"The most readable introduction to the theory of vector spaces available in English and possibly any other language."--J. L. B. Cooper, MathSciNet Review Mathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers. The...
"The most readable introduction to the theory of vector spaces available in English and possibly any other language."--J. L. B. Cooper, MathSciNet ...
This text introduces the methods of applied functional analysis and applied convexity. Suitable for advanced undergraduates and graduate students of mathematics, science, and technology, it focuses on the solutions to two closely related problems. The first concerns finding roots of systems of equations and operative equations in a given region. The second involves extremal problems of minimizing or maximizing functions defined on subsets of finite and infinite dimensional spaces. Rather than citing practical algorithms for solving problems, this treatment provides the tools for studying...
This text introduces the methods of applied functional analysis and applied convexity. Suitable for advanced undergraduates and graduate students of m...
The calculus of finite differences is an area of mathematics important to a broad range of professions, from physical science and engineering to social sciences and statistics. This comprehensive study, directed to advanced undergraduate-level students, graduate students, and professionals, concentrates primarily on how the calculus of finite differences may be used as an approximation method for solving troublesome differential equations. Stressing problem solving rather than pure mathematics, the authors begin with elementary difference operations, treat interpolation and extrapolation,...
The calculus of finite differences is an area of mathematics important to a broad range of professions, from physical science and engineering to socia...
Stimulating, thought-provoking study shows how abstract methods of pure mathematics can be used to systematize problem-solving techniques in applied mathematics. Topics include methods for solving integral equations, finding Green s function for ordinary or partial differential equations, and for finding the spectral representation of ordinary differential operators. Problems. Appendices. Bibliography."
Stimulating, thought-provoking study shows how abstract methods of pure mathematics can be used to systematize problem-solving techniques in applied m...
Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the...
Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these...
Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary development of mathematics. Rather than conducting a survey of the history or philosophy of mathematics, Raymond L. Wilder envisions mathematics as a broad cultural phenomenon. His treatment examines and illustrates how such concepts as number and length were affected by historic and social events. Starting with a brief consideration of preliminary notions, this study explores the early evolution of numbers, the evolution of geometry, and the...
Accessible to students and relevant to specialists, this remarkable book by a prominent educator offers a unique perspective on the evolutionary devel...
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...
Widely praised for its clarity and thorough coverage, this comprehensive overview of mathematical logic is suitable for readers of many different back...
Concise and user-friendly, this college-level text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theory. The introductory approach bridges the gap between mere manipulation and a genuine understanding of an important aspect of both pure and applied mathematics. Beginning with a consideration of coordinate transformations and mappings, the treatment examines loci in three-space, transformation of coordinates in space and differentiation, tensor algebra and analysis, and vector analysis and algebra. Additional topics include differentiation of...
Concise and user-friendly, this college-level text assumes only a knowledge of basic calculus in its elementary and gradual development of tensor theo...
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 elementary properties and operations are the first subjects, followed by examinations of paths and searching, trees, and...
This introduction to graph theory focuses on well-established topics, covering primary techniques and including both algorithmic and theoretical probl...
This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and useful alternative to customary approaches. The treatment can be understood by any reader with a solid background in advanced calculus, and it features many problems with hints and answers. -The exposition is fresh and sophisticated, - declared Sci-Tech Book News, -and will engage the interest of accomplished mathematicians.- Part one is devoted to the integral, moving from the Reimann integral and step functions to a general theory,...
This graduate-level textbook and monograph defines the functions of a real variable through consistent use of the Daniell scheme, offering a rare and ...