Book Description
The study of the zeroes of polynomials, which for one variable is essentially algebraic, becomes a geometric theory for several variables. In this book, Fischer looks at the classic entry point to the subject: plane algebraic curves. Here one quickly sees the mix of algebra and geometry, as well as analysis and topology, that is typical of complex algebraic geometry, but without the need for advanced techniques from commutative algebra or the abstract machinery of sheaves and schemes.
In the first half of this book, Fischer introduces some elementary geometrical aspects, such as tangents, singularities, inflection points, and so on. The main technical tool is the concept of intersection multiplicity and Bézout's theorem. This part culminates in the beautiful Plücker formulas, which relate the various invariants introduced earlier.
The second part of the book is essentially a detailed outline of modern methods of local analytic geometry in the context of complex curves. This provides the stronger tools needed for a good understanding of duality and an efficient means of computing intersection multiplicities introduced earlier. Thus, we meet rings of power series, germs of curves, and formal parametrizations. Finally, through the patching of the local information, a Riemann surface is associated to an algebraic curve, thus linking the algebra and the analysis.
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Curves and Fractal Dimension
Claude Tricot
Manufacturer: Springer
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ASIN: 0387940952 |
Book Description
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 rough surfaces, and other curves of finite and fractal length. The approach is through precise definitions from which properties are deduced and applications and computational methods are derived. Written without the traditional heavy symbolism of mathematics texts, this book requires two years of calculus as a prerequisite to understanding. This text also contains material appropriate for graduate coursework in curve analysis and/or fractal dimension.
Book Description
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
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Introduction to Singularities and Deformations (Springer Monographs in Mathematics)
G.-M. Greuel ,
C. Lossen , and
E. Shustin
Manufacturer: Springer
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Binding: Hardcover
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ASIN: 3540283803 |
Book Description
Singularity theory is a field of intensive study in modern mathematics with fascinating relations to algebraic geometry, complex analysis, commutative algebra, representation theory, theory of Lie groups, topology, dynamical systems, and many more, and with numerous applications in the natural and technical sciences.
This book presents the basic singularity theory of analytic spaces, including local deformation theory, and the theory of plane curve singularities. Plane curve singularities are a classical object of study, rich of ideas and applications, which still is in the center of current research and as such provides an ideal introduction to the general theory. Deformation theory is an important technique in many branches of contemporary algebraic geometry and complex analysis. This introductory text provides the general framework of the theory while still remaining concrete.
In the first part of the book the authors develop the relevant techniques, including the Weierstraß preparation theorem, the finite coherence theorem etc., and then treat isolated hypersurface singularities, notably the finite determinacy, classification of simple singularities and topological and analytic invariants. In local deformation theory, emphasis is laid on the issues of versality, obstructions, and equisingular deformations. The book moreover contains a new treatment of equisingular deformations of plane curve singularities including a proof for the smoothness of the mu-constant stratum which is based on deformations of the parameterization. Computational aspects of the theory are discussed as well. Three appendices, including basic facts from sheaf theory, commutative algebra, and formal deformation theory, make the reading self-contained.
The material, which can be found partly in other books and partly in research articles, is presented from a unified point of view for the first time. It is given with complete proofs, new in many cases. The book thus can serve as source for special courses in singularity theory and local algebraic and analytic geometry.
Book Description
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. Kontsevich's formula is initially established in the framework of classical enumerative geometry, then as a statement about reconstruction for Gromov–Witten invariants, and finally, using generating functions, as a special case of the associativity of the quantum product.
Emphasis is given throughout the exposition to examples, heuristic discussions, and simple applications of the basic tools to best convey the intuition behind the subject. The book demystifies these new quantum techniques by showing how they fit into classical algebraic geometry.
Some familiarity with basic algebraic geometry and elementary intersection theory is assumed. Each chapter concludes with some historical comments and an outline of key topics and themes as a guide for further study, followed by a collection of exercises that complement the material covered and reinforce computational skills. As such, the book is ideal for self-study, as a text for a mini-course in quantum cohomology, or as a special topics text in a standard course in intersection theory. The book will prove equally useful to graduate students in the classroom setting as to researchers in geometry and physics who wish to learn about the subject.
Customer Reviews:
New Theories in Enumerative Geometry.......2006-12-16
This book is an elementary introduction to some ideas and techniques that have revolutionized enumerative geometry: stable maps and quantum cohomology. It uses as a basis Kontsevich's formula and provides a complete proof of the formula.
The book assumes some basic algebraic geometry and some elementary intersection theory. This would include algebraic curves, divisors and line bundles, blowup, Grassmannians.
This book was originally published in Portuguese in 1999 as part of a mini-course. The further developments in the field have and the need for a more introductory book than Fulton and Pandharipande 'Notes on Stable Maps and Quantum Cohomology' have led to this revised, expanded and English language translation.
