# a-first-course-in-computational-algebraic-geometry

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## A First Course In Computational Algebraic Geometry

**Author :**Wolfram Decker

**ISBN :**9781107612532

**Genre :**Computers

**File Size :**53. 16 MB

**Format :**PDF, ePub

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A quick guide to computing in algebraic geometry with many explicit computational examples introducing the computer algebra system Singular.

## Computational Algebra Course And Exercises With Solutions

**Author :**Ihsen Yengui

**ISBN :**9811239304

**Genre :**Mathematics

**File Size :**22. 77 MB

**Format :**PDF, ePub

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This book intends to provide material for a graduate course on computational commutative algebra and algebraic geometry, highlighting potential applications in cryptography. Also, the topics in this book could form the basis of a graduate course that acts as a segue between an introductory algebra course and the more technical topics of commutative algebra and algebraic geometry.This book contains a total of 124 exercises with detailed solutions as well as an important number of examples that illustrate definitions, theorems, and methods. This is very important for students or researchers who are not familiar with the topics discussed. Experience has shown that beginners who want to take their first steps in algebraic geometry are usually discouraged by the difficulty of the proposed exercises and the absence of detailed answers. Therefore, exercises (and their solutions) as well as examples occupy a prominent place in this course.This book is not designed as a comprehensive reference work, but rather as a selective textbook. The many exercises with detailed answers make it suitable for use in both a math or computer science course.

## Ideals Varieties And Algorithms

**Author :**David A. Cox

**ISBN :**9783319167213

**Genre :**Mathematics

**File Size :**48. 18 MB

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This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book. A comprehensive chart in the Preface illustrates a variety of ways to proceed with the material once these chapters are covered. In addition to the fundamentals of algebraic geometry—the elimination theorem, the extension theorem, the closure theorem and the Nullstellensatz—this new edition incorporates several substantial changes, all of which are listed in the Preface. The largest revision incorporates a new Chapter (ten), which presents some of the essentials of progress made over the last decades in computing Gröbner bases. The book also includes current computer algebra material in Appendix C and updated independent projects (Appendix D). The book may serve as a first or second course in undergraduate abstract algebra and with some supplementation perhaps, for beginning graduate level courses in algebraic geometry or computational algebra. Prerequisites for the reader include linear algebra and a proof-oriented course. It is assumed that the reader has access to a computer algebra system. Appendix C describes features of MapleTM, Mathematica® and Sage, as well as other systems that are most relevant to the text. Pseudocode is used in the text; Appendix B carefully describes the pseudocode used. From the reviews of previous editions: “...The book gives an introduction to Buchberger’s algorithm with applications to syzygies, Hilbert polynomials, primary decompositions. There is an introduction to classical algebraic geometry with applications to the ideal membership problem, solving polynomial equations and elimination theory. ...The book is well-written. ...The reviewer is sure that it will be an excellent guide to introduce further undergraduates in the algorithmic aspect of commutative algebra and algebraic geometry.” —Peter Schenzel, zbMATH, 2007 “I consider the book to be wonderful. ... The exposition is very clear, there are many helpful pictures and there are a great many instructive exercises, some quite challenging ... offers the heart and soul of modern commutative and algebraic geometry.” —The American Mathematical Monthly

## A Course In Computational Algebraic Number Theory

**Author :**Henri Cohen

**ISBN :**UOM:39015029948612

**Genre :**Mathematics

**File Size :**37. 34 MB

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Mathematics of Computing -- General.

## A First Course In Modular Forms

**Author :**Fred Diamond

**ISBN :**038723229X

**Genre :**Mathematics

**File Size :**45. 13 MB

**Format :**PDF, ePub, Docs

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This book introduces the theory of modular forms with an eye toward the Modularity Theorem, covering topics not included in other texts on elliptic curves. Suitable for beginning graduate students and advanced undergraduates, with exercises throughout.

