Lectures on Algebra

Lectures on Algebra
Author: Shreeram Shankar Abhyankar
Publisher: World Scientific
Total Pages: 758
Release: 2006
Genre: Mathematics
ISBN: 9812568263
GET BOOK

Download Lectures on Algebra Book in PDF, Epub and Kindle

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling. The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel. Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author's fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author's lectures at Purdue University over the last few years.

Lectures on Linear Algebra

Lectures on Linear Algebra
Author: I. M. Gelfand
Publisher: Courier Corporation
Total Pages: 212
Release: 1989-01-01
Genre: Mathematics
ISBN: 9780486660820
GET BOOK

Download Lectures on Linear Algebra Book in PDF, Epub and Kindle

Prominent Russian mathematician's concise, well-written exposition considers n-dimensional spaces, linear and bilinear forms, linear transformations, canonical form of an arbitrary linear transformation, and an introduction to tensors. While not designed as an introductory text, the book's well-chosen topics, brevity of presentation, and the author's reputation will recommend it to all students, teachers, and mathematicians working in this sector.

Introduction to Applied Linear Algebra

Introduction to Applied Linear Algebra
Author: Stephen Boyd
Publisher: Cambridge University Press
Total Pages: 477
Release: 2018-06-07
Genre: Business & Economics
ISBN: 1316518965
GET BOOK

Download Introduction to Applied Linear Algebra Book in PDF, Epub and Kindle

A groundbreaking introduction to vectors, matrices, and least squares for engineering applications, offering a wealth of practical examples.

Six Lectures on Commutative Algebra

Six Lectures on Commutative Algebra
Author: J. Elias
Publisher: Springer Science & Business Media
Total Pages: 402
Release: 2010-03-17
Genre: Mathematics
ISBN: 3034603290
GET BOOK

Download Six Lectures on Commutative Algebra Book in PDF, Epub and Kindle

Interest in commutative algebra has surged over the past decades. In order to survey and highlight recent developments in this rapidly expanding field, the Centre de Recerca Matematica in Bellaterra organized a ten-days Summer School on Commutative Algebra in 1996. Lectures were presented by six high-level specialists, L. Avramov (Purdue), M.K. Green (UCLA), C. Huneke (Purdue), P. Schenzel (Halle), G. Valla (Genova) and W.V. Vasconcelos (Rutgers), providing a fresh and extensive account of the results, techniques and problems of some of the most active areas of research. The present volume is a synthesis of the lectures given by these authors. Research workers as well as graduate students in commutative algebra and nearby areas will find a useful overview of the field and recent developments in it. Reviews "All six articles are at a very high level; they provide a thorough survey of results and methods in their subject areas, illustrated with algebraic or geometric examples." - Acta Scientiarum Mathematicarum Avramov lecture: "... it contains all the major results [on infinite free resolutions], it explains carefully all the different techniques that apply, it provides complete proofs (...). This will be extremely helpful for the novice as well as the experienced." - Mathematical reviews Huneke lecture: "The topic is tight closure, a theory developed by M. Hochster and the author which has in a short time proved to be a useful and powerful tool. (...) The paper is extremely well organized, written, and motivated." - Zentralblatt MATH Schenzel lecture: "... this paper is an excellent introduction to applications of local cohomology." - Zentralblatt MATH Valla lecture: "... since he is an acknowledged expert on Hilbert functions and since his interest has been so broad, he has done a superb job in giving the readers a lively picture of the theory." - Mathematical reviews Vasconcelos lecture: "This is a very useful survey on invariants of modules over noetherian rings, relations between them, and how to compute them." - Zentralblatt MATH

Lectures on Algebra

Lectures on Algebra
Author: Shreeram Shankar Abhyankar
Publisher: World Scientific
Total Pages: 758
Release: 2006
Genre: Mathematics
ISBN: 9812773444
GET BOOK

Download Lectures on Algebra Book in PDF, Epub and Kindle

This book is a timely survey of much of the algebra developed during the last several centuries including its applications to algebraic geometry and its potential use in geometric modeling.The present volume makes an ideal textbook for an abstract algebra course, while the forthcoming sequel, Lectures on Algebra II, will serve as a textbook for a linear algebra course. The author''s fondness for algebraic geometry shows up in both volumes, and his recent preoccupation with the applications of group theory to the calculation of Galois groups is evident in the second volume which contains more local rings and more algebraic geometry. Both books are based on the author''s lectures at Purdue University over the last few years.

