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1. Applications of polynomial systems [2020]
 Cox, David A. author.
 Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2020]
 Description
 Book — 1 online resource
 Summary

 Elimination theory Numerical algebraic geometry Geometric modeling Rigidity theory Chemical reaction networks Illustration credits Bibliography Index.
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2. Applications of polynomial systems [2020]
 Cox, David A., author.
 Providence, Rhode Island : Published for the Conference Board of the Mathematical Sciences by the American Mathematical Society, [2020]
 Description
 Book — ix, 250 pages : illustrations (some color) ; 26 cm
 Summary

 Elimination theory Numerical algebraic geometry Geometric modeling Rigidity theory Chemical reaction networks Illustration credits Bibliography Index.
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QA1 .R33 NO.134  Unknown 
 Cox, David A. author.
 Fourth edition.  Cham : Springer, 2015.
 Description
 Book — 1 online resource (xi, 513 pages) : illustrations.
 Summary

 Preface
 Notation for Sets and Functions
 1. Geometry, Algebra, and Algorithms
 2. Groebner Bases
 3. Elimination Theory
 4. The AlgebraGeometry Dictionary
 5. Polynomial and Rational Functions on a Variety
 6. Robotics and Automatic Geometric Theorem Proving
 7. Invariant Theory of Finite Groups
 8. Projective Algebraic Geometry
 9. The Dimension of a Variety
 10. Additional Groebner Basis Algorithms
 Appendix A. Some Concepts from Algebra
 Appendix B. Pseudocode
 Appendix C. Computer Algebra Systems
 Appendix D. Independent Projects
 References
 Index.
 Cox, David A. author.
 Second edition.  Hoboken, New Jersey : Wiley, [2013]
 Description
 Book — 1 online resource (xvi, 359 pages) : illustrations.
 Summary

 Preface to the First Edition ix
 Preface to the Second Edition xi
 Notation xiii
 Introduction 1
 Chapter One: From Fermat to Gauss
 Chapter Two: Class Field Theory
 Chapter Three: Complex Multiplication
 Chapter Four: Additional Topics
 Refrences
 Additional References
 Index.
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 Cox, David A.
 Second edition.  Hoboken, New Jersey : John Wiley & Sons, Inc., [2013]
 Description
 Book — 1 online resource (1 volume) : illustrations.
 Summary

 From Fermat to Gauss
 Class field theory
 Complex multiplication
 Additional topics.
 Cox, David A.
 Providence, Rhode Island : American Mathematical Society, 2013.
 Description
 Book — ix, 116 pages ; 25 cm.
 Summary

 Introduction, terminology, and preliminary results The general lemma The triple lemma The BiProj Lemma Singularities of multiplicity equal to degree divided by two The space of true triples of forms of degree $d$: the base point free locus, the birational locus, and the generic HilbertBurch matrix Decomposition of the space of true triples The Jacobian matrix and the ramification locus The conductor and the branches of a rational plane curve Rational plane quartics: A stratification and the correspondence between the HilbertBurch matrices and the configuration of singularities Bibliography.
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7. Galois theory [2012]
 Cox, David A.
 2nd ed.  Hoboken, NJ : Wiley & Sons, c2012.
 Description
 Book — xxviii, 570 p. : ill ; 24 cm.
 Summary

