Chapter 1 Polynomial Equations-Solving in Ancient Times， Mainly in Ancient China 1.1 A Brief Description of History of Ancient China and Mathematics Classics in Ancient China 1.2 Polynomial Equations-Solving in Ancient China 1.3 Polynomial Equations-Solving in Ancient Times beyond China and the Program of Descartes Chapter 2 Historical Development of Geometry Theorem-Proving and Geometry Problem-Solving in Ancient Times 2.1 Geometry Theorem-Proving from Euclid to Hilbert 2.2 Geometry Theorem-Proving in the Computer Age 2.3 Geometry Problem-Solving and Geometry Theorem-Proving in Ancient China Chapter 3 Algebraic Varieties as Zero-Sets and Characteristic-Set Method 3.1 Affine and Projective SpaceExtended Points and Specialization 3.2 Algebraic Varieties and Zero-Sets 3.3 Polsets and Ascending SetsPartial Ordering 3.4 Characteristic Set of a Polset and Well-Ordering Principle 3.5 Zero-Decomposition Theorems 3.6 Variety-Decomposition Theorems Chapter 4 Some Topics in Computer Algebra 4.1 Tuples of integers 4.2 Well-Arranged Basis of a Polynomial Ideal 4.3 Well-Behaved Basis of a Polynomial Idea l 4.4 Properties of Well-Behaved Basis and its Relationship with Groebner Basis 4.5 Factorization and GCD of Multivariate Polynomials over Arbitrary Extension Fields Chapter 5 Some Topics in Computational Algebraic Geometry 5.1 Some Important Characters of Algebraic Varieties Complex and Real Varieties 5.2 Algebraic Correspondence and Chow Form 5.3 Chern Classes and Chern Numbers of an Irreducible Algebraic Variety with Arbitrary Singularities 5.4 A Projection Theorem on Quasi-Varieties 5.5 Extremal Properties of Real Polynomials Chapter 6 Applications to Polynomial Equations-Solving 6.1 Basic Principles of Polynomial Equations-Solving: The Char-Set Method 6.2 A Hybrid Method of Polynomial Equations-Solving 6.3 Solving of Problems in Enumerative Geometry 6.4 Central Configurations in Planet Motions and Vortex Motions 6.5 Solving of Inverse Kinematic Equations in Robotics Chapter 7 Appicaltions to Geometry Theorem-Proving 7.1 Basic Principles of Mechanical Geometry Theorem-Proving 7.2 Mechanical Proving of Geometry Theorems of Hilbertian Type 7.3 Mechanical Proving of Geometry Theorems involving Equalities Alone 7.4 Mechanical Proving of Geometry Theorems involving Inequalities Chapter 8 Diverse Applications 8.1 Applications to Automated Discovering of Unknown Relations and Automated Determination of Geometric Loci 8.2 yApplications to Problems involving Inequalities， Optimization Problems， and Non-Linear Programming 8.3 Applications to 4-Bar Linkage Design 8.4 Applications to Surface-Fitting Problem in CAGD 8.5 Some Miscellaneous Complements and Extensions Bibliography Index
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