"This book describes the driving forces behind the evolutionary process at the molecular and genome levels, the effects of the various molecular mechanisms on the structure of genes, proteins, and genomes, the methodology and the analytical tools involved in dealing with molecular data from an evolutionary perspective, and the logic of evolutionary hypothesis testing. Evolutionary phenomena at the molecular level are detailed in a way that can be understood without much prerequisite knowledge of molecular biology, evolution, or mathematics. Numerous examples that support and clarify the theoretical arguments and methodological discussions are included."--

This book provides the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbits structure. The third and fourth parts develop in depth the theories of low-dimensional dynamical systems and hyperbolic dynamical systems.

The study of transcendental numbers has now developed into a fertile and extensive theory, enriching widespread branches of mathematics; and the time has seemed opportune to prepare a systematic treatise. My aim has been to provide a comprehensive account of the recent major discoveries in the field. Classical aspects of the subject are discussed in the course of the narrative; in particular, to facilitate the acquisition of a true historical perspective, a survey of the theory as it existed at about the turn of the century is given at the beginning. Notwithstanding its long history, it will be apparent that the theory of transcendental numbers bears a youthful countenance. If this book should play some small role in promoting future progress, the author will be well satisfied. The text has arisen from numerous lectures delivered in Cambridge, America and elsewhere, and it has also formed the substance of an Adams Prize essay.