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Algebraic Codes on Lines, Planes, and Curves: An Engineering Approach
Richard Blahut
Manufacturer: Cambridge University Press
ProductGroup: Book
Binding: Hardcover
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ASIN: 0521771943 |
Book Description
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 principal concept is that of using algebraic curves over finite fields to construct error-correcting codes. The most recent developments are presented including the theory of codes on curves, without the use of detailed mathematics, substituting the intense theory of algebraic geometry with Fourier transform where possible. The author describes the codes and corresponding decoding algorithms in a manner that allows the reader to evaluate these codes against practical applications, or to help with the design of encoders and decoders. This book is relevant to practicing communication engineers and those involved in the design of new communication systems, as well as graduate students and researchers in electrical engineering.
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- An Excellent Introductory Book on the Study of Curves
|
Geometry of Curves (Chapman Hall/Crc Mathematics Series)
J.W. Rutter
Manufacturer: Chapman & Hall/CRC
ProductGroup: Book
Binding: Paperback
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ASIN: 1584881666 |
Book Description
Interest in the study of geometry is currently enjoying a resurgence-understandably so, as the study of curves was once the playground of some very great mathematicians. However, many of the subject's more exciting aspects require a somewhat advanced mathematics background. For the "fun stuff" to be accessible, we need to offer students an introduction with modest prerequisites, one that stimulates their interest and focuses on problem solving. Integrating parametric, algebraic, and projective curves into a single text, Geometry of Curves offers students a unique approach that provides a mathematical structure for solving problems, not just a catalog of theorems. The author begins with the basics, then takes students on a fascinating journey from conics, higher algebraic and transcendental curves, through the properties of parametric curves, the classification of limaçons, envelopes, and finally to projective curves, their relationship to algebraic curves, and their application to asymptotes and boundedness. The uniqueness of this treatment lies in its integration of the different types of curves, its use of analytic methods, and its generous number of examples, exercises, and illustrations. The result is a practical text, almost entirely self-contained, that not only imparts a deeper understanding of the theory, but inspires a heightened appreciation of geometry and interest in more advanced studies.
Customer Reviews:
An Excellent Introductory Book on the Study of Curves.......2000-11-30
John W. Rutter's book is an excellent introduction to the fascinating study of curves. Most introductory books on differential and algebraic geometry are somewhat incomprehensible. Rutter's book is at a U.S. college undergraduate level with many examples and explanations of notions passed over in other introductions. His book is a very good companion to the fine book "Curves and Singularities" by Bruce and Giblin. I highly recommend this book to anyone wanting to learn more about beautiful and interesting world of curves.
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Le probleme des modules pour les branches planes: Cours donne au Centre de mathematiques de l'Ecole polytechnique
Oscar Zariski
Manufacturer: Hermann
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Binding: Unknown Binding
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ASIN: 2705660364 |
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The Moduli Problem for Plane Branches (University Lecture Series)
Oscar Zariski
Manufacturer: American Mathematical Society
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Binding: Paperback
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ASIN: 0821829831
Release Date: 2006-12-01 |
Product Description
Moduli problems in algebraic geometry date back to Riemann's famous count of the $3g-3$ parameters needed to determine a curve of genus $g$. In this book, Zariski studies the moduli space of curves of the same equisingularity class. After setting up and reviewing the basic material, Zariski devotes one chapter to the topology of the moduli space, including an explicit determination of the rare cases when the space is compact. Chapter V looks at specific examples where the dimension of the generic component can be determined through rather concrete methods. Zariski's last chapter concerns the application of deformation theory to the moduli problem, including the determination of the dimension of the generic component for a particular family of curves. An appendix by Bernard Teissier reconsiders the moduli problem from the point of view of deformation theory. He gives new proofs of some of Zariski's results, as well as a natural construction of a compactification of the moduli space.
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Plane Algebraic Curves (Pure and Applied Mathematics)
G. Orzech
Manufacturer: CRC
ProductGroup: Book
Binding: Hardcover
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ASIN: 0824711599 |
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- It is easy to see why I am this mans biggest fan
|
she forgets the color of her hair
Anthony Ziegler
Manufacturer: Lulu.com
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Binding: Paperback
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ASIN: 1430307978 |
Book Description
Published in eight languages, beginning at the age of 9, when Zieglers works brought attention to a social concern and outraged the community. This is the latest published work by the acclaimed poet. Anthony is the founder of Silver Sate Fiction Writers, the editor of the Okra-Chicken, and is known in some circles as "the man who threw out Ginsberg." This latest work is unique as it is a selection of prose hand picked by the poet himself. These are the pieces that Anthony feels a unique part of his life.
Customer Reviews:
It is easy to see why I am this mans biggest fan.......2007-03-17
This is an incredible selection of life that Anthony gives us. Pictures of his world are vivid and his internal struggles with self are evident. I have read all his works and have purchased some of his fine art. I have even traveled to places he is reading or speaking to hear him. Though he has a career in automotive sales training (my career choice as well) I feel that he can relate well with the normal, every day humdrum of people and places. He is a true man. A car guy? Yes. But a man, first.
Book Description
Car guys scratch and sniff at their posts. They turn around throughout the month and try to get that last up out the door and down the street. They burn out and burn up and die trying to get someone to burn gas. It's the way it's happened for years and the way it will always be. One day it's the middle of the month and everybody is working to make their paycheck and the next day it's over.
