Elementary Geometry of Algebraic Curves (Paperback)

C.G. Gibson

ISBN 10: 0521646413 / ISBN 13: 9780521646413

Published by Cambridge University Press, Cambridge, 1998

About this Item

Paperback. 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 contains several hundred worked examples and exercises, making it suitable for adoption as a course text. From the 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, whilst the ideas of linear systems are used to discuss the classical group structure on the cubic. This is an introduction to plane algebraic curves from a geometric viewpoint. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability.

Seller Inventory # 9780521646413

Bibliographic Details

• Title: Elementary Geometry of Algebraic Curves (Paperback)
• Publisher: Cambridge University Press, Cambridge
• Publication Date: 1998
• Language: English
• ISBN 10: 0521646413
• ISBN 13: 9780521646413
• Binding: Paperback
• Edition: 1st Edition
• Condition: new

About this title

Synopsis

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.

About the Author

Chris Gibson received an honours degree in Mathematics from St Andrews University in 1963, and later the degrees of Drs Math and Dr Math from the University of Amsterdam, returning to England in 1967 to begin his 35 year mathematics career at the University of Liverpool. His interests turned towards the geometric areas, and he was a founder member of the Liverpool Singularities Group until his retirement in 2002 as Reader in Pure Mathematics, with over 60 published papers in that area. In 1974 he co-authored the significant 'Topological Stability of Smooth Mappings' (published by Springer Verlag) presenting the first detailed proof of Thom's Topological Stability Theorem. In addition to purely theoretical work in singularity theory, he jointly applied singular methods to specific questions about caustics arising in the physical sciences. His later interests lay largely in the applications to theoretical kinematics, and to problems arising in theoretical robotics. This interest gave rise to a substantial collaboration with Professor K. H. Hunt in the Universities of Monash and Melbourne, and produced a formal classification of screw systems. At the teaching level his major contribution was to pioneer the re-introduction of undergraduate geometry teaching. The practical experience of many years of undergraduate teaching was distilled into three undergraduate texts published by Cambridge University Press, now widely adopted internationally for undergraduate (and graduate) teaching.