Undergraduate Algebraic Geometry

Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521356626
Format: PDF, Docs
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This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time.

Undergraduate Commutative Algebra

Author: Miles Reid
Publisher: Cambridge University Press
ISBN: 9780521458894
Format: PDF
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In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.

Complex Algebraic Curves

Author: Frances Clare Kirwan
Publisher: Cambridge University Press
ISBN: 9780521423533
Format: PDF, ePub
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This development of the theory of complex algebraic curves was one of the peaks of nineteenth century mathematics. They have many fascinating properties and arise in various areas of mathematics, from number theory to theoretical physics, and are the subject of much research. By using only the basic techniques acquired in most undergraduate courses in mathematics, Dr. Kirwan introduces the theory, observes the algebraic and topological properties of complex algebraic curves, and shows how they are related to complex analysis.

Computational Algebraic Geometry

Author: Hal Schenck
Publisher: Cambridge University Press
ISBN: 9780521536509
Format: PDF, ePub, Docs
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This 2003 book investigates interplay between algebra and geometry. Covers: homological algebra, algebraic combinatorics and algebraic topology, and algebraic geometry.

Steps in Commutative Algebra

Author: R. Y. Sharp
Publisher: Cambridge University Press
ISBN: 9780521646239
Format: PDF, ePub, Mobi
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This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

Elementary Algebraic Geometry

Author: Klaus Hulek
Publisher: American Mathematical Soc.
ISBN: 0821829521
Format: PDF
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This book is a true introduction to the basic concepts and techniques of algebraic geometry. The language is purposefully kept on an elementary level, avoiding sheaf theory and cohomology theory. The introduction of new algebraic concepts is always motivated by a discussion of the corresponding geometric ideas. The main point of the book is to illustrate the interplay between abstract theory and specific examples. The book contains numerous problems that illustrate the general theory. The text is suitable for advanced undergraduates and beginning graduate students. It contains sufficient material for a one-semester course. The reader should be familiar with the basic concepts of modern algebra. A course in one complex variable would be helpful, but is not necessary.

Algebraic and Analytic Geometry

Author: Amnon Neeman
Publisher: Cambridge University Press
ISBN: 0521709830
Format: PDF
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Modern introduction to algebraic geometry for undergraduates; uses analytic ideas to access algebraic theory.

Introduction to Algebraic Geometry

Author: Brendan Hassett
Publisher: Cambridge University Press
ISBN: 1139464590
Format: PDF, ePub, Docs
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Algebraic geometry, central to pure mathematics, has important applications in such fields as engineering, computer science, statistics and computational biology, which exploit the computational algorithms that the theory provides. Users get the full benefit, however, when they know something of the underlying theory, as well as basic procedures and facts. This book is a systematic introduction to the central concepts of algebraic geometry most useful for computation. Written for advanced undergraduate and graduate students in mathematics and researchers in application areas, it focuses on specific examples and restricts development of formalism to what is needed to address these examples. In particular, it introduces the notion of Gröbner bases early on and develops algorithms for almost everything covered. It is based on courses given over the past five years in a large interdisciplinary programme in computational algebraic geometry at Rice University, spanning mathematics, computer science, biomathematics and bioinformatics.

Young Tableaux

Author: William Fulton
Publisher: Cambridge University Press
ISBN: 9780521567244
Format: PDF, Kindle
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Describes combinatorics involving Young tableaux and their uses in representation theory and algebraic geometry.

An Introduction to Twistor Theory

Author: S. A. Huggett
Publisher: Cambridge University Press
ISBN: 9780521456890
Format: PDF, ePub, Mobi
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This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. It will be valuable also to the physicist as an introduction to some of the mathematics that has proved useful in these areas, and to the mathematician as an example of where sheaf cohomology and complex manifold theory can be used in physics.