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College Algebra with Modeling and Visualization
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Gary K Rockswold
Gary Rockswold focuses on teaching algebra in context, answering the question, "Why am I learning this?" and ultimately motivating the students to succeed in this class. In addition, the author's understanding of what instructors need from a text (great 'real' examples and lots of exercises) makes this book fun and easy to teach from. Integrating ...
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Unknown Quantity: A Real and Imaginary History of Algebra
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John Derbyshire
Prime Obsession taught us not to be afraid to put the math in a math book. "Unknown Quantity" heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages - and it promises to be just what his die-hard fans have been waiting for. "Here is the story ...
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Algebraic Geometry
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Richard Hartshorne, Robin Hartshorne
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the ...
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The Arithmetic of Elliptic Curves
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Joseph H Silverman
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the ...
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Ideals, Varieties, and Algorithms: An Introduction to Computational Algebraic Geometry and Commutative Algebra
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David A Cox, PH.D.
Algebraic Geometry is the study of systems of polynomial equations in one or more variables, asking such questions as: does the system have finitely many solutions, and if so how can one find them? And if there are infinitely many solutions, how can they be described and manipulated? The solutions of a system of polynomial equations form a ...
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Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach
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Richard E Blahut
Algebraic geometry is often employed to encode and decode signals transmitted in communication systems. This book describes the fundamental principles of algebraic coding theory from the perspective of an engineer, discussing a number of applications in communications and signal processing. The principle concept is that of using algebraic curves ...
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Basic Algebraic Geometry Volume 1: Varieties in Projective Space
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Igor R Shafarevich
"Basic Algebraic Geometry, Volume I" is a revised and expanded new edition of the first four chapters of Shafarevich's well-known introductory book on algebraic geometry. The author has added plenty of new, mostly concrete geometrical material such as Grassmannian varieties, plane cubic curves, the cubic surface, degenerations of quadrics and ...
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An Invitation to Quantum Cohomology: Kontsevich's Formula for Rational Plane Curves
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Joachim Kock, Israel Vainsencher
This book is an elementary introduction to stable maps and quantum cohomology, starting with an introduction to stable pointed curves, and culminating with a proof of the associativity of the quantum product. The viewpoint is mostly that of enumerative geometry, and the red thread of the exposition is the problem of counting rational plane curves. ...
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Convex polytopes
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by
Branko Grünbaum
The appearance of Gruenbaum's book Convex Polytopes in 1967 was a moment of grace to geometers and combinatorialists. The special spirit of the book is very much alive even in those chapters where the book's immense influence made them quickly obsolete. Some other chapters promise beautiful unexplored land for future research. The appearance of ...
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Frobenius Algebras and 2-D Topological Quantum Field Theories
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Joachim Kock, C M Series (Editor), J W Bruce (Editor)
This book describes a striking connection between topology and algebra, namely that 2D topological quantum field theories are equivalent to commutative Frobenius algebras. The precise formulation of the theorem and its proof is given in terms of monoidal categories, and the main purpose of the book is to develop these concepts from an elementary ...
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Rational Algebraic Curves: A Computer Algebra Approach
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Franz Winkler, J Rafael Sendra, Sonia Perez-Diaz
The central problem considered in this book is the determination of rational parametrizability of an algebraic curve, and, in the positive case, the computation of a good rational parametrization. This amounts to determining the genus of a curve, i.e. its complete singularity structure, computing regular points of the curve in small coordinate ...
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Algebraic Geometry: A First Course
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Joe Harris
This book is intended to introduce students to algebraic geometry; to give them a sense of the basic objects considered, the questions asked about them, and the sort of answers one can expect to obtain. It thus emplasizes the classical roots of the subject. For readers interested in simply seeing what the subject is about, this avoids the more ...
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Spinning tops a course on integrable systems
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by
Audin
Since the time of Lagrange and Euler, it has been well known that an understanding of algebraic curves can illuminate the picture of rigid bodies provided by classical mechanics. A modern view of the role played by algebraic geometry has been established in recent years by many mathematicians. This book presents some of these modern techniques, ...
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Algebraic Geometry I: Complex Projective Varieties
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D Mumford
Deals with modern algebraic geometry.
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Rational Points on Elliptic Curves
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Joseph H Silverman
The theory of elliptic curves involves a pleasing blend of algebra, geometry, analysis, and number theory. "Rational Points on Elliptic Curves" stresses this interplay as it develops the basic theory, thereby providing an opportunity for advance undergraduates to appreciate the unity of modern mathematics. At the same time, every effort has been ...
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Geometric Invariant Theory
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David Mumford
"Geometric Invariant Theory" by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a ...
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Algebraic Geometry and Arithmetic Curves
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by
Qing Liu
This new-in-paperback edition provides a general introduction to algebraic and arithmetic geometry, starting with the theory of schemes, followed by applications to arithmetic surfaces and to the theory of reduction of algebraic curves. The first part introduces basic objects such as schemes, morphisms, base change, local properties (normality, ...
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Shafarevich Maps and Automorphic Forms
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Janos Kollar
This text studies various geometric properties and algebraic invariants of smooth projective varieties with infinite fundamental groups. This approach allows for much interplay between methods of algebraic geometry, complex analysis, the theory of harmonic maps and topology. Making systematic use of Shafarevich maps, this work isolates those ...
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Introduction to Algebraic Geometry
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Serge Lang
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Advanced topics in the arithmetic of elliptic curves
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by
Joseph H Silverman
This book continues the treatment of the arithmetic theory of elliptic curves begun in the first volume. The book begins with the theory of elliptic and modular functions for the full modular group r(1), including a discussion of Hekcke operators and the L-series associated to cusp forms. This is followed by a detailed study of elliptic curves ...
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Oeuvres Scientifiques Collected Papers, Volume III: (1964-1978)
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Andre Weil
From the reviews: 'All of Weil's works except for books and lecture notes are compiled here, in strict chronological order for easy reference. But the value goes beyond the convenience of easy reference and accessibility. In the first place, these volumes contain several essays, letters, and addresses which were either published in obscure places ...
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Algebraic Curves and Riemann Surfaces
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by
Rick Miranda
In this book, Miranda takes the approach that algebraic curves are best encountered for the first time over the complex numbers, where the reader's classical intuition about surfaces, integration, and other concepts can be brought into play. Therefore, many examples of algebraic curves are presented in the first chapters. In this way, the book ...
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Conics and Cubics: A Concrete Introduction to Algebraic Curves
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by
Robert Bix
"Conics and Cubics" is an accessible introduction to algebraic curves. Its focus on curves of degree at most three keeps results tangible and proofs transparent. Theorems follow naturally from high school algebra and two key ideas, homogeneous coordinates and intersection multiplicities. By classifying irreducible cubics over the real numbers and ...
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Introduction to the Mori Program
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Kenji Matsuki
The purpose of this book is to give a comprehensible account of what is called Mori's Program, that is an approach to the following problem: classify all the projective varieties X /in P^n over C up to isomorphism. Mori's Program is a fusion of the so-called Minimal Model Program and the IItaka Program toward the biregular and/or birational ...
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Hodge Theory and Complex Algebraic Geometry II
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by
Claire Voisin, Leila Schneps (Translator)
The second volume of this modern account of Kaehlerian geometry and Hodge theory starts with the topology of families of algebraic varieties. Proofs of the Lefschetz theorem on hyperplane sections, the Picard-Lefschetz study of Lefschetz pencils, and Deligne theorems on the degeneration of the Leray spectral sequence and the global invariant ...
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