Foundations of Modern Analysis

Nonfiction, Science & Nature, Mathematics
Cover of the book Foundations of Modern Analysis by J. Dieudonne, Read Books Ltd.
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: J. Dieudonne ISBN: 9781446547519
Publisher: Read Books Ltd. Publication: March 23, 2011
Imprint: Hesperides Press Language: English
Author: J. Dieudonne
ISBN: 9781446547519
Publisher: Read Books Ltd.
Publication: March 23, 2011
Imprint: Hesperides Press
Language: English

In this text, the whole structure of analysis is built up from the foundations. The only things assumed at the outset are the rules of logic and the usual properties of the natural numbers, and with these two exceptions all the proofs in the text rest on the axioms and theorems proved earlier. Nevertheless this treatise (including the first volume) is not suitable for students who have not yet covered the first two years of an undergraduate honours course in mathematics. A striking characteristic of the elementary parts of analysis is the small amount of algebra required. Effectively all that is needed is some elementary linear algebra (which is included in an appendix at the end of the first volume, for the reader’s convenience). However, the role played by algebra increases in the subsequent volumes, and we shall finally leave the reader at the point where this role becomes preponderant, notably with the appearance of advanced commutative algebra and homological algebra. As reference books in algebra we have taken R. Godement’s “Abstract Algebra,” and S. A. Lang’s “Algebra” which we shall possibly augment in certain directions by means of appendices. As with the first volume, I have benefited greatly during the preparation of this work from access to numerous unpublished manuscripts of N. Bourbaki and his collaborators. To them alone is due any originality in the presentation of certain topics.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

In this text, the whole structure of analysis is built up from the foundations. The only things assumed at the outset are the rules of logic and the usual properties of the natural numbers, and with these two exceptions all the proofs in the text rest on the axioms and theorems proved earlier. Nevertheless this treatise (including the first volume) is not suitable for students who have not yet covered the first two years of an undergraduate honours course in mathematics. A striking characteristic of the elementary parts of analysis is the small amount of algebra required. Effectively all that is needed is some elementary linear algebra (which is included in an appendix at the end of the first volume, for the reader’s convenience). However, the role played by algebra increases in the subsequent volumes, and we shall finally leave the reader at the point where this role becomes preponderant, notably with the appearance of advanced commutative algebra and homological algebra. As reference books in algebra we have taken R. Godement’s “Abstract Algebra,” and S. A. Lang’s “Algebra” which we shall possibly augment in certain directions by means of appendices. As with the first volume, I have benefited greatly during the preparation of this work from access to numerous unpublished manuscripts of N. Bourbaki and his collaborators. To them alone is due any originality in the presentation of certain topics.

More books from Read Books Ltd.

Cover of the book 12 Etudes Vol. I. Numbers 1-12 by Fr D Ric Chopin for Solo Piano (1832) Op.10 by J. Dieudonne
Cover of the book The Unfortunate Traveller or the Life of Jack Wilton by J. Dieudonne
Cover of the book Vocal Score of Iolanthe - Or, The Peer and The Peri by J. Dieudonne
Cover of the book Earth Dams, A Study by J. Dieudonne
Cover of the book The Archko Volume or the Archeological Writings of the Sanhedrim and Talmuds of the Jews by J. Dieudonne
Cover of the book Fighting the Flames - A Tale of the London Fire Brigade by J. Dieudonne
Cover of the book Bob Dexter and the Storm Mountain Mystery or, The Secret of the Log Cabin by J. Dieudonne
Cover of the book The Strange Case of Cyril Bycourt (A Classic Short Story of Detective Max Carrados) by J. Dieudonne
Cover of the book Variation on a Waltz by Diabelli D.718 - For Solo Piano by J. Dieudonne
Cover of the book The Scientific Aspect of the Supernatural by J. Dieudonne
Cover of the book The Chesapeake Bay Retriever - A Complete Anthology of the Dog - by J. Dieudonne
Cover of the book How to Prune the Apple Orchard - Selected Articles by J. Dieudonne
Cover of the book The Stranger Child (Fantasy and Horror Classics) by J. Dieudonne
Cover of the book The Haunted Chamber (Fantasy and Horror Classics) by J. Dieudonne
Cover of the book The Pearl - A Journal of Facetiae and Voluptuous Reading - No. 4 by J. Dieudonne
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy