Автор: Smullyan, Raymond Название: A Beginner`s Guide to Mathematical Logic ISBN: 0486492370 ISBN-13(EAN): 9780486492377 Издательство: Dover Рейтинг: Цена: 2293 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Written by a creative master of mathematical logic, this introductory text combines stories of great philosophers, quotations, and riddles with the fundamentals of mathematical logic. Author Raymond Smullyan offers clear, incremental presentations of difficult logic concepts. He highlights each subject with inventive explanations and unique problems. Smullyan's accessible narrative provides memorable examples of concepts related to proofs, propositional logic and first-order logic, incompleteness theorems, and incompleteness proofs. Additional topics include undecidability, combinatoric logic, and recursion theory. Suitable for undergraduate and graduate courses, this book will also amuse and enlighten mathematically minded readers. 2014 edition.
Автор: Hodel, Richard Название: An Introduction to Mathematical Logic ISBN: 0486497852 ISBN-13(EAN): 9780486497853 Издательство: Dover Рейтинг: Цена: 3443 р. Наличие на складе: Нет в наличии.
Описание: Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different backgrounds. Designed primarily for advanced undergraduates and graduate students of mathematics, the treatment also contains much of interest to advanced students in computer science and philosophy. An introductory section prepares readers for successive chapters on propositional logic and first-order languages and logic. Subsequent chapters shift in emphasis from an approach to logic from a mathematical point of view to the interplay between mathematics and logic. Topics include the theorems of Godel, Church, and Tarski on incompleteness, undecidability, and indefinability; a rigorous treatment of recursive functions and recursive relations; computability theory; and Hilbert's Tenth Problem. Numerous exercises appear throughout the text, and an appendix offers helpful background on number theory.
An expert and fascinating look at the subject of atmospheric phenomena, this text explores a multiplicity of subjects: the methods of collecting and analyzing data, the structure and growth of clouds from minute condensation nuclei to the familiar cloud forms, and the formation of rain, snow, and hail. The introduction is succeeded by discussions of condensation nuclei, the building blocks of clouds, and the formation of clouds and their variety orographic, layer, and cumuliform. Ice crystals and the formation of rain and snow are examined in detail, as are the properties and formation of hail. A review of the techniques for the scientific basis of cloud modifications includes the use of dry and silver-iodide particles; a look at the artificial stimulation of rainfall explores commercial cloud seeding; and a survey of methods for the modification of hailstorms covers the use of rockets and seeding with giant salt nuclei and silver iodide. In addition to its value to students of meteorology, "Cloud Physics "offers readers outside the classroom a nontechnical and informative""view of the nature of precipitation and clouds."
Описание: This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.
In the words of Bertrand Russell, "Because language is misleading, as well as because it is diffuse and inexact when applied to logic (for which it was never intended), logical symbolism is absolutely necessary to any exact or thorough treatment of mathematical philosophy." That assertion underlies this book, a seminal work in the field for more than 70 years. In it, Russell offers a nontechnical, undogmatic account of his philosophical criticism as it relates to arithmetic and logic. Rather than an exhaustive treatment, however, the influential philosopher and mathematician focuses on certain issues of mathematical logic that, to his mind, invalidated much traditional and contemporary philosophy. In dealing with such topics as number, order, relations, limits and continuity, propositional functions, descriptions, and classes, Russell writes in a clear, accessible manner, requiring neither a knowledge of mathematics nor an aptitude for mathematical symbolism. The result is a thought-provoking excursion into the fascinating realm where mathematics and philosophy meet -- a philosophical classic that will be welcomed by any thinking person interested in this crucial area of modern thought.
Fluid dynamics, the behavior of liquids and gases, is a field of broad impact -- in physics, engineering, oceanography, and meteorology for example -- yet full understanding demands fluency in higher mathematics, the only language fluid dynamics speaks. Dr. Richard Meyer's work is indeed introductory, while written for advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. A knowledge of calculus and vector analysis is presupposed. The author develops basic concepts from a semi-axiomatic foundation, noting that "for mathematics students such a treatment helps to dispel the all too common impression that the whole subject is built on a quicksand of assorted intuitions." Contents include: Kinematics: Lagrangian and Eulerian descriptions, Circulation and Vorticity. Momentum Principle and Ideal Fluid: Conservation examples, Euler equations, D'Alembert's and Kelvin's theorems. Newtonian Fluid: Constitutive and Kinetic theories, exact solutions. Fluids of Small Viscosity: Singular Perturbation, Boundary Layers. Some Aspects of Rotating Fluids: Rossby number, Ekman layer, Taylor-Proudman Blocking. Some Effects of Compressibility: Thermodynamics, Waves, Shock relations and structure, Navier-Stokes equations. Dr. Meyer writes, "This core of our knowledge concerns the relation between inviscid and viscous fluids, and the bulk of this book is devoted to a discussion of that relation."
Описание: Students must prove all of the theorems in this undergraduate-level text, which features extensive outlines to assist in study and comprehension. Thorough and well-written, the treatment provides sufficient material for a one-year undergraduate course. The logical presentation anticipates students' questions, and complete definitions and expositions of topics relate new concepts to previously discussed subjects. Most of the material focuses on point-set topology with the exception of the last chapter. Topics include sets and functions, infinite sets and transfinite numbers, topological spaces and basic concepts, product spaces, connectivity, and compactness. Additional subjects include separation axioms, complete spaces, and homotopy and the fundamental group. Numerous hints and figures illuminate the text.
Описание: Fluid dynamics, the behavior of liquids and gases, is a field of broad impact that encompasses aspects of physics, engineering, oceanography, and meteorology. Full understanding demands fluency in higher mathematics, the only language of fluid dynamics. This introductory text is geared toward advanced undergraduate and graduate students in applied mathematics, engineering, and the physical sciences. It assumes a knowledge of calculus and vector analysis. Author Richard E. Meyer notes, "This core of knowledge concerns the relation between inviscid and viscous fluids, and the bulk of this book is devoted to a discussion of that relation." Dr. Meyer develops basic concepts from a semi-axiomatic foundation, observing that such treatment helps dispel the common impression that the entire subject is built on a quicksand of assorted intuitions. His topics include kinematics, momentum principle and ideal fluid, Newtonian fluid, fluids of small viscosity, some aspects of rotating fluids, and some effects of compressibility. Each chapter concludes with a set of problems.
Автор: Rubinow S. I. Название: Introduction to Mathematical Biology ISBN: 0486425320 ISBN-13(EAN): 9780486425320 Издательство: Dover Рейтинг: Цена: 2868 р. Наличие на складе: Нет в наличии.
Описание: Designed to explore the applications of mathematical techniques and methods related to biology, this text explores five areas: cell growth, enzymatic reactions, physiological tracers, biological fluid dynamics and diffusion. Topics essentially follow a course in elementary differential equations - some linear algebra and graph theory; requires only a knowledge of elementary calculus.
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