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Author : Ray Paul Authement
Publisher :
ISBN 13 :
Total Pages : 54 pages
Book Rating : 4.:/5 (132 download)
Download or read book Finite Dimensional Vector Spaces Over the Ring of Rational Integers written by Ray Paul Authement and published by . This book was released on 1952 with total page 54 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Paul R. Halmos
Publisher : Courier Dover Publications
ISBN 13 : 0486822265
Total Pages : 209 pages
Book Rating : 4.4/5 (868 download)
Download or read book Finite-Dimensional Vector Spaces written by Paul R. Halmos and published by Courier Dover Publications. This book was released on 2017-05-24 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classic, widely cited, and accessible treatment offers an ideal supplement to many traditional linear algebra texts. "Extremely well-written and logical, with short and elegant proofs." — MAA Reviews. 1958 edition.
Author : Irving Kaplansky
Publisher : University of Chicago Press
ISBN 13 : 0226424510
Total Pages : 217 pages
Book Rating : 4.2/5 (264 download)
Download or read book Fields and Rings written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1972 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
Author : Fred Diamond
Publisher : Springer Science & Business Media
ISBN 13 : 0387272267
Total Pages : 462 pages
Book Rating : 4.3/5 (872 download)
Download or read book A First Course in Modular Forms written by Fred Diamond and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 462 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers elliptic curves as complex tori and as algebraic curves; modular curves as Riemann surfaces and as algebraic curves; Hecke operators and Atkin-Lehner theory; Hecke eigenforms and their arithmetic properties; the Jacobians of modular curves and the Abelian varieties associated to Hecke eigenforms. As it presents these ideas, the book states the Modularity Theorem in various forms, relating them to each other and touching on their applications to number theory. The authors assume no background in algebraic number theory and algebraic geometry. Exercises are included.
Author : P.R. Halmos
Publisher : Springer Science & Business Media
ISBN 13 : 1461263875
Total Pages : 207 pages
Book Rating : 4.4/5 (612 download)
Download or read book Finite-Dimensional Vector Spaces written by P.R. Halmos and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "The theory is systematically developed by the axiomatic method that has, since von Neumann, dominated the general approach to linear functional analysis and that achieves here a high degree of lucidity and clarity....The book contains about 350 well placed and instructive problems, which cover a considerable part of the subject. All in all this is an excellent work, of equally high value for both student and teacher." --ZENTRALBLATT FÜR MATHEMATIK
Author : Alexander Abian
Publisher : Elsevier
ISBN 13 : 1483186792
Total Pages : 175 pages
Book Rating : 4.4/5 (831 download)
Download or read book Linear Associative Algebras written by Alexander Abian and published by Elsevier. This book was released on 2014-05-09 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear Associative Algebras focuses on finite dimensional linear associative algebras and the Wedderburn structure theorems. The publication first elaborates on semigroups and groups, rings and fields, direct sum and tensor product of rings, and polynomial and matrix rings. The text then ponders on vector spaces, including finite dimensional vector spaces and matrix representation of vectors. The book takes a look at linear associative algebras, as well as the idempotent and nilpotent elements of an algebra, ideals of an algebra, total matrix algebras and the canonical forms of matrices, matrix representation of algebras, and division of algebras. The manuscript also tackles the Wedderburn structure theorems, including direct sum and tensor product decomposition of algebras, nilpotent algebras and the radical of an algebra, and structure of simple and semi-simple algebras. The publication is highly recommended for mathematicians and students interested in the Wedderburn structure theorems and finite dimensional linear associative algebras.
Author : Michael M. Richter
Publisher : Springer Science & Business Media
ISBN 13 : 354065013X
Total Pages : 450 pages
Book Rating : 4.5/5 (46 download)
Download or read book Algorithmic Learning Theory written by Michael M. Richter and published by Springer Science & Business Media. This book was released on 1998 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains all the papers presented at the Ninth International Con- rence on Algorithmic Learning Theory (ALT’98), held at the European education centre Europ ̈aisches Bildungszentrum (ebz) Otzenhausen, Germany, October 8{ 10, 1998. The Conference was sponsored by the Japanese Society for Arti cial Intelligence (JSAI) and the University of Kaiserslautern. Thirty-four papers on all aspects of algorithmic learning theory and related areas were submitted, all electronically. Twenty-six papers were accepted by the program committee based on originality, quality, and relevance to the theory of machine learning. Additionally, three invited talks presented by Akira Maruoka of Tohoku University, Arun Sharma of the University of New South Wales, and Stefan Wrobel from GMD, respectively, were featured at the conference. We would like to express our sincere gratitude to our invited speakers for sharing with us their insights on new and exciting developments in their areas of research. This conference is the ninth in a series of annual meetings established in 1990. The ALT series focuses on all areas related to algorithmic learning theory including (but not limited to): the theory of machine learning, the design and analysis of learning algorithms, computational logic of/for machine discovery, inductive inference of recursive functions and recursively enumerable languages, learning via queries, learning by arti cial and biological neural networks, pattern recognition, learning by analogy, statistical learning, Bayesian/MDL estimation, inductive logic programming, robotics, application of learning to databases, and gene analyses.
