Here is an introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is well illustrated and contains several hundred worked examples and exercises. From the familiar lines and conics of elementary geometry the reader proceeds to general curves in the real affine plane, with excursions to more general fields to illustrate applications, such as number theory. By adding points at infinity the affine plane is extended to the projective plane, yielding a natural setting for curves and providing a flood of illumination into the underlying geometry. A minimal amount of algebra leads to the famous theorem of Bezout, while the ideas of linear systems are used to discuss the classical group structure on the cubic.
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Editorial Reviews
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"This book amply fulfills the promise of its title...far less forbidding than the vast majority of more ambitious textbooks...the author clearly motivates the study of projective curves by showing that several affine problems are more easily studied via the projective setting...a good abstract introduction for mathematicians." Theory of Computation
Book Description
This is a genuine introduction to plane algebraic curves from a geometric viewpoint, designed as a first text for undergraduates in mathematics, or for postgraduate and research workers in the engineering and physical sciences. The book is extremely well illustrated, and contains several hundred worked examples and exercises, making it suitable for adoption as a course text.
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6 of 8 people found the following review helpful:
4.0 out of 5 stars
Does what it claims,
By "another_anonymous" (Dallas, Texas United States) - See all my reviews
This review is from: Elementary Geometry of Algebraic Curves: An Undergraduate Introduction (Paperback)
We used this for a class introducing algebraic geometry. It's necessary to know linear algebra and multivariable calculus, and very helpful to know groups, rings, and fields. The book keeps it's feet on the ground (equal distribution of computation and abstraction in problems). Some examples throughout. Very good as an introduction.
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Inside This Book
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First Sentence:
Plane curves arise naturally in numerous areas of the physical sciences (such as particle physics, engineering robotics and geometric optics) and within areas of pure mathematics itself (such as number theory, complex analysis and differential equations). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
primitive complex cube root, dehomogenize with respect, affine equivalent curves, affine views, delta invariants, corresponding projective curve, distinct flexes, intersection polynomial, affine conics, central reflexion, rational parametrization, pedal curve, real affine plane, irreducible conic, parametrized line, affine classification, real ellipse, unique singular point, projective conic, three flexes, standard parabola, imaginary parallel lines, projective map, real algebraic curves, one singular point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Four Point Lemma, Proof Let, Multiplicity Inequality, Euler Lemma, Chain Rule, Proof Suppose, Theorem of the Nine Associated Points, Introductory Examples, Proof Write New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Plane curves arise naturally in numerous areas of the physical sciences (such as particle physics, engineering robotics and geometric optics) and within areas of pure mathematics itself (such as number theory, complex analysis and differential equations). Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
primitive complex cube root, dehomogenize with respect, affine equivalent curves, affine views, delta invariants, corresponding projective curve, distinct flexes, intersection polynomial, affine conics, central reflexion, rational parametrization, pedal curve, real affine plane, irreducible conic, parametrized line, affine classification, real ellipse, unique singular point, projective conic, three flexes, standard parabola, imaginary parallel lines, projective map, real algebraic curves, one singular point Key Phrases - Capitalized Phrases (CAPs): (learn more)
Four Point Lemma, Proof Let, Multiplicity Inequality, Euler Lemma, Chain Rule, Proof Suppose, Theorem of the Nine Associated Points, Introductory Examples, Proof Write New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 1
book:
3
books
cite this book:
- Ebene Algebraische Kurven by BRIESKORN on page 187
- Applied Geometry for Computer Graphics and CAD (Springer Undergraduate Mathematics Series) by Duncan Marsh in Index
- Advances in Robot Kinematics: Mechanisms and Motion by Jadran Lenarcic on page 314
- Elementary Geometry of Algebraic Curves: An Undergraduate Introduction by C. G. Gibson in Front Matter
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