 Preface to the First Edition xvii Preface to the Second Edition xxi Notation xxiii
 1 Basic Notation xxiii
 2 ChapterbyChapter Notation xxv PART I POLYNOMIALS
 1 Cubic Equations 3 1.1 Cardan's Formulas 4 1.2 Permutations of the Roots 10 1.3 Cubic Equations over the Real Numbers 15
 2 Symmetric Polynomials 25 2.1 Polynomials of Several Variables 25 2.2 Symmetric Polynomials 30 2.3 Computing with Symmetric Polynomials (Optional) 42 2.4 The Discriminant 46
 3 Roots of Polynomials 55 3.1 The Existence of Roots 55 3.2 The Fundamental Theorem of Algebra 62 PART II FIELDS
 4 Extension Fields 73 4.1 Elements of Extension Fields 73 4.2 Irreducible Polynomials 81 4.3 The Degree of an Extension 89 4.4 Algebraic Extensions 95
 5 Normal and Separable Extensions 101 5.1 Splitting Fields 101 5.2 Normal Extensions 107 5.3 Separable Extensions 109 5.4 Theorem of the Primitive Element 119
 6 The Galois Group 125 6.1 Definition of the Galois Group 125 6.2 Galois Groups of Splitting Fields 130 6.3 Permutations of the Roots 132 6.4 Examples of Galois Groups 136 6.5 Abelian Equations (Optional) 143
 7 The Galois Correspondence 147 7.1 Galois Extensions 147 7.2 Normal Subgroups and Normal Extensions 154 7.3 The Fundamental Theorem of Galois Theory 161 7.4 First Applications 167 7.5 Automorphisms and Geometry (Optional) 173 PART III APPLICATIONS
 8 Solvability by Radicals 191 8.1 Solvable Groups 191 8.2 Radical and Solvable Extensions 196 8.3 Solvable Extensions and Solvable Groups 201 8.4 Simple Groups 210 8.5 Solving Polynomials by Radicals 215 8.6 The Casus Irreducbilis (Optional) 220
 9 Cyclotomic Extensions 229 9.1 Cyclotomic Polynomials 229 9.2 Gauss and Roots of Unity (Optional) 238
 10 Geometric Constructions 255 10.1 Constructible Numbers 255 10.2 Regular Polygons and Roots of Unity 270 10.3 Origami (Optional) 274
 11 Finite Fields 291 11.1 The Structure of Finite Fields 291 11.2 Irreducible Polynomials over Finite Fields (Optional) 301 PART IV FURTHER TOPICS
 12 Lagrange, Galois, and Kronecker 315 12.1 Lagrange 315 12.2 Galois 334 12.3 Kronecker 347
 13 Computing Galois Groups 357 13.1 Quartic Polynomials 357 13.2 Quintic Polynomials 368 13.3 Resolvents 386 13.4 Other Methods 400
 14 Solvable Permutation Groups 413 14.1 Polynomials of Prime Degree 413 14.2 Imprimitive Polynomials of PrimeSquared Degree 419 14.3 Primitive Permutation Groups 429 14.4 Primitive Polynomials of PrimeSquared Degree 444
 15 The Lemniscate 463 15.1 Division Points and Arc Length 464 15.2 The Lemniscatic Function 470 15.3 The Complex Lemniscatic Function 482 15.4 Complex Multiplication 489 15.5 Abel's Theorem 504 A Abstract Algebra 515 A.1 Basic Algebra 515 A.2 Complex Numbers 524 A.3 Polynomials with Rational Coefficients 528 A.4 Group Actions 530 A.5 More Algebra 532 Index 557.
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QA214 .C69 2012  Unknown 
8. Toric varieties [2011]
 Cox, David A.
 Providence, R.I. : American Mathematical Society, c2011.
 Description
 Book — xxiv, 841 p. : ill. ; 26 cm.
 Summary

Toric varieties form a beautiful and accessible part of modern algebraic geometry. This book covers the standard topics in toric geometry; a novel feature is that each of the first nine chapters contains an introductory section on the necessary background material in algebraic geometry. Other topics covered include quotient constructions, vanishing theorems, equivariant cohomology, GIT quotients, the secondary fan, and the minimal model program for toric varieties. The subject lends itself to rich examples reflected in the 134 illustrations included in the text. The book also explores connections with commutative algebra and polyhedral geometry, treating both polytopes and their unbounded cousins, polyhedra. There are appendices on the history of toric varieties and the computational tools available to investigate nontrivial examples in toric geometry. Readers of this book should be familiar with the material covered in basic graduate courses in algebra and topology, and to a somewhat lesser degree, complex analysis. In addition, the authors assume that the reader has had some previous experience with algebraic geometry at an advanced undergraduate level. The book will be a useful reference for graduate students and researchers who are interested in algebraic geometry, polyhedral geometry, and toric varieties.
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QA564 .C6882 2011  Unavailable Checked out  Overdue 
 Cox, David A.
 3rd ed.  New York : Springer, c2007.
 Description
 Book — xv, 551 p. : ill. ; 25 cm.
 Summary