Author : William J. LeVeque
Publisher : Courier Corporation
ISBN 13 : 0486141500
Total Pages : 292 pages
Book Rating : 4.4/5 (861 download)
Download or read book Fundamentals of Number Theory written by William J. LeVeque and published by Courier Corporation. This book was released on 2014-01-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect. The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few. Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.
Author : Atsushi Moriwaki
Publisher : American Mathematical Soc.
ISBN 13 : 1470410745
Total Pages : 298 pages
Book Rating : 4.4/5 (74 download)
Download or read book Arakelov Geometry written by Atsushi Moriwaki and published by American Mathematical Soc.. This book was released on 2014-11-05 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geometry, i.e., the study of big linear series on algebraic varieties. After explaining classical results about the geometry of numbers, the author starts with Arakelov geometry for arithmetic curves, and continues with Arakelov geometry of arithmetic surfaces and higher-dimensional varieties. The book includes such fundamental results as arithmetic Hilbert-Samuel formula, arithmetic Nakai-Moishezon criterion, arithmetic Bogomolov inequality, the existence of small sections, the continuity of arithmetic volume function, the Lang-Bogomolov conjecture and so on. In addition, the author presents, with full details, the proof of Faltings' Riemann-Roch theorem. Prerequisites for reading this book are the basic results of algebraic geometry and the language of schemes.
Author : Seth Warner
Publisher : Courier Corporation
ISBN 13 : 0486137090
Total Pages : 852 pages
Book Rating : 4.4/5 (861 download)
Download or read book Modern Algebra written by Seth Warner and published by Courier Corporation. This book was released on 2012-08-29 with total page 852 pages. Available in PDF, EPUB and Kindle. Book excerpt: Standard text provides an exceptionally comprehensive treatment of every aspect of modern algebra. Explores algebraic structures, rings and fields, vector spaces, polynomials, linear operators, much more. Over 1,300 exercises. 1965 edition.
Author : Wai Kiu Chan
Publisher : American Mathematical Soc.
ISBN 13 : 0821883186
Total Pages : 259 pages
Book Rating : 4.8/5 (218 download)
Download or read book Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms written by Wai Kiu Chan and published by American Mathematical Soc.. This book was released on 2013 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the International Workshop on Diophantine Methods, Lattices, and Arithmetic Theory of Quadratic Forms. The articles cover the arithmetic theory of quadratic forms and lattices, as well as the effective Diophantine analysis with height functions.
Author : Eric Jespers
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110372940
Total Pages : 460 pages
Book Rating : 4.1/5 (13 download)
Download or read book Orders and Generic Constructions of Units written by Eric Jespers and published by Walter de Gruyter GmbH & Co KG. This book was released on 2015-11-13 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume graduate textbook gives a comprehensive, state-of-the-art account of describing large subgroups of the unit group of the integral group ring of a finite group and, more generally, of the unit group of an order in a finite dimensional semisimple rational algebra. Since the book is addressed to graduate students as well as young researchers, all required background on these diverse areas, both old and new, is included. Supporting problems illustrate the results and complete some of the proofs. Volume 1 contains all the details on describing generic constructions of units and the subgroup they generate. Volume 2 mainly is about structure theorems and geometric methods. Without being encyclopaedic, all main results and techniques used to achieve these results are included. Basic courses in group theory, ring theory and field theory are assumed as background.
