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1.

図書
図書
1. Mirror symmetry and algebraic geometry (: pbk)
David A. Cox, Sheldon Katz
出版情報: Providence, R.I. : American Mathematical Society, c1999  xxi, 469 p. ; 26 cm
シリーズ名: Mathematical surveys and monographs ; v. 68
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目次情報: 続きを見る
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
Hodge theory and Yukawa couplings
Moduli spaces Gromov-Witten invariants
Quantum cohomology Localization
Quantum differential equations
The mirror theorem Conclusion
Singular varieties
Physical theories
Bibliography
Index
Introduction
The quintic threefold
Toric geometry Mirror symmetry constructions
2.

図書
図書
2. Applications of computational algebraic geometry : American Mathematical Society short course, January 6-7, 1997, San Diego, California
David A. Cox and Bernd Sturmfels, editors ; Dinesh Manocha ... [et al., authors]
出版情報: Providence, R.I. : American Mathematical Society, c1998  ix, 172 p. ; 27 cm
シリーズ名: Proceedings of symposia in applied mathematics ; v. 53 . AMS short course lecture notes
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3.

図書
図書
3. Using algebraic geometry (: hard ; : pbk)
David Cox, John Little, Donal O'Shea
出版情報: New York : Springer, c1998  xii, 499 p. ; 24 cm
シリーズ名: Graduate texts in mathematics ; 185
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4.

図書
図書
4. Ideals, varieties, and algorithms : an introduction to computational algebraic geometry and commutative algebra. 2nd ed
David Cox, John Little, Donal O'Shea
出版情報: New York ; Tokyo : Springer, c1997  xiii, 536 p. ; 25 cm
シリーズ名: Undergraduate texts in mathematics
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5.

図書
図書
5. Primes of the form x[2] + ny[2] : Fermat, class field theory, and complex multiplication (: pbk)
David A. Cox
出版情報: New York : Wiley, c1989  xi, 351 p.
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目次情報: 続きを見る
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 j-Invariants
The Class Equation
Ellpitic Curves
References
Index
From Fermat to Gauss
Fermat, Euler and Quadratic Reciprocity
Lagrange, Legendre and Quadratic Forms
6.

電子ブック
ＥＢ
6. Galois theory
David A. Cox
出版情報: Wiley Online Library - AutoHoldings Books , Hoboken : John Wiley & Sons, Incorporated, 2012
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目次情報: 続きを見る
Preface to the First Edition
Preface to the Second Edition
Notation
Basic Notation / 1：
Chapter-by-Chapter Notation / 2：
Polynomials / Part I：
Cubic Equations
Cardan's Formulas / 1.1：
Permutations of the Roots / 1.2：
Cubic Equations over the Real Numbers / 1.3：
Symmetric Polynomials
Polynomials of Several Variables / 2.1：
Computing with Symmetric Polynomials (Optional) / 2.2：
The Discriminant / 2.4：
Roots of Polynomials / 3：
The Existence of Roots / 3.1：
The Fundamental Theorem of Algebra / 3.2：
Fields / Part II：
Extension Fields / 4：
Elements of Extension Fields / 4.1：
Irreducible Polynomials / 4.2：
The Degree of an Extension / 4.3：
Algebraic Extensions / 4.4：
Normal and Separable Extensions / 5：
Splitting Fields / 5.1：
Normal Extensions / 5.2：
Separable Extensions / 5.3：
Theorem of the Primitive Element / 5.4：
The Galois Group / 6：
Definition of the Galois Group / 6.1：
Galois Groups of Splitting Fields / 6.2：
Examples of Galois Groups / 6.3：
Abelian Equations (Optional) / 6.5：
The Galois Correspondence / 7：
Galois Extensions / 7.1：
Normal Subgroups and Normal Extensions / 7.2：
The Fundamental Theorem of Galois Theory / 7.3：
First Applications / 7.4：
Automorphisms and Geometry (Optional) / 7.5：
Applications / Part III：
Solvability by Radicals / 8：
Solvable Groups / 8.1：
Radical and Solvable Extensions / 8.2：
Solvable Extensions and Solvable Groups / 8.3：
Simple Groups / 8.4：
Solving Polynomials by Radicals / 8.5：
The Casus Irreducbilis (Optional) / 8.6：
Cyclotomic Extensions / 9：
Cyclotomic Polynomials / 9.1：
Gauss and Roots of Unity (Optional) / 9.2：
Geometric Constructions / 10：
Constructible Numbers / 10.1：
Regular Polygons and Roots of Unity / 10.2：
Origami (Optional) / 10.3：
Finite Fields / 11：
The Structure of Finite Fields / 11.1：
Irreducible Polynomials over Finite Fields (Optional) / 11.2：
Further Topics / Part IV：
Lagrange, Galois, and Kronecker / 12：
Lagrange / 12.1：
Galois / 12.2：
Kronecker / 12.3：
Computing Galois Groups / 13：
Quartic Polynomials / 13.1：
Quintic Polynomials / 13.2：
Resolvents / 13.3：
Other Methods / 13.4：
Solvable Permutation Groups / 14：
Polynomials of Prime Degree / 14.1：
Imprimitive Polynomials of Prime-Squared Degree / 14.2：
Primitive Permutation Groups / 14.3：
Primitive Polynomials of Prime-Squared Degree / 14.4：
The Lemniscate / 15：
Division Points and Arc Length / 15.1：
The Lemniscatic Function / 15.2：
The Complex Lemniscatic Function / 15.3：
Complex Multiplication / 15.4：
Abel's Theorem / 15.5：
Abstract Algebra / A：
Basic Algebra / A.1：
Complex Numbers / A.2：
Polynomials with Rational Coefficients / A.3：
Group Actions / A.4：
More Algebra / A.5：
Index
Preface to the First Edition
Preface to the Second Edition
Notation
7.