On the last day your pulse shakes while you look at the chalkboard counting units sold. Eyes comparing worth and worthiness and wide eyed wondering when they'll get some rest. The night fucks you like you're standing against a streetlamp. One minute you're off and the next you're all lit up and shining on the hood of a strangers' car with a thong around your ears. One minute it's the last day of the month and you need to sell one more car and the next minute it's midnight, December fucking first, and that's all. It's over. It rolls around on the ground like a cat masturbating. It rolls around on the ground looking inviting until it scratches you. It rolls around in the sunlight of morning, licking its end.
Download Description
Car guys scratch and sniff at their posts. They turn around throughout the month and try to get that last up out the door and down the street. They burn out and burn up and die trying to get someone to burn gas. It's the way it's happened for years and the way it will always be. One day it's the middle of the month and everybody is working to make their paycheck and the next day it's over.
On the last day your pulse shakes while you look at the chalkboard counting units sold. Eyes comparing worth and worthiness and wide eyed wondering when they'll get some rest. The night fucks you like you're standing against a streetlamp. One minute you're off and the next you're all lit up and shining on the hood of a strangers' car with a thong around your ears. One minute it's the last day of the month and you need to sell one more car and the next minute it's midnight, December fucking first, and that's all. It's over. It rolls around on the ground like a cat masturbating. It rolls around on the ground looking inviting until it scratches you. It rolls around in the sunlight of morning, licking its end.
Customer Reviews:
A good, self-published book.......2005-09-27
Most people are wary of checking out self-published authors. the mindset is, "If this book was good, the author wouldn't have to pay to have it printed himself." This has been my thinking, but this book is an exception. At a time when contemporary American writers are innocuous, this is a refreshing breath of air. it takes you someplace. It spits tiny episodes of the lives of car dealers and other various people at you. It sits in my bathroom, and is perfect for picking up and reading wherever. This book deserves to be published by a major house and sold in the main-stream.
A readers delight. Very good book. Wonderful prose........2005-07-08
I was taken back immediately, from the very first sentence; "If silence. . ." I enjoy reading and always have companion (book) with me wherever I go. I'll go through two novels a week, sometimes more. "Pissing," I had to read over and again. What an absolute pleasure. Vivid characters. Intense imagery. Passive storyline, seems accidental. Not like most books with their deliberate movements, this book walks WITH you, like a friend, showing you his old neighborhood. What a great book!!!
Excellent grasp on the English language. Poetic. Profound........2005-04-30
Do not buy this book if you are looking for sales training. It was not written for a simple mind. The author plays games with words which share insight into the characters he writes of. What I appreciated most was the way that the author allows the readers to form their own reference points for the characters; there is no race or age or overly descriptive information regarding the characters, yet they become vivid and further defined through self exploration by the reader. Very well done. I did not give it a five because there is always room for improvement. However, if I were to give a five to any book, this would most likely be the one. It's a 4.9, but I round down.
The absolute worst I have ever seen.......2005-04-22
Pissing at 60 mph is a crude title but I am interested in my business. I have been in the car business and this is the most worthles thing I have ever read. THe reviews are totaly inacurate. It has nothing to do with selling cars.
It is depressing and just plain stupid. If you want to learn about selling cars read a book by Patrick Davis such as Selling cars.
What a crazy book! I wasn't expecting this sort of writing........2005-03-20
I was thinking it was a novel or maybe (like another one of his books) a sales training type of book. I'm a fool. Should have read the reviews better. It's amazing the way the author uses words. His imagery is stunning. The characters are unique. This is definitely a book for any adult library. I bought mine as an e-book and now I'm buying a hardback to keep forever.
Books:
- Positivity in Algebraic Geometry I: Classical Setting: Line Bundles and Linear Series (Ergebnisse Der Mathematik Und Ihrer Grenzgebiete)
- Power Estimation and Optimization Methodologies for VLIW-based Embedded Systems
- Practical Inverse Analysis in Engineering (Crc Mechanical Engineering Series)
- Programming the Boundary Element Method: An Introduction for Engineers
- Quantitative Conservation Biology: Theory and Practice of Population Viability Analysis
- Radar System Performance Modeling, Second Edition
- Scattering Operator, Eisenstein Series, Inner Product Formula and "Maass-Selberg" Relations (Memoirs of the American Mathematical Society)
- Solid Freeform Fabrication: A New Direction in Manufacturing
- Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, No. 92) (Cbms Regional Conference Series in Mathematics)
- Spectral Methods: Fundamentals in Single Domains (Scientific Computation)
Books Index
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Introduction to Plane Algebraic Curves
Undergraduate Algebraic Geometry (London Mathematical Society Student Texts)
Conics and Cubics: A Concrete Introduction to Algebraic Curves (Undergraduate Texts in Mathematics)
Elementary Algebraic Geometry (Student Mathematical Library, Vol. 20) (Student Mathematical Library, V. 20)
Complex Algebraic Curves (London Mathematical Society Student Texts)
