Behnke, Fladt, & Bachman : Fundamentals of Mathematics (3 Volume Set)

Fundamentals of Mathematics (3 Volume Set) by H. Behnke (Editor), K. Fladt (Editor), F. Bachmann (Editor)  $25.00

From the Publisher: Fundamentals of Mathematics represents a new kind of mathematical publication. While excellent technical treatises have been written about specialized fields, they provide little help for the nonspecialist; and other books, some of them semipopular in nature, give an overview of mathematics while omitting some necessary details. Fundamentals of Mathematics strikes a unique balance, presenting an irreproachable treatment of specialized fields and at the same time providing a very clear view of their interrelations, a feature of great value to students, instructors, and those who use mathematics in applied and scientific endeavors. Moreover, as noted in a review of the German edition in Mathematical Reviews, the work is “designed to acquaint [the student] with modern viewpoints and developments. The articles are well illustrated and supplied with references to the literature, both current and ‘classical.’” The outstanding pedagogical quality of this work was made possible only by the unique method by which it was written. There are, in general, two authors for each chapter: one a university researcher, the other a teacher of long experience in the German educational system. (In a few cases, more than two authors have collaborated.) And the whole book has been coordinated in repeated conferences, involving altogether about 150 authors and coordinators.

• Volume I opens with a section on mathematical foundations. It covers such topics as axiomatization, the concept of an algorithm, proofs, the theory of sets, the theory of relations, Boolean algebra, and antinomies. The closing section, on the real number system and algebra, takes up natural numbers, groups, linear algebra, polynomials, rings and ideals, the theory of numbers, algebraic extensions of a fields, complex numbers and quaternions, lattices, the theory of structure, and Zorn’s lemma.
• Volume II begins with eight chapters on the foundations of geometry, followed by eight others on its analytic treatment. The latter include discussions of affine and Euclidean geometry, algebraic geometry, the Erlanger Program and higher geometry, group theory approaches, differential geometry, convex figures, and aspects of topology.
• Volume III, on analysis, covers convergence, functions, integral and measure, fundamental concepts of probability theory, alternating differential forms, complex numbers and variables, points at infinity, ordinary and partial differential equations, difference equations and definite integrals, functional analysis, real functions, and analytic number theory. An important concluding chapter examines “The Changing Structure of Modern Mathematics

Thomas N. Scortia : Artery of Fire

Duda and Hart : Pattern Classification and Scene Analysis

PATTERN CLASSIFICATION AND SCENE ANALYSIS: Duda, Richard O.; Hart, Peter E.


A long-standing, essential classic. If you work in PR, you need a copy just to chase down references to it. Contents are well-described by the jacket blurb, appended below.


Price: $50.00 (includes Media Mail shipping in the US)


Details:
Pub. Date: January 1973
Publisher: Wiley, John & Sons, Incorporated
Format: Hardcover, 482pp
ISBN-13: 9780471223610
ISBN: 0471223611
Edition: First Edition, 4th Printing



Condition: Very Good in a Very Good jacket. No marks or highlights, but has a bookplate and owner name stamps put in before the bookplate. Light wear to the edges of the boards. Dust jacket a little worn, in a Mylar protector.

(From the jacket) Here is a unified, comprehensive, and up-to-date treatment of the theoretical principles of pattern recognition. These principles are applicable to a great variety of problems of current interest, such as character recognition, speech recognition, speaker identification, fingerprint recognition, the analysis of biomedical photographs, aerial photoreconnaissance, automatic inspection for industrial quality control, and visual systems for robots. Throughout Pattern Classification and Scene Analysis, the authors have balanced their presentation to reflect the relative importance of the many theoretical topics in the field. Pattern Classification and Scene Analysis is the first book to provide comprehensive coverage of both statistical classification theory and computer analysis of pictures. Part I covers Bayesian decision theory, supervised and unsupervised learning, nonparametric techniques, discriminant analysis, and clustering. Part II describes many techniques of current interest in automatic scene analysis, including preprocessing of pictorial data, spatial filtering, shape-description techniques, perspective transformations, projective invariants, linguistic procedures, and artificial intelligence techniques for scene analysis. Although the theories and techniques of pattern recognition are largely mathematical, the authors have been more concerned with providing insight and understanding than with establishing rigorous mathematical foundations. The many illustrative examples, plausibility arguments, and discussions of the behavior of solutions reflect this concern. Extensive bibliographical and historical remarks at the end of each chapter further enhance the presentation. Standard notation is used wherever possible, and a comprehensive index is included. Typical first-year graduate students will find most of the mathematical arguments well within their grasp. Because the exposition is clear and balanced, Pattern Classification and Scene Analysis is suitable for both college and professional use. In particular, it will appeal to graduate students and professionals in the fields of computer science, electrical engineering, and statistics. Students and professionals in psychology, biomedical science, meteorology, and biology will also find it of value for the light it sheds on such areas as visual perception, image processing, and numerical taxonomy.

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