Lectures on Algebraic Statistics

Lectures on Algebraic Statistics
Author: Mathias Drton
Publisher: Springer Science & Business Media
Total Pages: 177
Release: 2009-04-25
Genre: Mathematics
ISBN: 3764389052
GET BOOK

Download Lectures on Algebraic Statistics Book in PDF, Epub and Kindle

How does an algebraic geometer studying secant varieties further the understanding of hypothesis tests in statistics? Why would a statistician working on factor analysis raise open problems about determinantal varieties? Connections of this type are at the heart of the new field of "algebraic statistics". In this field, mathematicians and statisticians come together to solve statistical inference problems using concepts from algebraic geometry as well as related computational and combinatorial techniques. The goal of these lectures is to introduce newcomers from the different camps to algebraic statistics. The introduction will be centered around the following three observations: many important statistical models correspond to algebraic or semi-algebraic sets of parameters; the geometry of these parameter spaces determines the behaviour of widely used statistical inference procedures; computational algebraic geometry can be used to study parameter spaces and other features of statistical models.

Lectures on Algebraic Quantum Groups

Lectures on Algebraic Quantum Groups
Author: Ken Brown
Publisher: Birkhäuser
Total Pages: 339
Release: 2012-12-06
Genre: Mathematics
ISBN: 303488205X
GET BOOK

Download Lectures on Algebraic Quantum Groups Book in PDF, Epub and Kindle

This book consists of an expanded set of lectures on algebraic aspects of quantum groups. It particularly concentrates on quantized coordinate rings of algebraic groups and spaces and on quantized enveloping algebras of semisimple Lie algebras. Large parts of the material are developed in full textbook style, featuring many examples and numerous exercises; other portions are discussed with sketches of proofs, while still other material is quoted without proof.

Lectures in Abstract Algebra

Lectures in Abstract Algebra
Author: N. Jacobson
Publisher: Springer
Total Pages: 304
Release: 1975
Genre: Mathematics
ISBN:
GET BOOK

Download Lectures in Abstract Algebra Book in PDF, Epub and Kindle

The present volume is the second in the author's series of three dealing with abstract algebra. For an understanding of this volume a certain familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundamental concepts needed have been treated again. In short, it is hoped that this volume can be read with complete understanding by any student who is mathematically sufficiently mature and who has a familiarity with the standard notions of modern algebra. Our point of view in the present volume is basically the abstract conceptual one. However, from time to time we have deviated somewhat from this. Occasionally formal calculational methods yield sharper results. Moreover, the results of linear algebra are not an end in themselves but are essential tools for use in other branches of mathematics and its applications. It is therefore useful to have at hand methods which are constructive and which can be applied in numerical problems. These methods sometimes necessitate a somewhat lengthier discussion but we have felt that their presentation is justified on the grounds indicated. A stu dent well versed in abstract algebra will undoubtedly observe short cuts. Some of these have been indicated in footnotes. We have included a large number of exercises in the text.

Exercises in Modules and Rings

Exercises in Modules and Rings
Author: T.Y. Lam
Publisher: Springer Science & Business Media
Total Pages: 427
Release: 2009-12-08
Genre: Mathematics
ISBN: 0387488995
GET BOOK

Download Exercises in Modules and Rings Book in PDF, Epub and Kindle

This volume offers a compendium of exercises of varying degree of difficulty in the theory of modules and rings. It is the companion volume to GTM 189. All exercises are solved in full detail. Each section begins with an introduction giving the general background and the theoretical basis for the problems that follow.