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

Robert Bix (Author)

Book Description

Publication Date: June 12, 1998 | ISBN-10: 0387984011 | ISBN-13: 978-0387984018 | Edition: 1

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, homogeneous 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 any two curves without common factors. The book is a text for a one-semester course. The course can serve both as the one undergraduate geometry course taken by mathematics majors in general and as a sequel to college geometry for prospective or current teachers of secondary school mathematics. The only prerequisite is first-year calculus.

Editorial Reviews

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)

--This text refers to an alternate Hardcover edition.

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

--This text refers to an alternate Hardcover edition.

Product Details

• Hardcover: 308 pages
• Publisher: Springer; 1 edition (June 12, 1998)
• Language: English
• ISBN-10: 0387984011
• ISBN-13: 978-0387984018
• Product Dimensions: 9.5 x 6.2 x 0.8 inches
• Shipping Weight: 1.3 pounds
• Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #3,827,259 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

7 of 8 people found the following review helpful:

5.0 out of 5 stars A perfect introduction!, March 19, 2008

By 

Erick Galinkin (New York, United States) - See all my reviews
(REAL NAME)   

This review is from: Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics) (Hardcover)

I'm a freshman in college and I wanted to start doing research in mathematics. This was a perfect way for me to get a leg up on my peers as algebraic geometry is a vital tool in mathematics today and most undergraduates never get an exposure to it.

The language is formal enough to be a textbook, but it's certainly not detached, it's much like reading the transcript of a lecture. The only knowledge that the book assumes is single variable calculus and high school algebra and geometry.

Overall, the book is just very accessible and well worth the price.

8 of 13 people found the following review helpful:

4.0 out of 5 stars Welcome Addition to the Literature, June 10, 2000

By 

James M. Cargal (Montgomery, AL USA) - See all my reviews
(REAL NAME)   

This review is from: Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics) (Hardcover)

This book may be the most elementary introduction to algebraic geometry. Still it is roughly senior level and unlike the review above I am not sure that it is suitable for students in secondary education. Nonetheless, it fills a niche that has been largely vacant in the undergraduate literature and I recommend it to serious students and undergraduates alike.