Author : Paul R. Halmos
Publisher : Courier Dover Publications
Page : 209 pages
File Size : 17,28 MB
Release : 2017-05-24
Category : Mathematics
ISBN : 0486822265
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 : Thomas L., Saaty
Publisher : RWS Publications
Page : 404 pages
File Size : 34,77 MB
Release : 2014-12-22
Category : Business & Economics
ISBN : 1888603380
"We are surrounded and deeply involved, in the natural world, with non- linear events which are not necessarily mathematical," the authors write. "For example . . . the nonlinear problem of pedalling a bicycle up and down a hillside. On a grand scale . . . the struggle for existence between two species, one of which preys exclusively on the other." This book is' for mathematicians and researchers who believe that "nonlinear mathematics is' the mathematics of today"; it is also for economists, engineers, operations analysts, "the reader who has been thus bemused into an artificially linear conception of the universe." Nonlinear Mathematics is the first attempt to consider the widest range of nonlinear topics found in the -scattered literature. Accessible to non- mathematics professionals as well as college seniors and graduates, it offers a discussion both particular and broad enough to stimulate research towards a unifying theory of nonlinear mathematics. Ideas are presented "according to existence and uniqueness theorems, characterization (e.g., stability and asymptotic behavior), construction of solutions, convergence, approximation and errors."
Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 488 pages
File Size : 31,45 MB
Release : 2007-12-31
Category : Mathematics
ISBN : 038727474X
Covers a notably broad range of topics, including some topics not generally found in linear algebra books Contains a discussion of the basics of linear algebra
Author : Douglas C. Ravenel
Publisher : Princeton University Press
Page : 225 pages
File Size : 33,75 MB
Release : 2016-03-02
Category : Mathematics
ISBN : 1400882486
Nilpotence and Periodicity in Stable Homotopy Theory describes some major advances made in algebraic topology in recent years, centering on the nilpotence and periodicity theorems, which were conjectured by the author in 1977 and proved by Devinatz, Hopkins, and Smith in 1985. During the last ten years a number of significant advances have been made in homotopy theory, and this book fills a real need for an up-to-date text on that topic. Ravenel's first few chapters are written with a general mathematical audience in mind. They survey both the ideas that lead up to the theorems and their applications to homotopy theory. The book begins with some elementary concepts of homotopy theory that are needed to state the problem. This includes such notions as homotopy, homotopy equivalence, CW-complex, and suspension. Next the machinery of complex cobordism, Morava K-theory, and formal group laws in characteristic p are introduced. The latter portion of the book provides specialists with a coherent and rigorous account of the proofs. It includes hitherto unpublished material on the smash product and chromatic convergence theorems and on modular representations of the symmetric group.
Author : Sheldon Axler
Publisher : Springer Science & Business Media
Page : 276 pages
File Size : 12,37 MB
Release : 1997-07-18
Category : Mathematics
ISBN : 9780387982595
This text for a second course in linear algebra, aimed at math majors and graduates, adopts a novel approach by banishing determinants to the end of the book and focusing on understanding the structure of linear operators on vector spaces. The author has taken unusual care to motivate concepts and to simplify proofs. For example, the book presents - without having defined determinants - a clean proof that every linear operator on a finite-dimensional complex vector space has an eigenvalue. The book starts by discussing vector spaces, linear independence, span, basics, and dimension. Students are introduced to inner-product spaces in the first half of the book and shortly thereafter to the finite- dimensional spectral theorem. A variety of interesting exercises in each chapter helps students understand and manipulate the objects of linear algebra. This second edition features new chapters on diagonal matrices, on linear functionals and adjoints, and on the spectral theorem; some sections, such as those on self-adjoint and normal operators, have been entirely rewritten; and hundreds of minor improvements have been made throughout the text.
Author : Nicholas M. Katz
Publisher : Princeton University Press
Page : 257 pages
File Size : 12,64 MB
Release : 2016-03-02
Category : Mathematics
ISBN : 1400882125
The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
Author : Max-Albert Knus
Publisher : American Mathematical Soc.
Page : 624 pages
File Size : 26,98 MB
Release : 1998-06-30
Category : Mathematics
ISBN : 9780821873212
This monograph is an exposition of the theory of central simple algebras with involution, in relation to linear algebraic groups. It provides the algebra-theoretic foundations for much of the recent work on linear algebraic groups over arbitrary fields. Involutions are viewed as twisted forms of (hermitian) quadrics, leading to new developments on the model of the algebraic theory of quadratic forms. In addition to classical groups, phenomena related to triality are also discussed, as well as groups of type $F_4$ or $G_2$ arising from exceptional Jordan or composition algebras. Several results and notions appear here for the first time, notably the discriminant algebra of an algebra with unitary involution and the algebra-theoretic counterpart to linear groups of type $D_4$. This volume also contains a Bibliography and Index. Features: original material not in print elsewhere a comprehensive discussion of algebra-theoretic and group-theoretic aspects extensive notes that give historical perspective and a survey on the literature rational methods that allow possible generalization to more general base rings
Author : Ali H. Sayed
Publisher : Cambridge University Press
Page : 1105 pages
File Size : 22,3 MB
Release : 2022-11-30
Category : Computers
ISBN : 1009218123
Discover core topics in inference and learning with the first volume of this extraordinary three-volume set.
Author : Steven H. Weintraub
Publisher : Courier Dover Publications
Page : 129 pages
File Size : 49,64 MB
Release : 2017-05-03
Category : Mathematics
ISBN : 0486821234
Every mathematician and student of mathematics needs a familiarity with mathematical induction. This volume provides advanced undergraduates and graduate students with an introduction and a thorough exposure to these proof techniques. 2017 edition.
Author : Lynn Harold Loomis
Publisher : World Scientific Publishing Company
Page : 595 pages
File Size : 37,57 MB
Release : 2014-02-26
Category : Mathematics
ISBN : 9814583952
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
