Mathematics

Rudiments of Algebraic Geometry

Author: W.E. Jenner

Publisher: Courier Dover Publications

ISBN: 0486818063

Category: Mathematics

Page: 112

View: 3221

Aimed at advanced undergraduate students of mathematics, this concise text covers the basics of algebraic geometry. Topics include affine spaces, projective spaces, rational curves, algebraic sets with group structure, more. 1963 edition.
Mathematics

Foundations of Algebraic Geometry

Author: AndrŽ Weil

Publisher: American Mathematical Soc.

ISBN: 0821810294

Category: Mathematics

Page: 363

View: 2000

This classic is one of the cornerstones of modern algebraic geometry. At the same time, it is entirely self-contained, assuming no knowledge whatsoever of algebraic geometry, and no knowledge of modern algebra beyond the simplest facts about abstract fields and their extensions, and the bare rudiments of the theory of ideals.
Mathematics

Algebra

A Graduate Course

Author: I. Martin Isaacs

Publisher: American Mathematical Soc.

ISBN: 9780821847992

Category: Mathematics

Page: 516

View: 7292

as a student." --Book Jacket.
Mathematics

Lectures on Invariant Theory

Author: Igor Dolgachev

Publisher: Cambridge University Press

ISBN: 9780521525480

Category: Mathematics

Page: 220

View: 5271

The primary goal of this 2003 book is to give a brief introduction to the main ideas of algebraic and geometric invariant theory. It assumes only a minimal background in algebraic geometry, algebra and representation theory. Topics covered include the symbolic method for computation of invariants on the space of homogeneous forms, the problem of finite-generatedness of the algebra of invariants, the theory of covariants and constructions of categorical and geometric quotients. Throughout, the emphasis is on concrete examples which originate in classical algebraic geometry. Based on lectures given at University of Michigan, Harvard University and Seoul National University, the book is written in an accessible style and contains many examples and exercises. A novel feature of the book is a discussion of possible linearizations of actions and the variation of quotients under the change of linearization. Also includes the construction of toric varieties as torus quotients of affine spaces.
Mathematics

Lectures on Curves, Surfaces and Projective Varieties

A Classical View of Algebraic Geometry

Author: Mauro Beltrametti

Publisher: European Mathematical Society

ISBN: 9783037190647

Category: Mathematics

Page: 491

View: 7955

This book offers a wide-ranging introduction to algebraic geometry along classical lines. It consists of lectures on topics in classical algebraic geometry, including the basic properties of projective algebraic varieties, linear systems of hypersurfaces, algebraic curves (with special emphasis on rational curves), linear series on algebraic curves, Cremona transformations, rational surfaces, and notable examples of special varieties like the Segre, Grassmann, and Veronese varieties. An integral part and special feature of the presentation is the inclusion of many exercises, not easy to find in the literature and almost all with complete solutions. The text is aimed at students of the last two years of an undergraduate program in mathematics. It contains some rather advanced topics suitable for specialized courses on the advanced undergraduate or beginning graduate level, as well as interesting topics for a senior thesis. The prerequisites have been deliberately limited to basic elements of projective geometry and abstract algebra. Thus, for example, some knowledge of the geometry of subspaces and properties of fields is assumed. The book will be welcomed by teachers and students of algebraic geometry who are seeking a clear and panoramic path leading from the basic facts about linear subspaces, conics and quadrics to a systematic discussion of classical algebraic varieties and the tools needed to study them. The text provides a solid foundation for approaching more advanced and abstract literature.
Mathematics

Principles of Algebraic Geometry

Author: Phillip Griffiths,Joseph Harris

Publisher: John Wiley & Sons

ISBN: 111862632X

Category: Mathematics

Page: 832

View: 4280

A comprehensive, self-contained treatment presenting general results of the theory. Establishes a geometric intuition and a working facility with specific geometric practices. Emphasizes applications through the study of interesting examples and the development of computational tools. Coverage ranges from analytic to geometric. Treats basic techniques and results of complex manifold theory, focusing on results applicable to projective varieties, and includes discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex as well as special topics in complex manifolds.
Mathematics

Analytical Geometry

Author: Izu Vaisman

Publisher: World Scientific

ISBN: 9789810231583

Category: Mathematics

Page: 284

View: 8385

This volume discusses the classical subjects of Euclidean, affine and projective geometry in two and three dimensions, including the classification of conics and quadrics, and geometric transformations. These subjects are important both for the mathematical grounding of the student and for applications to various other subjects. They may be studied in the first year or as a second course in geometry.The material is presented in a geometric way, and it aims to develop the geometric intuition and thinking of the student, as well as his ability to understand and give mathematical proofs. Linear algebra is not a prerequisite, and is kept to a bare minimum.The book includes a few methodological novelties, and a large number of exercises and problems with solutions. It also has an appendix about the use of the computer program MAPLEV in solving problems of analytical and projective geometry, with examples.
Naval architecture

