Algebraic Geometry: A Problem-solving Approach

Thomas Garrity, Richard Belshoff, Lynette Boos, Ryan Brown, Carl Lienert, David Murphy, Junalyn Navarra-Madsen, Pedro Poitevin, Shawn Robinson, Brian Snyder, Caryn Werner

ISBN: 9781470425975 | Year: 2016 | Paperback | Pages: 340 | Language : English

Book Size: 140 x 216 mm | Territorial Rights: Restricted| Series American Mathematical Society

Price: 1270.00

About the Book

Algebraic geometry has been at the centre 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.

Contributors (Author(s), Editor(s), Translator(s), Illustrator(s) etc.)

Thomas Garrity is the William R. Kenan Jr. Professor of Mathematics at the Department of Mathematics, Williams College, Williamstown, USA. 

Richard Belshoff is Professor at the Department of Mathematics, Missouri State University, Springfield, USA. 

Lynette Boos is Associate Professor of Math at Providence College, Providence, USA. 

Ryan Brown Is Associate Professor at the Department of Mathematics, Georgia College and State University, Milledgeville, USA
Carl Lienert is Professor at the Department of Mathematics, Fort Lewis College, Durango, USA.
 
David Murphy is Associate Professor of Mathematics at the Department of Mathematics and Computer Science, Hillsdale College, Hillsdale, USA. 

Junalyn Navarra-Madsen is Assistant Professor at the Department of Mathematics and Computer Science, Texas Woman’s University, Denton, USA.
 
Pedro Poitevin is Associate Professor at the Department of Mathematics, Salem State University, Salem, USA
Shawn Robinson is Assistant Professor of Mathematics at the Department of Computer Science, Mathematics and Statistics, Colorado Mesa University, Grand Junction, USA
 
Brian Snyder is Associate Professor at the School of Mathematics and Computer Science, Lake Superior State University, Sault Ste. Marie, USA.
 
Caryn Werner is Professor at the Department of Mathematics, Allegheny College, Meadville, USA

Table of Content

Preface 
Chapter 1. Conics 
Chapter 2. Cubic Curves and Elliptic Curves 
Chapter 3. Higher Degree Curves 
Chapter 4. Affine Varieties 
Chapter 5. Projective Varieties 
Chapter 6. The Next Steps: Sheaves and Cohomology 
Bibliography 
Index

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