Undergraduate Algebraic Geometry
Undergraduate Algebraic Geometry

Author: Miles Reid

Publisher: Cambridge University Press

Published: 1988-12-15

Total Pages: 144

ISBN-13: 9780521356626

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Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to the basic concepts of algebraic geometry including: plane conics, cubics and the group law, affine and projective varieties, and non-singularity and dimension. He is at pains to stress the connections the subject has with commutative algebra as well as its relation to topology, differential geometry, and number theory. The book arises from an undergraduate course given at the University of Warwick and contains numerous examples and exercises illustrating the theory.

An Introduction to Algebraic Topology
An Introduction to Algebraic Topology

Author: Joseph J. Rotman

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 447

ISBN-13: 1461245761

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A clear exposition, with exercises, of the basic ideas of algebraic topology. Suitable for a two-semester course at the beginning graduate level, it assumes a knowledge of point set topology and basic algebra. Although categories and functors are introduced early in the text, excessive generality is avoided, and the author explains the geometric or analytic origins of abstract concepts as they are introduced.

A Concise Course in Algebraic Topology
A Concise Course in Algebraic Topology

Author: J. P. May

Publisher: University of Chicago Press

Published: 1999-09

Total Pages: 262

ISBN-13: 9780226511832

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Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

The $K$-book
The $K$-book

Author: Charles A. Weibel

Publisher: American Mathematical Soc.

Published: 2013-06-13

Total Pages: 634

ISBN-13: 0821891324

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Informally, $K$-theory is a tool for probing the structure of a mathematical object such as a ring or a topological space in terms of suitably parameterized vector spaces and producing important intrinsic invariants which are useful in the study of algebr

Algebraic Topology from a Homotopical Viewpoint
Algebraic Topology from a Homotopical Viewpoint

Author: Marcelo Aguilar

Publisher: Springer Science & Business Media

Published: 2008-02-02

Total Pages: 499

ISBN-13: 0387224890

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The authors present introductory material in algebraic topology from a novel point of view in using a homotopy-theoretic approach. This carefully written book can be read by any student who knows some topology, providing a useful method to quickly learn this novel homotopy-theoretic point of view of algebraic topology.