Algebraic Geometry: A Problem Solving Approach (Student Mathematical Library) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 66)

Thomas Garrity

ISBN 10: 0821893963 / ISBN 13: 9780821893968

Published by American Mathematical Society in corporation with IAS/Park City Mathematics Institute, 2013

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Bibliographic Details

• Title: Algebraic Geometry: A Problem Solving Approach (Student Mathematical Library) (Student Mathematical Library: IAS/Park City Mathematical Subseries, 66)
• Publisher: American Mathematical Society in corporation with IAS/Park City Mathematics Institute
• Publication Date: 2013
• Language: English
• ISBN 10: 0821893963
• ISBN 13: 9780821893968
• Binding: Paperback
• Condition: new

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Synopsis

Algebraic Geometry has been at the center of much of mathematics for hundreds of years. It is not an easy field to break into, despite its humble beginnings in the study of circles, ellipses, hyperbolas, and parabolas. This text consists of a series of exercises, plus some background information and explanations, starting with conics and ending with sheaves and cohomology. The first chapter on conics is appropriate for first-year college students (and many high school students). Chapter 2 leads the reader to an understanding of the basics of cubic curves, while Chapter 3 introduces higher degree curves. Both chapters are appropriate for people who have taken multivariable calculus and linear algebra. Chapters 4 and 5 introduce geometric objects of higher dimension than curves. Abstract algebra now plays a critical role, making a first course in abstract algebra necessary from this point on. The last chapter is on sheaves and cohomology, providing a hint of current work in algebraic geometry.