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＜図書＞
Fundamentals of mathematics

責任表示 edited by H. Behnke ... [et al.] ; with the assistance of H. Gerike ... [et al.] ; translated by S.H. Gould
データ種別 図書
出版情報 Cambridge, Mass. : MIT Press , c1974
本文言語 英語
大きさ 2 v. : ill. ; 24 cm
概要 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 nonspeci...list; 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."
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." 続きを見る
目次 v. 2. Geometry
v. 3. Analysis

所蔵情報


v. 3 芸工図 2F 書架 410.1/B32/3 1974
072032175002368

書誌詳細

別書名 原タイトル:Grundzüge der Mathematik
内容注記 v. 2. Geometry
v. 3. Analysis
一般注記 Translation of Grundzüge der Mathematik
子書誌あり
Includes bibliographies and index
著者標目 Behnke, Heinrich, 1898-
件　名 LCSH:Mathematics -- 1961-  全ての件名で検索
分　類 LCC:QA37.2
DC19:510
書誌ID 1001202352
ISBN 0262020696
NCID BA4371181X
巻冊次 v. 2 ; ISBN:0262020696
v. 3 ; ISBN:0262020491
登録日 2009.09.18
更新日 2009.09.18

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