An exploration of mathematical style through 99 different proofs of the same theoremThis book offers a multifaceted perspective on mathematics by demonstrating 99 different proofs of the same theorem.
Many industries, such as transportation and manufacturing, use control systems to insure that parameters such as temperature or altitude behave in a desirable way over time.
Using set theory in the first part of his book, and proof theory in the second, Gaisi Takeuti gives us two examples of how mathematical logic can be used to obtain results previously derived in less elegant fashion by other mathematical techniques, especially analysis.
The concept of entropy arose in the physical sciences during the nineteenth century, particularly in thermodynamics and statistical physics, as a measure of the equilibria and evolution of thermodynamic systems.
Diffusive motion--displacement due to the cumulative effect of irregular fluctuations--has been a fundamental concept in mathematics and physics since Einstein's work on Brownian motion.
By studying the degeneration of abelian varieties with PEL structures, this book explains the compactifications of smooth integral models of all PEL-type Shimura varieties, providing the logical foundation for several exciting recent developments.
The essential reference book on matrices-now fully updated and expanded, with new material on scalar and vector mathematicsSince its initial publication, this book has become the essential reference for users of matrices in all branches of engineering, science, and applied mathematics.
Ever since the Irish mathematician William Rowan Hamilton introduced quaternions in the nineteenth century--a feat he celebrated by carving the founding equations into a stone bridge--mathematicians and engineers have been fascinated by these mathematical objects.
The year's finest mathematics writing from around the worldThis annual anthology brings together the year's finest mathematics writing from around the world.
Motivated by the theory of turbulence in fluids, the physicist and chemist Lars Onsager conjectured in 1949 that weak solutions to the incompressible Euler equations might fail to conserve energy if their spatial regularity was below 1/3-Holder.
This book offers a survey of recent developments in the analysis of shock reflection-diffraction, a detailed presentation of original mathematical proofs of von Neumann's conjectures for potential flow, and a collection of related results and new techniques in the analysis of partial differential equations (PDEs), as well as a set of fundamental open problems for further development.
Quantal Response Equilibrium presents a stochastic theory of games that unites probabilistic choice models developed in psychology and statistics with the Nash equilibrium approach of classical game theory.
Modular Forms and Special Cycles on Shimura Curves is a thorough study of the generating functions constructed from special cycles, both divisors and zero-cycles, on the arithmetic surface "e;M"e; attached to a Shimura curve "e;M"e; over the field of rational numbers.
Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn).
A comprehensive look at the mathematics, physics, and philosophy of Henri PoincareHenri Poincare (1854-1912) was not just one of the most inventive, versatile, and productive mathematicians of all time-he was also a leading physicist who almost won a Nobel Prize for physics and a prominent philosopher of science whose fresh and surprising essays are still in print a century later.
An interdisciplinary history of trigonometry from the mid-sixteenth century to the early twentiethThe Doctrine of Triangles offers an interdisciplinary history of trigonometry that spans four centuries, starting in 1550 and concluding in the 1900s.
This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology.
This collection of essays brings together many of the world's most distinguished statisticians to discuss a wide array of the most important recent developments in data analysis.
John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P.
Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "e;math camp"e; or a semester-long or yearlong course to acquire the necessary skills.
The first complete proof of Arnold diffusion-one of the most important problems in dynamical systems and mathematical physicsArnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics.
Actuator and sensor delays are among the most common dynamic phenomena in engineering practice, and when disregarded, they render controlled systems unstable.
How mathematics helped build the world's most important buildings from early Egypt to the presentFrom the pyramids and the Parthenon to the Sydney Opera House and the Bilbao Guggenheim, this book takes readers on an eye-opening tour of the mathematics behind some of the world's most spectacular buildings.
An essential introduction to the analysis and verification of control system softwareThe verification of control system software is critical to a host of technologies and industries, from aeronautics and medical technology to the cars we drive.
How our understanding of calculus has evolved over more than three centuries, how this has shaped the way it is taught in the classroom, and why calculus pedagogy needs to changeCalculus Reordered takes readers on a remarkable journey through hundreds of years to tell the story of how calculus evolved into the subject we know today.
A comprehensive introduction to hybrid control systems and designHybrid control systems exhibit both discrete changes, or jumps, and continuous changes, or flow.
This book aims first to prove the local Langlands conjecture for GLn over a p-adic field and, second, to identify the action of the decomposition group at a prime of bad reduction on the l-adic cohomology of the "e;simple"e; Shimura varieties.
This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrodinger equation in the semiclassical asymptotic regime.
A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics.
Plato's Ghost is the first book to examine the development of mathematics from 1880 to 1920 as a modernist transformation similar to those in art, literature, and music.
This book describes the latest advances in the theory of mean field games, which are optimal control problems with a continuum of players, each of them interacting with the whole statistical distribution of a population.
From the winner of the Turing Award and the Abel Prize, an introduction to computational complexity theory, its connections and interactions with mathematics, and its central role in the natural and social sciences, technology, and philosophyMathematics and Computation provides a broad, conceptual overview of computational complexity theorythe mathematical study of efficient computation.