Author : I.R. Shafarevich
Publisher : Springer Science & Business Media
ISBN 13 : 3642962009
Total Pages : 450 pages
Book Rating : 4.6/5 (429 download)
Download or read book Basic Algebraic Geometry written by I.R. Shafarevich and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry occupied a central place in the mathematics of the last century. The deepest results of Abel, Riemann, Weierstrass, many of the most important papers of Klein and Poincare belong to this do mam. At the end of the last and the beginning of the present century the attitude towards algebraic geometry changed abruptly. Around 1910 Klein wrote: "When I was a student, Abelian functions*-as an after-effect of Jacobi's tradition-were regarded as the undIsputed summit of mathe matics, and each of us, as a matter of course, had the ambition to forge ahead in this field. And now? The young generation hardly know what Abelian functions are." (Vorlesungen tiber die Entwicklung der Mathe matik im XIX. Jahrhundert, Springer-Verlag, Berlin 1926, Seite 312). The style of thinking that was fully developed in algebraic geometry at that time was too far removed from the set-theoretical and axio matic spirit, which then determined the development of mathematics. Several decades had to lapse before the rise of the theory of topolo gical, differentiable and complex manifolds, the general theory of fields, the theory of ideals in sufficiently general rings, and only then it became possible to construct algebraic geometry on the basis of the principles of set-theoretical mathematics. Around the middle of the present century algebraic geometry had undergone to a large extent such a reshaping process. As a result, it can again lay claim to the position it once occupied in mathematics
Author : Ernest Shult
Publisher : Springer
ISBN 13 : 3319197347
Total Pages : 551 pages
Book Rating : 4.3/5 (191 download)
Download or read book Algebra written by Ernest Shult and published by Springer. This book was released on 2015-07-14 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditions, Galois connections, and dependence theories. Here, the general Jordan–Holder Theorem becomes a theorem on interval measures of certain lower semilattices. This is followed by basic courses on groups, rings and modules; the arithmetic of integral domains; fields; the categorical point of view; and tensor products. Beginning with introductory concepts and examples, each chapter proceeds gradually towards its more complex theorems. Proofs progress step-by-step from first principles. Many interesting results reside in the exercises, for example, the proof that ideals in a Dedekind domain are generated by at most two elements. The emphasis throughout is on real understanding as opposed to memorizing a catechism and so some chapters offer curiosity-driven appendices for the self-motivated student.
Author : B S Vatssa
Publisher : New Age International
ISBN 13 : 9788122411911
Total Pages : 384 pages
Book Rating : 4.4/5 (119 download)
Download or read book Modern Algebra written by B S Vatssa and published by New Age International. This book was released on 1999 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Book Is Meant To Provide A Text For The Graduate And Post-Graduate Classes On Modern Algebra At All Indian Universities And At The Institutes Of Technology, But Is Also Intended To Be Useful For All Competitive Examinations Such As I.A.S., Net Etc.This Book Presents Basic And More Important Results In Group Theory, Ring Theory, Linear Algebra And Field Theory. It Is A Self-Contained Book And Also Provides An Understanding Of Basic Mathematical Concepts To Science, Engineering And Social Science Students.There Is Always A Danger Of Introducing The Abstract Concepts Too Suddenly And Without Sufficient Base Of Examples. In Order To Mitigate It The Concepts Have Been Motivated Beforehand. The Topics Have Been Presented In A Simple, Clear And Coherent Style With A Number Of Examples And Exercises. Exercises Of Various Levels Of Difficulty Are Given At The End Each Section.
Author : Gerald J. Janusz
Publisher : American Mathematical Soc.
ISBN 13 : 0821804294
Total Pages : 288 pages
Book Rating : 4.8/5 (218 download)
Download or read book Algebraic Number Fields written by Gerald J. Janusz and published by American Mathematical Soc.. This book was released on 1996 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the basic information about finite dimensional extension fields of the rational numbers, algebraic number fields, and the rings of algebraic integers in them. The important theorems regarding the units of the ring of integers and the class group are proved and illustrated with many examples given in detail. The completion of an algebraic number field at a valuation is discussed in detail and then used to provide economical proofs of global results. The book contains many concrete examples illustrating the computation of class groups, class numbers, and Hilbert class fields. Exercises are provided to indicate applications of the general theory.
Author : Mark Pankov
Publisher : World Scientific
ISBN 13 : 9814651095
Total Pages : 181 pages
Book Rating : 4.8/5 (146 download)
Download or read book Geometry Of Semilinear Embeddings: Relations To Graphs And Codes written by Mark Pankov and published by World Scientific. This book was released on 2015-05-28 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers semilinear embeddings of vector spaces over division rings and the associated mappings of Grassmannians. In contrast to classical books, we consider a more general class of semilinear mappings and show that this class is important. A large portion of the material will be formulated in terms of graph theory, that is, Grassmann graphs, graph embeddings, and isometric embeddings. In addition, some relations to linear codes will be described. Graduate students and researchers will find this volume to be self-contained with many examples.
