The Story of Algebraic Numbers in the First Half of the 20th Century - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Story of Algebraic Numbers in the First Half of the 20th Century write by Władysław Narkiewicz. This book was released on 2019-01-18. The Story of Algebraic Numbers in the First Half of the 20th Century available in PDF, EPUB and Kindle. The book is aimed at people working in number theory or at least interested in this part of mathematics. It presents the development of the theory of algebraic numbers up to the year 1950 and contains a rather complete bibliography of that period. The reader will get information about results obtained before 1950. It is hoped that this may be helpful in preventing rediscoveries of old results, and might also inspire the reader to look at the work done earlier, which may hide some ideas which could be applied in contemporary research.
An Invitation To Algebraic Numbers And Algebraic Functions
An Invitation To Algebraic Numbers And Algebraic Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Invitation To Algebraic Numbers And Algebraic Functions write by Franz Halter-Koch. This book was released on 2020-05-04. An Invitation To Algebraic Numbers And Algebraic Functions available in PDF, EPUB and Kindle. The author offers a thorough presentation of the classical theory of algebraic numbers and algebraic functions which both in its conception and in many details differs from the current literature on the subject. The basic features are: Field-theoretic preliminaries and a detailed presentation of Dedekind’s ideal theory including non-principal orders and various types of class groups; the classical theory of algebraic number fields with a focus on quadratic, cubic and cyclotomic fields; basics of the analytic theory including the prime ideal theorem, density results and the determination of the arithmetic by the class group; a thorough presentation of valuation theory including the theory of difference, discriminants, and higher ramification. The theory of function fields is based on the ideal and valuation theory developed before; it presents the Riemann-Roch theorem on the basis of Weil differentials and highlights in detail the connection with classical differentials. The theory of congruence zeta functions and a proof of the Hasse-Weil theorem represent the culminating point of the volume. The volume is accessible with a basic knowledge in algebra and elementary number theory. It empowers the reader to follow the advanced number-theoretic literature, and is a solid basis for the study of the forthcoming volume on the foundations and main results of class field theory. Key features: • A thorough presentation of the theory of Algebraic Numbers and Algebraic Functions on an ideal and valuation-theoretic basis. • Several of the topics both in the number field and in the function field case were not presented before in this context. • Despite presenting many advanced topics, the text is easily readable. Franz Halter-Koch is professor emeritus at the university of Graz. He is the author of “Ideal Systems” (Marcel Dekker,1998), “Quadratic Irrationals” (CRC, 2013), and a co-author of “Non-Unique Factorizations” (CRC 2006).
Class Field Theory and L Functions
Class Field Theory and L Functions - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Class Field Theory and L Functions write by Franz Halter-Koch. This book was released on 2022-03-13. Class Field Theory and L Functions available in PDF, EPUB and Kindle. The book contains the main results of class field theory and Artin L functions, both for number fields and function fields, together with the necessary foundations concerning topological groups, cohomology, and simple algebras. While the first three chapters presuppose only basic algebraic and topological knowledge, the rest of the books assumes knowledge of the basic theory of algebraic numbers and algebraic functions, such as those contained in my previous book, An Invitation to Algebraic Numbers and Algebraic Functions (CRC Press, 2020). The main features of the book are: A detailed study of Pontrjagin’s dualtiy theorem. A thorough presentation of the cohomology of profinite groups. A introduction to simple algebras. An extensive discussion of the various ray class groups, both in the divisor-theoretic and the idelic language. The presentation of local and global class field theory in the algebra-theoretic concept of H. Hasse. The study of holomorphy domains and their relevance for class field theory. Simple classical proofs of the functional equation for L functions both for number fields and function fields. A self-contained presentation of the theorems of representation theory needed for Artin L functions. Application of Artin L functions for arithmetical results.
Algebraic Number Theory and Fermat's Last Theorem
Algebraic Number Theory and Fermat's Last Theorem - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Algebraic Number Theory and Fermat's Last Theorem write by Ian Stewart. This book was released on 2001-12-12. Algebraic Number Theory and Fermat's Last Theorem available in PDF, EPUB and Kindle. First published in 1979 and written by two distinguished mathematicians with a special gift for exposition, this book is now available in a completely revised third edition. It reflects the exciting developments in number theory during the past two decades that culminated in the proof of Fermat's Last Theorem. Intended as a upper level textbook, it
Milestones in Analog and Digital Computing
Milestones in Analog and Digital Computing - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Milestones in Analog and Digital Computing write by Herbert Bruderer. This book was released on 2021-01-04. Milestones in Analog and Digital Computing available in PDF, EPUB and Kindle. This Third Edition is the first English-language edition of the award-winning Meilensteine der Rechentechnik; illustrated in full color throughout in two volumes. The Third Edition is devoted to both analog and digital computing devices, as well as the world's most magnificient historical automatons and select scientific instruments (employed in astronomy, surveying, time measurement, etc.). It also features detailed instructions for analog and digital mechanical calculating machines and instruments, and is the only such historical book with comprehensive technical glossaries of terms not found in print or in online dictionaries. The book also includes a very extensive bibliography based on the literature of numerous countries around the world. Meticulously researched, the author conducted a worldwide survey of science, technology and art museums with their main holdings of analog and digital calculating and computing machines and devices, historical automatons and selected scientific instruments in order to describe a broad range of masterful technical achievements. Also covering the history of mathematics and computer science, this work documents the cultural heritage of technology as well.
