Elements of the History of Mathematics (Elements of Mathematics)

This work gathers together, without substantial modification, the major­ ity of the historical Notes which have appeared to date in my Elements de M atMmatique. Only the flow has been made independent of the Elements to which these Notes were attached; they are therefore, in principle, accessible to every reader who possesses a sound classical mathematical background, of undergraduate standard. Of course, the separate studies which make up this volume could not in any way pretend to sketch, even in a summary manner, a complete and con­ nected history of the development of Mathematics up to our day. Entire parts of classical mathematics such as differential Geometry, algebraic Geometry, the Calculus of variations, are only mentioned in passing; others, such as the theory of analytic functions, that of differential equations or partial differ­ ential equations, are hardly touched on; all the more do these gaps become more numerous and more important as the modern era is reached. It goes without saying that this is not a case of intentional omission; it is simply due to the fact that the corresponding chapters of the Elements have not yet been published. Finally the reader will find in these Notes practically no bibliographic or anecdotal information about the mathematicians in question; what has been attempted above all, for each theory, is to bring out as clearly as possible what were the guiding ideas, and how these ideas developed and reacted the ones on the others. Front Matter....Pages I-VIII Foundations of Mathematics; Logic; Set Theory....Pages 1-44 Notation; Combinatorial Analysis....Pages 45-46 The Evolution of Algebra....Pages 47-55 Linear Algebra and Multilinear Algebra....Pages 57-67 Polynomials and Commutative Fields....Pages 69-83 Divisibility; Ordered Fields....Pages 85-92 Commutative Algebra. Algebraic Number Theory....Pages 93-115 Non Commutative Algebra....Pages 117-123 Quadratic Forms; Elementary Geometry....Pages 125-138 Topological Spaces....Pages 139-143 Uniform Spaces....Pages 145-146 Real Numbers....Pages 147-156 Exponentials and Logarithms....Pages 157-158 N Dimensional Spaces....Pages 159-160 Complex Numbers; Measurement of Angles....Pages 161-164 Metric Spaces....Pages 165-166 Infinitesimal Calculus....Pages 167-198 Asymptotic Expansions....Pages 199-202 The Gamma Function....Pages 203-203 Function Spaces....Pages 205-206 Topological Vector Spaces....Pages 207-218 Integration in Locally Compact Spaces....Pages 219-229 Haar Measure. Convolution....Pages 231-236 Integration in Non Locally Compact Spaces....Pages 237-246 Lie Groups and Lie Algebras....Pages 247-267 Groups Generated by Reflections; Root Systems....Pages 269-274 Back Matter....Pages 275-301

Each volume of Nicolas Bourbakis well-known work, The Elements of Mathematics, contains a section or chapter devoted to the history of the subject. This book collects together those historical segments with an emphasis on the emergence, development, and interaction of the leading ideas of the mathematical theories presented in the Elements. In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century.

Elements in the History of Mathematics offers a convenient and compact way of learning the history of several subfields of mathematics, including modern, 20th-century developments. Approx.

"Nicolas Bourbaki's multi-volume treatise 'The Elements of Mathematics' contains, in each volume, a section or chapter devoted to the history of the subject. This book collects together these historical segments, without any claim to establishing a complete or chronological history of mathematics, but with an emphasis on the emergence, development and interaction of the leading ideas of the mathematical theories presented in the 'Elements.' In particular, the book provides a highly readable account of the evolution of algebra, geometry, infinitesimal calculus, and of the concepts of number and structure, from the Babylonian era through to the 20th century."--Publisher's description