Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)

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9781441921789: Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)

Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout’s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course.

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From the Back Cover:

Conics and Cubics is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas: homogenous coordinates and intersection multiplicities.

By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout's Theorem on the number of intersections of two curves.

The book is a text for a one-semester course on algebraic curves for junior-senior mathematics majors. The only prerequisite is first-year calculus.

The new edition introduces the deeper study of curves through parametrization by power series. Two uses of parametrizations are presented: counting multiple intersections of curves and proving the duality of curves and their envelopes.

About the first edition:

"The book...belongs in the admirable tradition of laying the foundations of a difficult and potentially abstract subject by means of concrete and accessible examples."

- Peter Giblin, MathSciNet

Review:

"...This book therefore belongs to the admirable tradition of laying the foundations of a difficult and potentially abstract subject by means of concrete and accessible examples. ... Two major strengths of the book are its historical perspective, in the form of informative introductions to the chapters which give the main developments in non-technical language, and its exercises, which are numerous and interesting." Peter Giblin for MathSciNet

From the reviews of the second edition:

"Algebraic geometry is a hard subject. ... But could it, or at least some of it, be presented, at the undergraduate level? This book attempts to do that. ... At the beginning of each of the four chapters, the author provides a synopsis of the historical development of the subject. And within each section many exercises are provided for further discussion and illumination. ... And the author manages to keep things concrete. So, the end result is a book which is accessible ... ." (Donald L. Vestal, MathDL – online, October, 2006)

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Book Description Springer-Verlag New York Inc., United States, 2010. Paperback. Book Condition: New. Language: English . This book usually ship within 10-15 business days and we will endeavor to dispatch orders quicker than this where possible. Brand New Book. Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course. Softcover reprint of hardcover 2nd ed. 2006. Bookseller Inventory # LIE9781441921789

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Book Description Springer-Verlag New York Inc., United States, 2010. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****.Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course. Softcover reprint of hardcover 2nd ed. 2006. Bookseller Inventory # AAV9781441921789

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Book Description Springer-Verlag New York Inc., United States, 2010. Paperback. Book Condition: New. Language: English . Brand New Book ***** Print on Demand *****. Conics and Cubics offers an accessible and well illustrated introduction to algebraic curves. By classifying irreducible cubics over the real numbers and proving that their points form Abelian groups, the book gives readers easy access to the study of elliptic curves. It includes a simple proof of Bezout s Theorem on the number of intersections of two curves. The subject area is described by means of concrete and accessible examples. The book is a text for a one-semester course. Softcover reprint of hardcover 2nd ed. 2006. Bookseller Inventory # AAV9781441921789

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