Rudiments of Naval Architecture

An Exposition of the Elementary Principles of the Science and Their Practical Application to Naval Construction

Author: James Peake

Publisher: N.A

ISBN: N.A

Category: Naval architecture

Page: 316

View: 1307

Arithmetic

The Rudiments of Written Arithmetic

Containing Slate and Black-board Exercises for Beginners, and Designed for Graded Schools

Author: Horatio Nelson Robinson

Publisher: N.A

ISBN: N.A

Category: Arithmetic

Page: 192

View: 2800

Mathematics

Algebraic Geometry

Author: Solomon Lefschetz

Publisher: Courier Corporation

ISBN: 0486154726

Category: Mathematics

Page: 256

View: 1072

An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this text for advanced undergraduate students is particularly relevant to those more familiar with analysis than algebra. 1953 edition.
Mathematics

A Century of Mathematics in America

Author: Peter L. Duren,Richard Askey,Uta C. Merzbach

Publisher: American Mathematical Soc.

ISBN: 9780821801307

Category: Mathematics

Page: 585

View: 8597

The first section of the book deals with some of the influential mathematics departments in the United States. Functioning as centers of research and training, these departments played a major role in shaping the mathematical life in this country. The second section deals with an extraordinary conference held at Princeton in 1946 to commemorate the university's bicentennial. The influence of women in American mathematics, the burgeoning of differential geometry in the last 50 years, and discussions of the work of von Karman and Weiner are among other topics covered. To download free chapters of this book, click here.
Mathematics

Ebene algebraische Kurven

Author: Gerd Fischer

Publisher: Springer-Verlag

ISBN: 3322803112

Category: Mathematics

Page: 177

View: 8778

Neben den elementaren Dingen, wie Tangenten, Singularitäten und Wendepunkten werden auch schwierigere Begriffe wie lokale Zweige und Geschlecht behandelt. Höhepunkte sind die klassischen Formeln von Plücker und Clebsch, die Beziehungen zwischen verschiedenen globalen und lokalen Invarianten einer Kurve beschreiben.
Mathematics

Rudiments of Ramsey Theory

Author: Ronald L. Graham

Publisher: American Mathematical Soc.

ISBN: 0821816969

Category: Mathematics

Page: 65

View: 5785

It is no exaggeration to say that over the past several decades there has been a veritable explosion of activity in the general field of combinatorics. Ramsey theory, in particular, has shown remarkable growth. This book gives a picture of the state of the art of Ramsey theory at the time of Graham's CBMS lectures. In keeping with the style of the lectures, the exposition is informal. However, complete proofs are given for most of the basic results presented. In addition, many useful results may be found in the exercises and problems. Loosely speaking, Ramsey theory is the branch of combinatorics that deals with structures that are preserved under partitions. Typically, one looks at the following kind of question: If a particular structure (e.g., algebraic, combinatorial or geometric) is arbitrarily partitioned into finitely many classes, what kinds of substructures must always remain intact in at least one of the classes? At the time of these lectures, a number of spectacular advances had been made in the field of Ramsey theory. These include: the work of Szemeredi and Furstenberg settling the venerable conjecture of Erdos and Turan, the Nesetril-Rodl theorems on induced Ramsey properties, the results of Paris and Harrington on ``large'' Ramsey numbers and undecidability in first-order Peano arithmetic, Deuber's solution to the old partition regularity conjecture of Rado, Hindman's surprising generalization of Schur's theorem, and the resolution of Rota's conjecture on Ramsey's theorem for vector spaces by Graham, Leeb and Rothschild. It has also become apparent that the ideas and techniques of Ramsey theory span a rather broad range of mathematical areas, interacting in essential ways with parts of set theory, graph theory, combinatorial number theory, probability theory, analysis and even theoretical computer science. These lecture notes lay out the foundation on which much of this work is based. Relatively little specialized mathematical background is required for this book. It should be accessible to upper division students.
Mathematics

Übungsbuch Algebra für Dummies

Author: Mary Jane Sterling

Publisher: John Wiley & Sons

ISBN: 3527668276

Category: Mathematics

Page: 339

View: 3436

Algebra verstehen, üben und umsetzen Müssen Sie sich – ob Sie nun wollen oder nicht – in Schule, Beruf oder Studium mit Algebra beschäftigen? Dann hilft Ihnen dieses Buch. Mit Hunderten von Aufgaben, aus - führlichen Lösungen und Erklärungen führt Sie Mary Jane Sterling in die Welt der Algebra ein. Die Autorin erklärt Ihnen noch einmal die grundlegenden Regeln zum Rechnen mit Brüchen, Wurzeln und Co., wie Sie lineare und quadratische Gleichungen lösen und Textaufgaben bewältigen. Sie finden außerdem Übungen zur grafischen Darstellung von Geraden und Parabeln.