Introduction to Plane Algebraic Curves

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9780817643812: Introduction to Plane Algebraic Curves

* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed

*Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices

* Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography

* Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra

* Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

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From the Back Cover:

This work treats an introduction to commutative ring theory and algebraic plane curves, requiring of the student only a basic knowledge of algebra, with all of the algebraic facts collected into several appendices that can be easily referred to, as needed.

Kunz's proven conception of teaching topics in commutative algebra together with their applications to algebraic geometry makes this book significantly different from others on plane algebraic curves. The exposition focuses on the purely algebraic aspects of plane curve theory, leaving the topological and analytical viewpoints in the background, with only casual references to these subjects and suggestions for further reading.

Most important to this text:

* Emphasizes and utilizes the theory of filtered algebras, their graduated rings and Rees algebras, to deduce basic facts about the intersection theory of plane curves

* Presents residue theory in the affine plane and its applications to intersection theory

* Methods of proof for the Riemann–Roch theorem conform to the presentation of curve theory, formulated in the language of filtrations and associated graded rings

* Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook

From a review of the German edition:

"[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students... The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation...highly enlightening, motivating and entertaining at the same time... One simply cannot do better in writing such a textbook."

―Zentralblatt MATH

 

 

Review:

"This text stands out by the author's...writing style characterized by its systematic representations, didactical perfection, comprehensiveness, mathematical rigor, thematic determination, and striving for self-containedness. Like in most of his other textbooks on algebra and algebraic geometry [the author] focuses on the inseparable interplay between those two branches of mathematics, and again he presents and hits for further reading. There is no doubt that the international mathematical community, including students and teachers, will welcome the overdue English edition of this masterly textbook as a very special and useful addition to the great standard texts on plane curves."      ―Zentralblatt MATH

"The translation of the book is impeccable, one would never imagine that the book was written in another language. Moreover, the exposition is very clear and the reading flows nicely. The book is a very good choice for a first course in algebraic geometry. As a prerequisite the reader needs some basic notions of algebra; the rest of the needed algebraic requirements are developed in the appendices."   ―MAA Reviews

From a review of the German edition:  "[T]he reader is invited to learn some topics from commutative ring theory by mainly studying their illustrations and applications in plane curve theory. This methodical approach is certainly very enlightening and efficient for both teachers and students...The whole text is a real masterpiece of clarity, rigor, comprehension, methodical skill, algebraic and geometric motivation...highly enlightening, motivating and entertaining at the same time...One simply cannot do better in writing such a textbook."   ―Zentralblatt MATH

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1.

Ernst Kunz
Editorial: Birkhauser Boston, Germany (2005)
ISBN 10: 0817643818 ISBN 13: 9780817643812
Nuevos Paperback Cantidad: 10
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Descripción Birkhauser Boston, Germany, 2005. Paperback. Estado de conservación: New. Language: English . Brand New Book ***** Print on Demand *****.* Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook. Nº de ref. de la librería AAV9780817643812

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Ernst Kunz, Richard G. Belshoff (Translator)
Editorial: Birkhäuser (2005)
ISBN 10: 0817643818 ISBN 13: 9780817643812
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Descripción Birkhäuser, 2005. Paperback. Estado de conservación: New. 2005. Nº de ref. de la librería DADAX0817643818

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Ernst Kunz
Editorial: Birkhauser Boston, Germany (2005)
ISBN 10: 0817643818 ISBN 13: 9780817643812
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Descripción Birkhauser Boston, Germany, 2005. Paperback. Estado de conservación: New. Language: English . Brand New Book ***** Print on Demand *****. * Employs proven conception of teaching topics in commutative algebra through a focus on their applications to algebraic geometry, a significant departure from other works on plane algebraic curves in which the topological-analytic aspects are stressed *Requires only a basic knowledge of algebra, with all necessary algebraic facts collected into several appendices * Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography * Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra * Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook. Nº de ref. de la librería AAV9780817643812

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Kunz, Ernst
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Descripción Birkhäuser, 2016. Paperback. Estado de conservación: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Nº de ref. de la librería ria9780817643812_lsuk

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Descripción Birkhauser Boston, 2005. PAP. Estado de conservación: New. New Book. Delivered from our UK warehouse in 3 to 5 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería LQ-9780817643812

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Descripción BirkhÇÏuser, 2005. Paperback. Estado de conservación: NEW. 9780817643812 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Nº de ref. de la librería HTANDREE0285849

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Descripción Birkhauser Boston, 2005. PAP. Estado de conservación: New. New Book. Shipped from US within 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Nº de ref. de la librería IQ-9780817643812

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Descripción Birkhäuser, 2010. Paperback. Estado de conservación: New. book. Nº de ref. de la librería 0817643818

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Descripción Birkhäuser. Paperback. Estado de conservación: New. Paperback. 294 pages. Dimensions: 9.2in. x 6.1in. x 0.6in. Employs proven conception of teaching topics in commutative algebra through a focus ontheir applications to algebraic geometry, asignificant departure from other workson plane algebraic curves in whichthe topological-analytic aspects are stressed Requires only a basic knowledge of algebra, with all necessary algebraic factscollected into several appendices Studies algebraic curves over an algebraically closed field K and those of prime characteristic, which can be applied to coding theory and cryptography Covers filtered algebras, the associated graded rings and Rees rings to deduce basic facts about intersection theory of plane curves, applications of which are standard tools of computer algebra Examples, exercises, figures and suggestions for further study round out this fairly self-contained textbook This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback. Nº de ref. de la librería 9780817643812

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Descripción Birkhäuser. PAPERBACK. Estado de conservación: New. 0817643818 Special order direct from the distributor. Nº de ref. de la librería ING9780817643812

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