What's Happening in the Mathematical Sciences

What's Happening in the Mathematical Sciences

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  • Author: Barry Cipra
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821890431
  • Category : Science
  • Languages : en
  • Pages : 108

Mathematicians like to point out that mathematics is universal. In spite of this, most people continue to view it as either mundane (balancing a checkbook) or mysterious (cryptography). This fifth volume of the What's Happening series contradicts that view by showing that mathematics is indeed found everywhere-in science, art, history, and our everyday lives. Here is some of what you'll find in this volume: Mathematics and Science Mathematical biology: Mathematics was key tocracking the genetic code. Now, new mathematics is needed to understand the three-dimensional structure of the proteins produced from that code. Celestial mechanics and cosmology: New methods have revealed a multitude of solutions to the three-body problem. And other new work may answer one of cosmology'smost fundamental questions: What is the size and shape of the universe? Mathematics and Everyday Life Traffic jams: New models are helping researchers understand where traffic jams come from-and maybe what to do about them! Small worlds: Researchers have found a short distance from theory to applications in the study of small world networks. Elegance in Mathematics Beyond Fermat's Last Theorem: Number theorists are reaching higher ground after Wiles' astounding 1994 proof: new developments inthe elegant world of elliptic curves and modular functions. The Millennium Prize Problems: The Clay Mathematics Institute has offered a million dollars for solutions to seven important and difficult unsolved problems. These are just some of the topics of current interest that are covered in thislatest volume of What's Happening in the Mathematical Sciences. The book has broad appeal for a wide spectrum of mathematicians and scientists, from high school students through advanced-level graduates and researchers.


Transactions of the Moscow Mathematical Society

Transactions of the Moscow Mathematical Society

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  • Author: American Mathematical Society
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821816165
  • Category : Mathematics
  • Languages : en
  • Pages : 382

Focuses on differential equations and differential operators. This title includes such topics as convolution equations of variable order, hypoelliptic pseudodifferential operators, differential operators that decompose into wave factors, and nonlinear parabolic equations.


Geometry of Differential Forms

Geometry of Differential Forms

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  • Author: Shigeyuki Morita
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821810453
  • Category : Mathematics
  • Languages : en
  • Pages : 356

Since the times of Gauss, Riemann, and Poincare, one of the principal goals of the study of manifolds has been to relate local analytic properties of a manifold with its global topological properties. Among the high points on this route are the Gauss-Bonnet formula, the de Rham complex, and the Hodge theorem; these results show, in particular, that the central tool in reaching the main goal of global analysis is the theory of differential forms. The book by Morita is a comprehensive introduction to differential forms. It begins with a quick introduction to the notion of differentiable manifolds and then develops basic properties of differential forms as well as fundamental results concerning them, such as the de Rham and Frobenius theorems. The second half of the book is devoted to more advanced material, including Laplacians and harmonic forms on manifolds, the concepts of vector bundles and fiber bundles, and the theory of characteristic classes. Among the less traditional topics treated is a detailed description of the Chern-Weil theory. The book can serve as a textbook for undergraduate students and for graduate students in geometry.


Statistical Decision Rules and Optimal Inference

Statistical Decision Rules and Optimal Inference

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  • Author: N. N. Cencov
  • Publisher: American Mathematical Soc.
  • ISBN: 9780821813478
  • Category : Mathematics
  • Languages : en
  • Pages : 514

None available in plain English.


Foundations Of Mechanics

Foundations Of Mechanics

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  • Author: Ralph Abraham
  • Publisher: CRC Press
  • ISBN: 0429689047
  • Category : Science
  • Languages : en
  • Pages : 849

Foundations of Mechanics is a mathematical exposition of classical mechanics with an introduction to the qualitative theory of dynamical systems and applications to the two-body problem and three-body problem.


Axes in Outer Space

Axes in Outer Space

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  • Author: Michael Handel
  • Publisher: American Mathematical Soc.
  • ISBN: 0821869272
  • Category : Mathematics
  • Languages : en
  • Pages : 117

"September 2011, volume 213, number 1004 (end of volume)."


Episodes in the History of Modern Algebra (1800-1950)

Episodes in the History of Modern Algebra (1800-1950)

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  • Author: Jeremy J. Gray
  • Publisher: American Mathematical Soc.
  • ISBN: 0821869043
  • Category : Mathematics
  • Languages : en
  • Pages : 346

Algebra, as a subdiscipline of mathematics, arguably has a history going back some 4000 years to ancient Mesopotamia. The history, however, of what is recognized today as high school algebra is much shorter, extending back to the sixteenth century, while the history of what practicing mathematicians call "modern algebra" is even shorter still. The present volume provides a glimpse into the complicated and often convoluted history of this latter conception of algebra by juxtaposing twelve episodes in the evolution of modern algebra from the early nineteenth-century work of Charles Babbage on functional equations to Alexandre Grothendieck's mid-twentieth-century metaphor of a ``rising sea'' in his categorical approach to algebraic geometry. In addition to considering the technical development of various aspects of algebraic thought, the historians of modern algebra whose work is united in this volume explore such themes as the changing aims and organization of the subject as well as the often complex lines of mathematical communication within and across national boundaries. Among the specific algebraic ideas considered are the concept of divisibility and the introduction of non-commutative algebras into the study of number theory and the emergence of algebraic geometry in the twentieth century. The resulting volume is essential reading for anyone interested in the history of modern mathematics in general and modern algebra in particular. It will be of particular interest to mathematicians and historians of mathematics.


A Mathematical Medley

A Mathematical Medley

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  • Author: George Szpiro
  • Publisher: American Mathematical Soc.
  • ISBN: 082184928X
  • Category : Mathematics
  • Languages : en
  • Pages : 250

Describes in layman's terms mathematical problems that have recently been solved (or thought to have been solved), research that has been published in scientific journals, and mathematical observations about contemporary life. Anecdotal stories about the lives of mathematicians and stories about famous old problems are interspersed among other vignettes.


Ergodic Theory

Ergodic Theory

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  • Author: Manfred Einsiedler
  • Publisher: Springer Science & Business Media
  • ISBN: 0857290215
  • Category : Mathematics
  • Languages : en
  • Pages : 486

This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.


Higher Operads, Higher Categories

Higher Operads, Higher Categories

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  • Author: Tom Leinster
  • Publisher: Cambridge University Press
  • ISBN: 0521532159
  • Category : Mathematics
  • Languages : en
  • Pages : 451

Foundations of higher dimensional category theory for graduate students and researchers in mathematics and mathematical physics.