図書
図書
7. Galois theory. 2nd ed (: cloth)
David A. Cox
出版情報: Hoboken, N.J. : J. Wiley, c2012  xxviii, 570 p. ; 24 cm
シリーズ名: Pure and applied mathematics
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目次情報: 続きを見る
Preface to the First Edition
Preface to the Second Edition
Notation
Basic Notation / 1：
Chapter-by-Chapter Notation / 2：
Polynomials / Part I：
Cubic Equations
Cardan's Formulas / 1.1：
Permutations of the Roots / 1.2：
Cubic Equations over the Real Numbers / 1.3：
Symmetric Polynomials
Polynomials of Several Variables / 2.1：
Computing with Symmetric Polynomials (Optional) / 2.2：
The Discriminant / 2.4：
Roots of Polynomials / 3：
The Existence of Roots / 3.1：
The Fundamental Theorem of Algebra / 3.2：
Fields / Part II：
Extension Fields / 4：
Elements of Extension Fields / 4.1：
Irreducible Polynomials / 4.2：
The Degree of an Extension / 4.3：
Algebraic Extensions / 4.4：
Normal and Separable Extensions / 5：
Splitting Fields / 5.1：
Normal Extensions / 5.2：
Separable Extensions / 5.3：
Theorem of the Primitive Element / 5.4：
The Galois Group / 6：
Definition of the Galois Group / 6.1：
Galois Groups of Splitting Fields / 6.2：
Examples of Galois Groups / 6.3：
Abelian Equations (Optional) / 6.5：
The Galois Correspondence / 7：
Galois Extensions / 7.1：
Normal Subgroups and Normal Extensions / 7.2：
The Fundamental Theorem of Galois Theory / 7.3：
First Applications / 7.4：
Automorphisms and Geometry (Optional) / 7.5：
Applications / Part III：
Solvability by Radicals / 8：
Solvable Groups / 8.1：
Radical and Solvable Extensions / 8.2：
Solvable Extensions and Solvable Groups / 8.3：
Simple Groups / 8.4：
Solving Polynomials by Radicals / 8.5：
The Casus Irreducbilis (Optional) / 8.6：
Cyclotomic Extensions / 9：
Cyclotomic Polynomials / 9.1：
Gauss and Roots of Unity (Optional) / 9.2：
Geometric Constructions / 10：
Constructible Numbers / 10.1：
Regular Polygons and Roots of Unity / 10.2：
Origami (Optional) / 10.3：
Finite Fields / 11：
The Structure of Finite Fields / 11.1：
Irreducible Polynomials over Finite Fields (Optional) / 11.2：
Further Topics / Part IV：
Lagrange, Galois, and Kronecker / 12：
Lagrange / 12.1：
Galois / 12.2：
Kronecker / 12.3：
Computing Galois Groups / 13：
Quartic Polynomials / 13.1：
Quintic Polynomials / 13.2：
Resolvents / 13.3：
Other Methods / 13.4：
Solvable Permutation Groups / 14：
Polynomials of Prime Degree / 14.1：
Imprimitive Polynomials of Prime-Squared Degree / 14.2：
Primitive Permutation Groups / 14.3：
Primitive Polynomials of Prime-Squared Degree / 14.4：
The Lemniscate / 15：
Division Points and Arc Length / 15.1：
The Lemniscatic Function / 15.2：
The Complex Lemniscatic Function / 15.3：
Complex Multiplication / 15.4：
Abel's Theorem / 15.5：
Abstract Algebra / A：
Basic Algebra / A.1：
Complex Numbers / A.2：
Polynomials with Rational Coefficients / A.3：
Group Actions / A.4：
More Algebra / A.5：
Index
Preface to the First Edition
Preface to the Second Edition
Notation
8.

図書
図書
8. Using algebraic geometry. 2nd ed (: hbk ; : pbk)
David A. Cox, John Little, Donal O'Shea
出版情報: New York : Springer, c2005  xii, 572 p. ; 25 cm
シリーズ名: Graduate texts in mathematics ; 185
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目次情報: 続きを見る
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 Berlekamp-Massey-Sakata Decoding Algorithm
Introduction
Solving Polynomial Equations
Resultants
9.

図書
図書
9. Toric varieties
David A. Cox, John B. Little, Henry K. Schenck
出版情報: Providence, R.I. : American Mathematical Society, c2011  xxiv, 841 p. ; 26 cm
シリーズ名: Graduate studies in mathematics ; v. 124
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10.

図書
図書
10. グレブナ基底と代数多様体入門 : イデアル・多様体・アルゴリズム (上 ; 下)
D.コックス, J.リトル, D.オシー著 ; 落合啓之 [ほか] 訳
出版情報: 東京 : シュプリンガー・フェアラーク東京, 2000.4  2冊 ; 21cm
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