Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The...
Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level...
Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to game theory. It opens with the theory of two-person zero-sum games, two-person non-zero sum games, and n-person games, at a level between nonmathematical introductory books and technical mathematical game theory books. Succeeding sections focus on a variety of applications -- including introductory explanations of gaming and meta games -- that offer nonspecialists information about new areas of game theory at a comprehensible level. Numerous exercises appear with full solutions, in...
Anyone with a knowledge of basic mathematics will find this an accessible and informative introduction to game theory. It opens with the theory of two...
With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical aspects of the process. A classic of sequential program verification, this volume has been translated into almost a dozen other languages and is much in demand among graduate and advanced undergraduate computer science students. Subjects include computability (with discussions of finite automata and Turing machines); predicate calculus (basic notions, natural deduction, and the resolution method); verification of programs (both flowchart and...
With the objective of making into a science the art of verifying computer programs (debugging), the author addresses both practical and theoretical as...
This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolving multidimensional boundary-value problems. Assuming minimal mathematical background, it profiles the relative merits of several general iterative procedures. Topics include polynomial acceleration of basic iterative methods, Chebyshev and conjugate gradient acceleration procedures applicable to partitioning the linear system into a -red/black- block form, adaptive computational algorithms for the successive overrelaxation (SOR) method, and...
This graduate-level text examines the practical use of iterative methods in solving large, sparse systems of linear algebraic equations and in resolvi...
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...
What are the laws of physics, and how did they develop? This reader-friendly guide offers illustrative examples of the rules of physical science an...
"A very good choice." -- MathSciNet, American Mathematical Society An exploration of the unity of several areas in harmonic analysis, this self-contained text emphasizes real-variable methods. Appropriate for advanced undergraduate and graduate students, it starts with classical Fourier series and discusses summability, norm convergence, and conjugate function. An examination of the Hardy-Littlewood maximal function and the Calderon-Zygmund decomposition is followed by explorations of the Hilbert transform and properties of harmonic functions. Additional topics include the...
"A very good choice." -- MathSciNet, American Mathematical Society An exploration of the unity of several areas in harmonic analysis, this ...
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developments in related series. Starting with a definition and explanation of the elements of Fourier series, the text follows with examinations of Legendre polynomials and Bessel functions. Boundary value problems consider Fourier series in conjunction with Laplace's equation in an infinite strip and in a rectangle, with a vibrating string, in three dimensions, in a sphere, and in other circumstances. An overview of Pearson frequency functions is...
This text for undergraduate and graduate students illustrates the fundamental simplicity of the properties of orthogonal functions and their developme...
This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpretation of the calculus undertaken by Augustin-Louis Cauchy and his peers. These intellectuals transformed the uses of calculus from problem-solving methods into a collection of well-defined theorems about limits, continuity, series, derivatives, and integrals. Beginning with a survey of the characteristic 19th-century view of analysis, the book proceeds to an examination of the 18th-century concept of calculus and focuses on the innovative...
This text for upper-level undergraduates and graduate students examines the events that led to a 19th-century intellectual revolution: the reinterpret...
To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable or is it? Understanding the world of Einstein and curved space requires a logical conception of the fourth dimension. This readable, informative volume provides an excellent introduction to that world, with 22 essays that employ a minimum of mathematics. Originally written for a contest sponsored by "Scientific American, "these essays are so well reasoned and lucidly written that they were judged to merit publication in book form. Their easily...
To remove the contents of an egg without puncturing its shell or to drink the liquor in a bottle without removing the cork is clearly unthinkable o...
This influential treatise presents upper-level undergraduates and graduate students with a mathematical analysis of choice behavior. It begins with the statement of a general axiom upon which the rest of the book rests; the following three chapters, which may be read independently of each other, are devoted to applications of the theory to substantive problems: psychophysics, utility, and learning. Applications to psychophysics include considerations of time- and space-order effects, the Fechnerian assumption, the power law and its relation to discrimination data, interaction of continua,...
This influential treatise presents upper-level undergraduates and graduate students with a mathematical analysis of choice behavior. It begins with th...
