Real Algebra by Manfred Knebusch
This book provides an introduction to fundamental methods and techniques of algebra over ordered fields. It is a revised and updated translation of the classic textbook Einführung in die reelle Algebra. Beginning with the basics of ordered fields and their real closures, the book proceeds to discuss methods for counting the number of real roots of polynomials. Followed by a thorough introduction to Krull valuations, this culminates in Artin's solution of Hilbert's 17th Problem. Next, the fundamental concept of the real spectrum of a commutative ring is introduced with applications. The final chapter gives a brief overview of important developments in real algebra and geometry—as far as they are directly related to the contents of the earlier chapters—since the publication of the original German edition. Real Algebra is aimed at advanced undergraduate and beginning graduate students who have a good grounding in linear algebra, field theory and ring theory. It also provides a carefully written reference for specialists in real algebra, real algebraic geometry and related fields.-
Linear Functional Analysis
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An Introduction to Manifolds
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Riemannian Geometry
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Galois Theory
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Symbolic Dynamics
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Stochastic Calculus
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Geometry I
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Galois Cohomology and Class Field Theory
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Mathematical Gauge Theory
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Nonlinear Differential Equations and Dynamical Systems
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Mathematical Analysis I
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Differential Forms and Applications
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Introduction to Partial Differential Equations
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Geometry
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From Elementary Probability to Stochastic Differential Equations with MAPLE (R)
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Applied Stochastic Control of Jump Diffusions
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Probability Essentials
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Stochastic Differential Equations
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Elements of Functional Analysis
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Selected Topics in Partial Differential Equations
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The Essentials of Measure Theory
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On the Theory of Maass Wave Forms
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Potential Theory
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Fluctuations of Levy Processes with Applications
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Discrete Mathematics
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Automorphic Forms
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Matrix Theory
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Frontiers of Numerical Analysis
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Spectra of Graphs
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Polyhedral and Algebraic Methods in Computational Geometry
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Theory and Numerics of Differential Equations
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Dynamical Systems
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A Course on Tug-of-War Games with Random Noise
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Sphere Packings
“More than 30 years after its initial publication, the present textbook is still a very valuable source for results in real algebraIt can serve as a textbook for a university course, but also experts will benefit from the nice account of concepts and results. It’s great that the book is available again, in particular in an English translation for an international audience.” (Tim Netzer, zbMATH 1505.13001, 2023)
Manfred Knebusch is Professor Emeritus at the University of Regensburg. He has written nine books and more than 80 papers on the algebraic theory of quadratic forms over rings and fields, valuation theory, real algebra and real algebraic geometry. His current research focusses on tropical geometry.
Claus Scheiderer is Professor at Konstanz University. His primary research interests are real algebraic geometry and convex algebraic geometry.
Thomas Unger is Associate Professor at University College Dublin. His research interests include quadratic and hermitian forms, algebras with involution, and noncommutative real algebra and geometry.
Claus Scheiderer is Professor at Konstanz University. His primary research interests are real algebraic geometry and convex algebraic geometry.
Thomas Unger is Associate Professor at University College Dublin. His research interests include quadratic and hermitian forms, algebras with involution, and noncommutative real algebra and geometry.
| SKU | Unavailable |
| ISBN 13 | 9783031097997 |
| ISBN 10 | 3031097998 |
| Title | Real Algebra |
| Author | Manfred Knebusch |
| Series | Universitext |
| Condition | Unavailable |
| Binding Type | Paperback |
| Publisher | Springer International Publishing AG |
| Year published | 2022-10-23 |
| Number of pages | 206 |
| Cover note | Book picture is for illustrative purposes only, actual binding, cover or edition may vary. |
| Note | Unavailable |