Classical algebraic geometry, inseparably connected with the names of Abel, Riemann, Weierstrass, Poincaré, Clebsch, Jacobi and other outstanding mathematicians of the last century, was mainly an analytical theory. In our century the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched it and seemed to have replaced once and forever the somewhat naive language of classical algebraic geometry. This classic book, written in 1897, covers the whole of algebraic geometry and associated theories. Baker discusses the subject in terms of transcendental functions, and theta functions in particular. Many of the ideas put forward are of continuing relevance today, and some of the most exciting ideas from theoretical physics draw on work presented here.
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"...offers welcome historical insight into a key point in the history of algebraic geometry." John B. Little, Mathematical Reviews
Book Description
In our century, the methods and ideas of topology, commutative algebra and Grothendieck's schemes enriched classical algebraic geometry and seemed to have replaced its somewhat naive language. Written in 1897, this classic book, however, stresses algebraic geometry's continuing relevance.
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9 of 9 people found the following review helpful:
5.0 out of 5 stars
A precious jewel !,
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This review is from: Abelian Functions: Abel's Theorem and the Allied Theory of Theta Functions (Cambridge Mathematical Library) (Paperback)
When I was a Ph.D. student and had some problems finding suitable functions in order to study the multiloop scattering of strings, I found this rarity of a book. Although it was first published a long time ago (1897) it is probably one of the most complete works on complex functions of many variables and particularly on theta functions of many variables. In this book you can find some material that is not in any other book I know of, and the style makes it relatively easy to read.It covers a large number of subjects, like Abel's theorem, abelian integrals of the first and second type, Riemann's theta functions, hyperelliptic (many variables) theta functions, radical and factorial functions, Jacobian functions, and degenerate abelian integrals. I consider it a jewel among the books that cover the same subject, both for its completenes and its writing style.
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THIS book is concerned with a particular development of the theory of the algebraic irrationally arising when a quantity y is defined in terms of a quantity x by means of an equation of the form wherein are rational integral polynomials in x. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Acta Math, Collected Works, Abel'schen Functionen, Solid Geometry, Zur Theorie, American Journal, Bulletin de la Soc, London Math, Neue Grundlagen, Crelle's Journal, Die Transformation, Elliptische Functionen New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
THIS book is concerned with a particular development of the theory of the algebraic irrationally arising when a quantity y is defined in terms of a quantity x by means of an equation of the form wherein are rational integral polynomials in x. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
Acta Math, Collected Works, Abel'schen Functionen, Solid Geometry, Zur Theorie, American Journal, Bulletin de la Soc, London Math, Neue Grundlagen, Crelle's Journal, Die Transformation, Elliptische Functionen New!
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:
- Report on the Theory of Numbers by Henry J. S. Smith on page 600, and page 639
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