 Preface to the First Edition. Preface to the Second Edition. Preface to the Third Edition. Geometry, Algebra, and Algorithms. Groebner Bases. Elimination Theory. The AlgebraGeometry Dictionary. Polynomial and Rational Functions on a Variety. Robotics and Automatic Geometric Theorem Proving. Invariant Theory of Finite Groups. Projective Algebraic Geometry. The Dimension of a Variety. Appendix A. Some Concepts from Algebra. Appendix B. Pseudocode. Appendix C. Computer Algebra Systems. Appendix D. Independent Projects. References. Index.
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QA564 .C688 2007  Unknown 
 Cox, David A.
 3rd ed.  New York : Springer, c2007.
 Description
 Book — xv, 551 p. : ill.
11. Using algebraic geometry [2005]
 Cox, David A.
 2nd ed.  New York : Springer, c2005.
 Description
 Book — xii, 572 p. : ill. ; 25 cm.
 Summary

 Introduction. Solving Polynomial Equations. Resultants. Computation in Local Rings. Modules. Free Resolutions. Polytopes, Resultants, and Equations. Integer Programming, Combinatorics, and Splines. Algebraic Coding Theory. The BerlekampMasseySakata Decoding Algorithm.
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QA564 .C6883 2005  Unknown 
 Cox, David A.
 2nd ed.  New York : Springer, c2005.
 Description
 Book — xii, 572 p. : ill.
13. Galois theory [2004]
 Cox, David A.
 Hoboken, N.J. : WileyInterscience, c2004.
 Description
 Book — xx, 559 p. : ill. ; 25 cm.
 Summary

 Preface. Notation. PART I: POLYNOMIALS.
 Chapter 1. Cubic Equations.
 Chapter 2. Symmetric Polynomials.
 Chapter 3. Roots of Polynomials. PART II: FIELDS.
 Chapter 4. Extension Fields.
 Chapter 5. Normal and Separable Extensions.
 Chapter 6. The Galois Group.
 Chapter 7. The Galois Correspondence. PART III: APPLICATIONS.
 Chapter 8. Solvability by Radicals.
 Chapter 9. Cyclotomic Extensions.
 Chapter 10. Geometric Constructions.
 Chapter 11. Finite Fields. PART IV: FURTHER TOPICS.
 Chapter 12. Lagrange, Galois, and Kronecker.
 Chapter 13. Computing Galois Groups.
 Chapter 14. Solvable Permutation Groups.
 Chapter 15. The Lemniscate. Appendix A: Abstract Algebra. Appendix B: Hints to Selected Exercises. References. Index.
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QA214 .C69 2004  Unknown 
14. Mirror symmetry and algebraic geometry [1999]
 Cox, David A.
 Providence, R.I. : American Mathematical Society, c1999.
 Description
 Book — xxi, 469 p. : ill. ; 26 cm.
 Summary

 The quintic threefold Toric geometry Mirror symmetry constructions Hodge theory and Yukawa couplings Moduli spaces GromovWitten invariants Quantum cohomology Localization Quantum differential equations The mirror theorem Conclusion Singular varieties.
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Mirror symmetry began when theoretical physicists made some astonishing predictions about rational curves on quintic hypersurfaces in fourdimensional projective space. Understanding the mathematics behind these predictions has been a substantial challenge. This book is the first completely comprehensive monograph on mirror symmetry, covering the original observations by the physicists through the most recent progress made to date. Subjects discussed include toric varieties, Hodge theory, Kahler geometry, moduli of stable maps, CalabiYau manifolds, quantum cohomology, GromovWitten invariants, and the mirror theorem. This title features: numerous examples worked out in detail; an appendix on mathematical physics; an exposition of the algebraic theory of GromovWitten invariants and quantum cohomology; and, a proof of the mirror theorem for the quintic threefold.
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QA3 .A4 NO.68  Unknown 
15. Using algebraic geometry [1998]
 Cox, David A.
 New York : Springer, c1998.
 Description
 Book — p. cm.
 Summary

 1: Introduction.
 2: Solving Polynomial Equations.
 3: Resultants.
 4: Computation in Local Rings.
 5: Modules.
 6: Free Resolutions.
 7: Polytopes, Resultants and Equations.
 8: Integer Programming, Combinatorics and Splines.
 9: Algebraic Coding Theory.
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In recent years, the discovery of new algorithms for dealing with polynomial equations, coupled with their implementation on inexpensive yet fast computers, has sparked a minor revolution in the study and practice of algebraic geometry. One of the aims of this text is to illustrate the various uses of algebraic geometry and to highlight the more recent applications of Groebner bases and resultants. In order to do this, an introduction to some advanced algebraic objects and techniques is provided.
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QA564 .C6883 1998  Unknown 
 Cox, David A.
 2nd ed.  New York : Springer, c1997.
 Description
 Book — xiii, 536 p. : ill. ; 25 cm.
 Summary

