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by Boris S. Tsukerblat (Author)This handbook on group theory is geared toward chemists and experimental physicists who use spectroscopy and require knowledge of the electronic structures of the materials they investigate. Accessible to undergraduate students, it takes an elementary approach to many of the key concepts. Rather than the deductive method common to books on mathematics and theoretical physics, the present volume introduces fundamental concepts with simple examples, relating them ...
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by Roe Goodman (Author)Newly revised by the author, this undergraduate-level text introduces the mathematical theory of probability and stochastic processes. Using both computer simulations and mathematical models of random events, it comprises numerous applications to the physical and biological sciences, engineering, and computer science. Subjects include sample spaces, probabilities distributions and expectations of random variables, conditional expectations, Markov chains, and the Poisson...
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by Ian N. Sneddon (Author)Geared toward students of applied rather than pure mathematics, this volume introduces elements of partial differential equations. Its focus is primarily upon finding solutions to particular equations rather than general theory.Topics include ordinary differential equations in more than two variables, partial differential equations of the first and second orders, Laplace's equation, the wave equation, and the diffusion equation. A helpful Appendix offers information ...
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by O. C. Zienkiewicz (Author), K. Morgan (Author)A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual metho...
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by A. Gardiner (Author)The term mathematics usually suggests an array of familiar problems with solutions derived from well-known techniques. Discovering Mathematics: The Art of Investigation takes a different approach, exploring how new ideas and chance observations can be pursued, and focusing on how the process invariably leads to interesting questions that would never have otherwise arisen.With puzzles involving coins, postage stamps, and other commonplace items, students are challenged t...
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by John David Jackson (Author)Advanced undergraduates and graduate students studying quantum mechanics will find this text a valuable guide to mathematical methods. Emphasizing the unity of a variety of different techniques, it is enduringly relevant to many physical systems outside the domain of quantum theory.Concise in its presentation, this text covers eigenvalue problems in classical physics, orthogonal functions and expansions, the Sturm-Liouville theory and linear operators on function...
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by Joseph Breuer (Author), Howard F. Fehr (Translator)Set theory permeates much of contemporary mathematical thought. This text for undergraduates offers a natural introduction, developing the subject through observations of the physical world. Its progressive development leads from concrete finite sets to cardinal numbers, infinite cardinals, and ordinals.Although set theory begins in the intuitive and the concrete, it ascends to a very high degree of abstraction. All that is necessary to it...
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by William H. McCrea (Author)Brief but rigorous, this text is geared toward advanced undergraduates and graduate students. It covers the coordinate system, planes and lines, spheres, homogeneous coordinates, general equations of the second degree, quadric in Cartesian coordinates, and intersection of quadrics. Mathematician, physicist, and astronomer, William H. McCrea conducted research in many areas and is best known for his work on relativity and cosmology. McCrea studied and taught at uni...
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by Robert T. Seeley (Author)A compact, sophomore-to-senior-level guide, Dr. Seeley's text introduces Fourier series in the way that Joseph Fourier himself used them: as solutions of the heat equation in a disk. Emphasizing the relationship between physics and mathematics, Dr. Seeley focuses on results of greatest significance to modern readers.Starting with a physical problem, Dr. Seeley sets up and analyzes the mathematical modes, establishes the principal properties, and then proceeds to ap...
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by Jean-Pierre Aubin (Author), Ivar Ekeland (Author)Nonlinear analysis, formerly a subsidiary of linear analysis, has advanced as an individual discipline, with its own methods and applications. Moreover, students can now approach this highly active field without the preliminaries of linear analysis. As this text demonstrates, the concepts of nonlinear analysis are simple, their proofs direct, and their applications clear. No prerequisites are necessary beyond the elementary theory of Hilbert...
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by David H. Krantz (Author), R. Duncan Luce (Author), Amos Tversky (Author)All of the sciences―physical, biological, and social―have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal foundations for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence.Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures...
