Elements of the History of Mathematics de J. Meldrum

Elements of the History of Mathematics

J. Meldrum

N. Bourbaki

en Limba Engleză Paperback – 17 noi 1998

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.

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Descriere

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.

Cuprins

1. Foundations of Mathematics; Logic; Set Theory.- 2. Notation; Combinatorial Analysis.- 3. The Evolution of Algebra.- 4. Linear Algebra and Multilinear Algebra.- 5. Polynomials and Commutative Fields.- 6. Divisibility; Ordered Fields.- 7. Commutative Algebra. Algebraic Number Theory.- 8. Non Commutative Algebra.- 9. Quadratic Forms; Elementary Geometry.- 10. Topological Spaces.- 11. Uniform Spaces.- 12. Real Numbers.- 13. Exponentials and Logarithms.- 14. n Dimensional Spaces.- 15. Complex Numbers; Measurement of Angles.- 16. Metric Spaces.- 17. Infinitesimal Calculus.- 18. Asymptotic Expansions.- 19. The Gamma Function.- 20. Function Spaces.- 21. Topological Vector Spaces.- 22. Integration in Locally Compact Spaces.- 23. Haar Measure. Convolution.- 24. Integration in Non Locally Compact Spaces.- 25. Lie Groups and Lie Algebras.- 26. Groups Generated by Reflections; Root Systems.