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.

Despite the increasing use of computers, the basic need for mathematical tables continues. Tables serve a vital role in preliminary surveys of problems before programming for machine operation, and they are indispensable to thousands of engineers and scientists without access to machines. Because of automatic computers, however, and because of recent scientific advances, a greater variety of functions and a higher accuracy of tabulation than have been available until now are required. In 1954, a conference on mathematical tables, sponsored by M.I.T. and the National Science Foundation, met to discuss a modernization and extension of Jahnke and Emde's classical tables of functions. This volume, published 10 years later by the U.S. Department of Commerce, is the result. Designed to include a maximum of information and to meet the needs of scientists in all fields, it is a monumental piece of work, a comprehensive and self-contained summary of the mathematical functions that arise in physical and engineering problems. The book contains 29 sets of tables, some to as high as 20 places: mathematical constants; physical constants and conversion factors (6 tables); exponential integral and related functions (7); error function and Fresnel integrals (12); Bessel functions of integer (12) and fractional (13) order; integrals of Bessel functions (2); Struve and related functions (2); confluent hypergeometric functions (2); Coulomb wave functions (2); hypergeometric functions; Jacobian elliptic and theta functions (2); elliptic integrals {9); Weierstrass elliptic and related functions; parabolic cylinder functions {3); Mathieu functions (2); spheroidal wave functions (5); orthogonal polynomials (13); combinatorial analysis (9); numerical interpolation, differentiation and integration (11); probability functions (ll); scales of notation (6); miscellaneous functions (9); Laplace transforms (2); and others. Each of these sections is prefaced by a list of related formulas and graphs: differential equations, series expansions, special functions, and other basic relations. These constitute an unusually valuable reference work in themselves. The prefatory material also includes an explanation "of "the numerical methods involved in using the tables that follow and a bibliography. Numerical examples illustrate the use of each table and explain the computation of function values which lie outside its range, while the editors' introduction describes higher-order interpolation procedures. Well over""100 figures illustrate the text. In all, this is one of the most ambitious and useful books of its type ever published, an essential aid in all scientific and engineering research, problem solving, experimentation and field work. This low-cost edition contains every page of the original government publication.

Описание: Translated into many languages, this book has been the standard university-level text for decades. Revised and enlarged by the author in 1952, it offers today's students exercises in construction problems, similitude, and homothecy, properties of the triangle and the quadrilateral, harmonic division, and circle and triangle geometry.

Описание: This versatile undergraduate text can be used in a variety of courses in linear algebra. It contains enough material for a two-semester course, and it also serves as a support text and reference. Chapter Ten, on linear programming, will be of special interest to students of business and economics. A balanced combination of formal theory and related computational techniques, this treatment begins with the familiar problem of solving a system of linear equations. Subsequent chapters explore linear spaces and mappings, matrices, determinants, inner product spaces, scalar-valued functions, and linear differential equations. The author introduces metric notions of Euclidean space at an early stage and employs the computational technique of Gaussian elimination throughout the book. Solutions to selected exercises appear at the end.

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.

Автор: Curry Haskell B. Название: Foundations of Mathematical Logic ISBN: 0486634620 ISBN-13(EAN): 9780486634623 Издательство: Dover Рейтинг: Цена: 2868 р. Наличие на складе: Нет в наличии.

Описание: This book is a thoroughly documented and comprehensive account of the constructive theory of the first-order predicate calculus. This is a calculus that is central to modern mathematical logic and important for mathematicians, philosophers, and scientists whose work impinges upon logic. Professor Curry begins by asking a simple question: What is mathematical logic? If we can define logic as "the analysis and criticism of thought" (W. E. Johnson), then mathematical logic is, according to Curry, "a branch of mathematics which has much the same relation to the analysis and criticism of thought as geometry does to the science of space." The first half of the book gives the basic principles and outlines of the field. After a general introduction to the subject, the author discusses formal methods including algorithms and epitheory. A brief treatment of the Markov treatment of algorithms is included here. The elementary facts about lattices and similar algebraic systems are then covered. In the second half of the book Curry investigates the possibility for a formulation that expresses the meaning to be attached to the logical connectives and to develop the properties that follow from the assumptions so motivated. The author covers positive connectives: implication, conjunction, and alternation. He then goes on to negation and quantification, and concludes with modal operations. Extensive use is made in these latter chapters of the work of Gentzen. Lists of exercises are included. Haskell B. Curry, Evan Pugh Research Professor, Emeritus, at Pennsylvania State University, was a member of the Institute for Advanced Study, Princeton; a former Director of the Institute for Foundational Research, the University of Amsterdam; and President of the Association for Symbolic Logic. His book avoids a doctrinaire stance, presenting various interpretations of logical systems, and offers philosophical and reflective as well as mathematical perspectives.

Описание: Whimsically and delightfully presented mathematical recreations by the author of Alice in Wonderland are solved by arithmetic, algebra, geometry, trigonometry, differential calculus and transcendental properties. 6 illustrations. Two books bound as one.

Автор: Stolyar A. A. Название: Introduction to Elementary Mathematical Logic ISBN: 0486645614 ISBN-13(EAN): 9780486645612 Издательство: Dover Цена: 1259 р. Наличие на складе: Нет в наличии.

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.

Автор: Russell, Bertrand Название: Introduction to Mathematical Philosophy ISBN: 0486277240 ISBN-13(EAN): 9780486277240 Издательство: Dover Цена: 1489 р. Наличие на складе: Нет в наличии.

Описание:

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.

Автор: Bitter Francis Название: Mathematical Physics: A Popular Introduction ISBN: 0486435016 ISBN-13(EAN): 9780486435015 Издательство: Dover Рейтинг: Цена: 1489 р. Наличие на складе: Нет в наличии.

Описание:

What are the laws of physics, and how did they develop? This reader-friendly guide offers illustrative examples of the rules of physical science and how they were formulated. It was written by Francis Bitter, a distinguished teacher and inventor who revolutionized the use of resistive magnets with his development of the Bitter plate. Dr. Bitter shares his scientific expertise in direct, nontechnical terminology as he explains methods of fact gathering, analysis, and experimentation. The four-part treatment begins with an introductory section on physical measurement. An overview of the basics of data assembly leads to the path of scientific investigation, which is exemplified by observations on planetary motions such as those of Earth, Venus, and Mercury. The heart of the book explores analytic methods: topics include the role of mathematics as the language of physics; the nature of mechanical vibrations; harmonic motion and shapes; the geometry of the laws of motion; and the geometry of oscillatory motions. A final section surveys experimentation and its procedures, with explanations of magnetic fields, the fields of coils, and variables involved in coil design. Appropriate for anyone with a grasp of high-school-level mathematics, this book is as well suited to classroom use as it is to self-study.

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