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by Patrick Suppes (Author), David H. Krantz (Author), R. Duncan Luce (Author)All of the sciences -- physical, biological, and social -- have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal basis for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence.Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative structur...
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by David H. Krantz (Author), R. Duncan Luce (Author), Amos Tversky (Author)All of the sciences -- physical, biological, and social -- have a need for quantitative measurement. This influential series, Foundations of Measurement, established the formal foundations for measurement, justifying the assignment of numbers to objects in terms of their structural correspondence.Volume I introduces the distinct mathematical results that serve to formulate numerical representations of qualitative stru...
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by T. Ewan Faulkner (Author)This text explores the methods of the projective geometry of the plane. Some knowledge of the elements of metrical and analytical geometry is assumed; a rigorous first chapter serves to prepare readers. Following an introduction to the methods of the symbolic notation, the text advances to a consideration of the theory of one-to-one correspondence. It derives the projective properties of the conic and discusses the representation of these properties by the general ...
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by I. M. Glazman (Author), Ju I. Ljubic (Author), G. Kuerti (Editor)A sequence of 2,400 propositions and problems features only hints. Suitable for advanced undergraduates and graduate students, this unique approach encourages students to work out their own proofs. 1974 edition. Number of Pages: 520 Dimensions: 1.08 x 8.6 x 5.46 IN Publication Date: September 15, 2006
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by Philip J. Davis (Author), Philip Rabinowitz (Author)Useful to programmers and stimulating for theoreticians, this text covers the major methods of numerical integration. It offers a balanced presentation: certain sections derive from or allude to deep results of analysis, but most of the final results are expressed in a form accessible to anyone with a background in calculus.An extensive introduction outlines the uses and advantages of numerical integration and includes formulas and guides...
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by Homer E. Newell (Author)When employed with skill and understanding, vector analysis can be a practical and powerful tool. This text develops the algebra and calculus of vectors in a manner useful to physicists and engineers. Numerous exercises (with answers) not only provide practice in manipulation but also help establish students' physical and geometric intuition in regard to vectors and vector concepts.Part I, the basic portion of the text, consists of a thorough treatment of vector alg...
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by Tobias Dantzig (Author)More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elega...
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by Francois Treves (Author)Focusing on the archetypes of linear partial differential equations, this text for upper-level undergraduates and graduate students employs nontraditional methods to explain classical material. Topics include the Cauchy problem, boundary value problems, and mixed problems and evolution equations. Nearly 400 exercises enable students to reconstruct proofs. 1975 edition. Number of Pages: 470 Dimensions: 0.94 x 8.48 x 5.7 IN Illustrated: Yes Publication Date: November ...
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by E. B. Dynkin (Author), V. A. Uspenskii (Author)Combining three books into a single volume, this text comprises Multicolor Problems, dealing with several of the classical map-coloring problems; Problems in the Theory of Numbers, an elementary introduction to algebraic number theory; and Random Walks, addressing basic problems in probability theory. The book's primary aim is not so much to impart new information as to teach an active, creative attitude toward mathematics. The sole prerequisi...
