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The Mobius Strip: Dr. August Mobius's Marvelous Band in Mathematics, Games, Literature, Art, Technology, and Cosmology
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Clifford A Pickover, Ph.D
The road that leads from the Mobius strip--a common-sense-defying continuous loop with only one side and one edge, made famous by the illustrations of M.C. Escher--goes to some of the strangest spots imaginable. It takes us to a place where the purely intellectual enters our daily world: where our outraged senses, overloaded with grocery bills, ...
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Algebraic Geometry
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Solomon Lefschetz
An introduction to algebraic geometry and a bridge between its analytical-topological and algebraical aspects, this book explores fundamental concepts of the general theory of algebraic varieties: general point, dimension, function field, rational transformations, and correspondences as well as formal power series and an extensive survey of ...
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Using Algebraic Geometry
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John B Little, David A Cox, PH.D., Donal O'Shea
In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on fast inexpensive computers, has sparked a minor revolution in the study and practice of algebraic geometry. These algorithmic methods have also given rise to some exciting new applications of algebraic geometry. This book ...
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Discriminants, Resultants, and Multidimensional Determinants
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I M Gelfand
"This book revives and vastly expands the classical theory of resultants and discriminants. Most of the main new results of the book have been published earlier in more than a dozen joint papers of the authors. The book nicely complements these original papers with many examples illustrating both old and new results of the theory."a "Mathematical ...
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Continuous geometry.
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John Von Neumann
In his work on rings of operators in Hilbert space, John von Neumann discovered a new mathematical structure that resembled the lattice system Ln. In characterizing its properties, von Neumann founded the field of continuous geometry. This book, based on von Neumann's lecture notes, begins with the development of the axioms of continuous geometry, ...
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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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Undergraduate algebraic geometry
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Miles Reid
Algebraic geometry is, essentially, the study of the solution of equations and occupies a central position in pure mathematics. This short and readable introduction to algebraic geometry will be ideal for all undergraduate mathematicians coming to the subject for the first time. With the minimum of prerequisites, Dr Reid introduces the reader to ...
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Geometric Algebra
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Emil Artin
This classic text, written by one of the foremost mathematicians of the 20th century, is now available in a low-priced paperback edition. Exposition is centered on the foundations of affine geometry, the geometry of quadratic forms, and the structure of the general linear group. Context is broadened by the inclusion of projective and symplectic ...
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The Geometry of Syzygies: A Second Course in Algebraic Geometry and Commutative Algebra
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David Eisenbud
Algebraic Geometry often seems very abstract, but in fact it is full of concrete examples and problems. This side of the subject can be approached through the equations of a variety, and the syzygies of these equations are a necessary part of the study. This book is the first textbook-level account of basic examples and techniques in this area. It ...
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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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Methods of algebraic geometry
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William Hodge, D Pedoe
This work provides a lucid and rigorous account of the foundations of modern algebraic geometry. The authors have confined themselves to fundamental concepts and geometrical methods, and do not give detailed developments of geometrical properties, but geometrical meaning has been emphasised throughout. This first volume is divided into two parts. ...
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The Geometry of Schemes
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David Eisenbud
The theory of schemes is the foundation for algebraic geometry proposed and elaborated by Alexander Grothendieck and his coworkers. It has allowed major progress in classical areas of algebraic geometry such as invariant theory and the moduli of curves. It integrates algebraic number theory with algebraic geometry, fulfilling the dreams of earlier ...
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An Introduction to Twistor Theory
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S A Huggett
This book is an introduction to twistor theory and modern geometrical approaches to space-time structure at the graduate or advanced undergraduate level. The choice of material presented has evolved from graduate courses given in London and Oxford and the authors have aimed to retain the informal tone of those lectures. Topics covered include ...
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Diophantine Geometry: An Introduction
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Marc Hindry, Joseph H Silverman
This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.
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Combinatorial Commutative Algebra
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Ezra Miller, Bernd Sturmfels
Combinatorial commutative algebra is an active area of research with thriving connections to other fields of pure and applied mathematics. This book provides a self-contained introduction to the subject, with an emphasis on combinatorial techniques for multigraded polynomial rings, semigroup algebras, and determinantal rings. The eighteen chapters ...
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Conics and Cubics: A Concrete Introduction to Algebraic Curves
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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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Lectures on the Geometry of Manifolds
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Liviu I Nicolaescu
The goal of this book is to introduce the reader to some of the most frequently used techniques in modern global geometry. Suited to the beginning graduate student willing to specialize in this very challenging field, the necessary prerequisite is a good knowledge of several variables calculus, linear algebra and point-set topology. The book's ...
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Curves and Fractal Dimension
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Claude Tricot
Written for mathematicians, engineers, researchers in experimental science, and anyone interested in fractals, this book presents the fundamentals of curve analysis with a new and clear introduction to fractal dimension. It explains the geometrical and analytical properties of trajectories, aggregate contours, geographical coastlines, profiles of ...
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Algebraic Surfaces
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Oscar Zariski
This text examines the field of algebraic surfaces.
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The 1-2-3 of Modular Forms: Lectures at a Summer School in Nordfjordeid, Norway
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Jan Hendrik Bruinier, Gerard Van Der Geer, Gunter Harder
This book grew out of three series of lectures given at the summer school on "Modular Forms and their Applications" at the Sophus Lie Conference Center in Nordfjordeid in June 2004. The first series treats the classical one-variable theory of elliptic modular forms. The second series presents the theory of Hilbert modular forms in two variables ...
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Spinning tops a course on integrable systems
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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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Principles of Algebraic Geometry
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Phillip Griffiths, Joseph Harris
Other volumes in the Pure and Applied Mathematics series The Algebraic Structure of Group Rings Donald S. Passman This book offers a comprehensive, self-contained treatment of group rings of infinite groups. It begins with basic definitions and contains background material on group theory and ring theory. Major topics considered include: the ...
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Introduction to Commutative Algebra and Algebraic Geometry
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Ernst Kunz
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Two-Dimensional Conformal Geometry and Vertex Operator Algebras
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Yi-Zhi Huang
The focus of this volume is to formulate and prove one main theorem, the equivalance between the algebraic and geometric formulations of the notion of vertex operator algebra. The author introduces a geomatric notion of vertex operator algebra in terms of complex powers of the determinant line bundles over certain moduli spaces (parameter spaces) ...
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Intersection Theory
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Mr. William Fulton
From the ancient origins of algebraic geometry in the solutions of polynomial equations, through the triumphs of algebraic geometry during the last two centuries, intersection theory has played a central role. The aim of this book is to develop the foundations of this theory, and to indicate the range of classical and modern applications. Although ...
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