Approximate Parametrisation of Confidence Sets -- Challenges in Surface-Surface Intersections -- Computing the Topology of Three-Dimensional Algebraic Curves -- Distance Properties of ?-Points on Algebraic Curves -- Distance Separation Measures Between Parametric Curves and Surfaces Toward Intersection and Collision Detection Applications -- Elementary Theory of Del Pezzo Surfaces -- The Geomet…
Foreword -- Introduction -- The Homogeneous Case -- Hilbert Functions -- Further Applications -- A. The ABC of CoCoA 5 -- B. Suggestions for Further Reading -- C. Hints for Selected Exercises -- Bibliography.Computational Commutative Algebra 2 is the natural continuation of Computational Commutative Algebra 1 with some twists, starting with the differently coloured cover graphics. The first vol…
Complex Numbers in Algebraic Form -- Complex Numbers in Trigonometric Form -- Complex Numbers and Geometry -- More on Complex Numbers and Geometry -- Olympiad-Caliber Problems -- Answers, Hints and Solutions to Proposed Problems.It is impossible to imagine modern mathematics without complex numbers. Complex Numbers from A to . . . Z introduces the reader to this fascinating subject that, from t…
Local Theory -- Complex Manifolds -- Kähler Manifolds -- Vector Bundles -- Applications of Cohomology -- Deformations of Complex Structures.Complex geometry studies (compact) complex manifolds. It discusses algebraic as well as metric aspects. The subject is on the crossroad of algebraic and differential geometry. Recent developments in string theory have made it an highly attractive area, bot…
Monomial Ideals -- Squarefree monomial ideals -- Borel-fixed monomial ideals -- Three-dimensional staircases -- Cellular resolutions -- Alexander duality -- Generic monomial ideals -- Toric Algebra -- Semigroup rings -- Multigraded polynomial rings -- Syzygies of lattice ideals -- Toric varieties -- Irreducible and injective resolutions -- Ehrhart polynomials -- Local cohomology -- Determinants…
Basic Computer Graphics -- Raster Algorithms -- Clipping -- Transformations and the Graphics Pipeline -- Approaches to Geometric Modeling -- Basic Geometric Modeling Tools -- Visible Surface Algorithms -- Color -- Illumination and Shading -- Rendering Techniques -- Geometric Modeling Topics -- Curves in Computer Graphics -- Surfaces in Computer Graphics -- Intersection Algorithms -- Global Geom…
From the contents: Part I Control Applications of Polynomial Positivity Control Applications of Sum of Squares Programming; Analysis of Non-polynomial Systems Using the Sum of Squares Decomposition; A Sum-of-Squares Approach to Fixed-Order H8-Synthesis; LMI Optimization for Fixed-Order H8 Controller Design; An LMI-based Technique for Robust Stability Analysis of Linear Systems with Polynomial P…
Holomorphic Functions -- Complex Manifolds -- Differential Forms, Vector Bundles, Sheaves -- Infinitesimal Deformation -- Theorem of Existence -- Theorem of Completeness -- Theorem of Stability.From the reviews: "The author, who with Spencer created the theory of deformations of a complex manifold, has written a book which will be of service to all who are interested in this by now vast subject…
Linear Algebra Topics -- Affine Geometry -- Projective Geometry -- Advanced Calculus Topics -- Point Set Topology -- Combinatorial Topology -- Algebraic Topology -- Differential Topology -- Differential Geometry -- Algebraic Geometry.Possibly the most comprehensive overview of computer graphics as seen in the context of geometric modelling, this two volume work covers implementation and theory …