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by A. I. Fetisov (Author), YA S. Dubnov (Author)This single-volume compilation of 2 books explores the construction of geometric proofs. It offers useful criteria for determining correctness and presents examples of faulty proofs that illustrate common errors. 1963 editions. Number of Pages: 146 Dimensions: 0.29 x 8.48 x 5.4 IN Illustrated: Yes Publication Date: November 17, 2006
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by Maurice Kraitchik (Author)Ranging from ancient Greek and Roman problems to modern applications and techniques, this book features 250 lively puzzles and problems, with solutions. Both beginners and advanced mathematicians will appreciate its variety of numerical pastimes, which include unusual historic problems from medieval European, Arabic, and Hindu sources. Number of Pages: 328 Dimensions: 0.65 x 8.5 x 6.4 IN Illustrated: Yes Publication Date: November 17, 2006
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by Maciej M. Syslo (Author), Narsingh Deo (Author), Janusz S. Kowalik (Author)Upper-level undergraduates and graduate students will benefit from this treatment of discrete optimization algorithms, which covers linear and integer programming and offers a collection of ready-to-use computer programs. 1983 edition. Number of Pages: 541 Dimensions: 1.1 x 9.2 x 6.56 IN Illustrated: Yes Publication Date: December 15, 2006
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by Avner Friedman (Author)This text develops the theory of systems of stochastic differential equations, and it presents applications in probability, partial differential equations, and stochastic control problems. Originally published in two volumes, it combines a book of basic theory and selected topics with a book of applications.The first part explores Markov processes and Brownian motion; the stochastic integral and stochastic differential equations; elliptic and parabolic partial differ...
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by Arthur Erdelyi (Author)This brief monograph by a distinguished professor is based on a mathematics course offered at the California Institute of Technology. The majority of students taking this course were advanced undergraduates and graduate students of engineering. A solid background in advanced calculus is a prerequisite.Topics include elementary and convergence theories of convolution quotients, differential equations involving operator functions, and exponential functions of operators...
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by John Heading (Author)The phase-integral method in mathematics, also known as the Wentzel-Kramers-Brillouin (WKB) method, is the focus of this introductory treatment. Author John Heading successfully steers a course between simplistic and rigorous approaches to provide a concise overview for advanced undergraduates and graduate students in mathematics and physics. Since the number of applications is vast, the text considers only a brief selection of topics and emphasizes the method itself r...
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by Donald S. Passman (Author)This groundbreaking monograph in advanced algebra addresses crossed products. Author Donald S. Passman notes that crossed products have advanced from their first occurrence in finite dimensional division algebras and central simple algebras to a closer relationship with the study of infinite group algebras, group-graded rings, and the Galois theory of noncommutative rings. Suitable for advanced undergraduates and graduate students of mathematics, the text examines...
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by Alfred Tarski (Author), Andrzej Mostowski (Author), Raphael M. Robinson (Author)This graduate-level book is well known for its proof that many mathematical systems--including lattice theory, abstract projective geometry, and closure algebras--are undecidable. Based on research conducted from 1938 to 1952, it consists of three treatises by a prolific author who ranks among the greatest logicians of all time. The first article, A General Method in Proofs of Undecidability, examines theories ...
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by Shlomo Sternberg (Author)Celebrated mathematician Shlomo Sternberg, a pioneer in the field of dynamical systems, created this modern one-semester introduction to the subject for his classes at Harvard University. Its wide-ranging treatment covers one-dimensional dynamics, differential equations, random walks, iterated function systems, symbolic dynamics, and Markov chains. Supplementary materials offer a variety of online components, including PowerPoint lecture slides for professors and M...
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by Ronald Gould (Author)This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical problems. The algorithms are presented with a minimum of advanced data structures and programming details. This thoroughly corrected 1988 edition provides insights to computer scientists as well as advanced undergraduates and graduate students of topology, algebra, and matrix theory. Fundamental concepts and notation and eleme...
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by R. L. Goodstein (Author)Recursive analysis develops natural number computations into a framework appropriate for real numbers. This text is based upon primary recursive arithmetic and presents a unique combination of classical analysis and intuitional analysis. Written by a master in the field, it is suitable for graduate students of mathematics and computer science and can be read without a detailed knowledge of recursive arithmetic.Introductory chapters on recursive convergence and recur...
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by Erhan Cinlar (Author)This clear presentation of the most fundamental models of random phenomena employs methods that recognize computer-related aspects of theory. The text emphasizes the modern viewpoint, in which the primary concern is the behavior of sample paths. By employing matrix algebra and recursive methods, rather than transform methods, it provides techniques readily adaptable to computing with machines.Topics include probability spaces and random variables, expectations and inde...