 Geometry, Algebra, and Algorithms. Groebner Bases. Elimination Theory. The AlgebraGeometry Dictionary. Polynomial and Rational Functions on a Variety. Robotics and Automatic Geometric Theorem Proving. Invariant Theory of Finite Groups. Projective Algebraic Geometry. The Dimension of a Variety. Some Concepts from Algebra. Pseudocode. Computer Algebra Systems. Independent Projects.
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QA564 .C688 1997  Unknown 
 Cox, David A.
 New York ; Chichester : John Wiley & Sons, 1989.
 Description
 Book — 1 online resource (362 pages).
 Summary

 FROM FERMAT TO GAUSS. Fermat, Euler and Quadratic Reciprocity. Lagrange, Legendre and Quadratic Forms. Gauss, Composition and Genera. Cubic and Biquadratic Reciprocity. CLASS FIELD THEORY. The Hilbert Class Field and p = x 2 + ny 2 . The Hilbert Class Field and Genus Theory. Orders in Imaginary Quadratic Fields. Class Fields Theory and the Cebotarev Density Theorem. Ring Class Field and p = x 2 + ny 2 . COMPLEX MULTIPLICATION. Elliptic Functions and Complex Multiplication. Modular Functions and Ring Class Fields. Modular Functions and Singular jInvariants. The Class Equation. Ellpitic Curves. References. Index.
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Modern number theory began with the work of Euler and Gauss to understand and extend the many unsolved questions left behind by Fermat. In the course of their investigations, they uncovered new phenomena in need of explanation, which over time led to the discovery of field theory and its intimate connection with complex multiplication. While most texts concentrate on only the elementary or advanced aspects of this story, Primes of the Form x2 + ny2 begins with Fermat and explains how his work ultimately gave birth to quadratic reciprocity and the genus theory of quadratic forms. Further, the book shows how the results of Euler and Gauss can be fully understood only in the context of class field theory. Finally, in order to bring class field theory down to earth, the book explores some of the magnificent formulas of complex multiplication. The central theme of the book is the story of which primes p can be expressed in the form x2 + ny2. An incomplete answer is given using quadratic forms. A better though abstract answer comes from class field theory, and finally, a concrete answer is provided by complex multiplication. Along the way, the reader is introduced to some wonderful number theory. Numerous exercises and examples are included. The book is written to be enjoyed by readers with modest mathematical backgrounds. Chapter 1 uses basic number theory and abstract algebra, while chapters 2 and 3 require Galois theory and complex analysis, respectively.
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 Cox, David A.
 New York : SpringerVerlag, ©1992.
 Description
 Book — xi, 513 pages : illustrations ; 25 cm.
 Summary

 Ch.
 1. Geometry, Algebra, and Algorithms.
 1. Polynomials and Affine Space.
 2. Affine Varieties.
 3. Parametrizations of Affine Varieties.
 4. Ideals.
 5. Polynomials of One Variable
 Ch.
 2. Groebner Bases.
 2. Orderings on the Monomials in [actual symbol not reproducible].
 3. A Division Algorithm in [actual symbol not reproducible].
 4. Monomial Ideals and Dickson's Lemma.
 5. The Hilbert Basis Theorem and Groebner Bases.
 6. Properties of Groebner Bases.
 7. Buchberger's Algorithm.
 8. First Applications of Groebner Bases.
 9. (Optional) Improvements on Buchberger's Algorithm.
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Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
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QA564 .C688 1992  Available 
 Cox, David A.
 New York : Wiley, c1989.
 Description
 Book — xi, 351 p. ; 25 cm.
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QA246 .C69 1989  Unknown 
QA246 .C69 1989  Unknown 
 Providence, R.I. : American Mathematical Society, c1998.
 Description
 Book — ix, 172 p. : ill. ; 26 cm.
 Summary

 Introduction to Grobner bases by D. A. Cox Introduction to resultants by B. Sturmfels Numerical methods for solving polynomial equations by D. Manocha Applications to computer aided geometric design by T. W. Sederberg Combinatorial homotopy of simplicial complexes and complex information systems by X. H. Kramer and R. C. Laubenbacher Applications to integer programming by R. R. Thomas Applications to coding theory by J. B. Little Index.
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QA1 .S95 V.53  Unknown 
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