## Computer Graphics And Geometric Modeling Mathematics

**Author :**Max K Agoston

**ISBN :**UCSD:31822033230939

**Genre :**Computer graphics

**File Size :**80. 51 MB

**Format :**PDF, ePub, Mobi

**Download :**428

**Read :**643

## The Bulletin Of Mathematics Books

**Author :**

**ISBN :**CORNELL:31924074863436

**Genre :**Computer software

**File Size :**62. 20 MB

**Format :**PDF, Docs

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## Using Algebraic Geometry

**Author :**David A. Cox

**ISBN :**9781475769111

**Genre :**Mathematics

**File Size :**23. 38 MB

**Format :**PDF, ePub

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An illustration of the many uses of algebraic geometry, highlighting the more recent applications of Groebner bases and resultants. Along the way, the authors provide an introduction to some algebraic objects and techniques more advanced than typically encountered in a first course. The book is accessible to non-specialists and to readers with a diverse range of backgrounds, assuming readers know the material covered in standard undergraduate courses, including abstract algebra. But because the text is intended for beginning graduate students, it does not require graduate algebra, and in particular, does not assume that the reader is familiar with modules.

## From Quadrangular Sets To The Budget Matroids

**Author :**Lyle Ramshaw

**ISBN :**UCSC:32106013458481

**Genre :**Geometry, Projective

**File Size :**40. 11 MB

**Format :**PDF, ePub, Mobi

**Download :**699

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## Results In Computational Algebra Of Bayesian Networks

**Author :**Steven James Sinnott

**ISBN :**CORNELL:31924105488484

**Genre :**

**File Size :**63. 99 MB

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## Algorithmic Computation Of Local And De Rham Cohomology In Characteristic Zero

**Author :**Hans Ulrich Walther

**ISBN :**MINN:31951P00693814X

**Genre :**

**File Size :**65. 91 MB

**Format :**PDF, ePub, Mobi

**Download :**897

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## Introduction To Commutative Algebra And Algebraic Geometry

**Author :**Ernst Kunz

**ISBN :**0817630651

**Genre :**Mathematics

**File Size :**84. 91 MB

**Format :**PDF, Kindle

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It has been estimated that, at the present stage of our knowledge, one could give a 200 semester course on commutative algebra and algebraic geometry without ever repeating himself. So any introduction to this subject must be highly selective. I first want to indicate what point of view guided the selection of material for this book. This introduction arose from lectures for students who had taken a basic course in algebra and could therefore be presumed to have a knowledge of linear algebra, ring and field theory, and Galois theory. The present text shouldn't require much more. In the lectures and in this text I have undertaken with the fewest possible auxiliary means to lead up to some recent results of commutative algebra and algebraic geometry concerning the representation of algebraic varieties as in tersections of the least possible number of hypersurfaces and- a closely related problem-with the most economical generation of ideals in Noetherian rings. The question of the equations needed to describe an algebraic variety was addressed by Kronecker in 1882. In the 1940s it was chiefly Perron who was interested in this question; his discussions with Severi made the problem known and contributed to sharpening the rei event concepts. Thanks to the general progress of commutative algebra many beautiful results in this circle of questions have been obtained, mainly after the solution of Serre's problem on projective modules. Because of their relatively elementary character they are especially suitable for an introduction to commutative algebra.

## Computer Algebra Systems

**Author :**Michael J. Wester

**ISBN :**UVA:X004339714

**Genre :**Computers

**File Size :**25. 35 MB

**Format :**PDF

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This thorough overview of the major computer algebra (symbolic mathematical) systems compares and contrasts their strengths and weaknesses, and gives tutorial information for using these systems in various ways. * Compares different packages quantitatively using standard 'test suites' * Ideal for assessing the most appropriate package for a particular user or application * Examines the performance and future developments from a user's and developer's viewpoint Internationally recognized specialists overview both the general and special purpose systems and discuss issues such as denesting nested roots, complex number calculations, efficiently computing special polynomials, solving single equations and systems of polynomial equations, computing limits, multiple integration, solving ordinary differential and nonlinear evolution equations, code generation, evaluation and computer algebra in education. The historical origins, computer algebra resources and equivalents for many common operations in seven major packages are also covered. By providing such a comprehensive survey, the experienced user is able to make an informed decision on which system(s) he or she might like to use. It also allows a user new to computer algebra to form an idea of where to begin. Since each system looked at in this book uses a different language, many examples are included to aid the user in adapting to these language differences. These examples can be used as a guide to using the various systems once one understands the basic principles of one CAS. The book also includes contributions which look at the broad issues of the needs of various users and future developments, both from the user's and the developer's viewpoint. The author is a leading figure in the development and analysis of mathematical software and is well known through the 'Wester test suite' of problems which provide a bench mark for measuring the performance of mathematical software systems. The book will help develop our range of titles for applied mathematcians. The book will provide a unique, fully up-to-date and independent assessment of particular systems and will be of interest to users and purchasers of CAS's.

## The Geometry Of Syzygies

**Author :**David Eisenbud

**ISBN :**9780387264561

**Genre :**Mathematics

**File Size :**29. 87 MB

**Format :**PDF, Kindle

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First textbook-level account of basic examples and techniques in this area. Suitable for self-study by a reader who knows a little commutative algebra and algebraic geometry already. David Eisenbud is a well-known mathematician and current president of the American Mathematical Society, as well as a successful Springer author.

## Abstracts Of Papers Presented To The American Mathematical Society

**Author :**American Mathematical Society

**ISBN :**CORNELL:31924074890850

**Genre :**Mathematics

**File Size :**74. 16 MB

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## Encyclopedia Of Physical Science And Technology

**Author :**Robert Allen Meyers

**ISBN :**0122274113

**Genre :**Physical sciences

**File Size :**80. 26 MB

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Following in the footsteps of the earlier editions, hundreds of the most respected scientists and engineers participated in the creation of this new edition, including many Nobel Laureates. The articles are in-depth, yet accessible, and address all of the key areas of physical science--including aeronautics, astronomy, chemistry, communications, computers, earth sciences, electronics, engineering, materials science, mathematics, nuclear technology, physics, power systems, propulsion, and space technology. (Midwest).

## A First Course In Abstract Algebra

**Author :**Joseph J. Rotman

**ISBN :**STANFORD:36105028605132

**Genre :**Mathematics

**File Size :**57. 23 MB

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This spectacularly clear introduction to abstract algebra is is designed to make the study of all required topics and the reading and writing of proofs both accessible and enjoyable for readers encountering the subject for the first time. Number Theory. Groups. Commutative Rings. Modules. Algebras. Principal Idea Domains. Group Theory II. Polynomials In Several Variables. For anyone interested in learning abstract algebra.

## Mathematical Reviews

**Author :**

**ISBN :**UOM:39015082440754

**Genre :**Mathematics

**File Size :**63. 16 MB

**Format :**PDF, Kindle

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## A First Course In Functional Analysis

**Author :**S. David Promislow

**ISBN :**UCSD:31822034624221

**Genre :**Mathematics

**File Size :**53. 74 MB

**Format :**PDF, ePub, Docs

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A concise introduction to the major concepts of functional analysis Requiring only a preliminary knowledge of elementary linear algebra and real analysis, A First Course in Functional Analysis provides an introduction to the basic principles and practical applications of functional analysis. Key concepts are illustrated in a straightforward manner, which facilitates a complete and fundamental understanding of the topic. This book is based on the author's own class-tested material and uses clear language to explain the major concepts of functional analysis, including Banach spaces, Hilbert spaces, topological vector spaces, as well as bounded linear functionals and operators. As opposed to simply presenting the proofs, the author outlines the logic behind the steps, demonstrates the development of arguments, and discusses how the concepts are connected to one another. Each chapter concludes with exercises ranging in difficulty, giving readers the opportunity to reinforce their comprehension of the discussed methods. An appendix provides a thorough introduction to measure and integration theory, and additional appendices address the background material on topics such as Zorn's lemma, the Stone-Weierstrass theorem, Tychonoff's theorem on product spaces, and the upper and lower limit points of sequences. References to various applications of functional analysis are also included throughout the book. A First Course in Functional Analysis is an ideal text for upper-undergraduate and graduate-level courses in pure and applied mathematics, statistics, and engineering. It also serves as a valuable reference for practitioners across various disciplines, including the physical sciences, economics, and finance, who would like to expand their knowledge of functional analysis.

## Galois Theory

**Author :**Harold M. Edwards

**ISBN :**UOM:49015002698836

**Genre :**Galois theory

**File Size :**54. 65 MB

**Format :**PDF, Kindle

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