Continuous Functions -- Topological Spaces -- Topological Properties -- Deconstructionist Topology -- Homotopy -- The Euler Number -- Homotopy Groups -- Simplicial Homology -- Singular Homology -- More Deconstructionism.Taking a direct route, Essential Topology brings the most important aspects of modern topology within reach of a second-year undergraduate student. Based on courses given at the…
A Fundamental Theorem -- Topics in Algebra -- Some Quadratic Problems -- The Genus of an Algebraic Curve -- Miscellany."... The exposition is not only clear, it is friendly, philosophical, and considerate even to the most naive or inexperienced reader. And it proves that the philosophical orientation of an author really can make a big difference. The mathematical content is intensely classical.…
1+1 Dimensional Integrable Systems -- 2+1 Dimensional Integrable Systems -- N + 1 Dimensional Integrable Systems -- Surfaces of Constant Curvature, Bäcklund Congruences and Darboux Transformation -- Darboux Transformation and Harmonic Map -- Generalized Self-Dual Yang-Mills Equations and Yang-Mills-Higgs Equations -- Two Dimensional Toda Equations and Laplace Sequences of Surfaces in Projectiv…
Basic Concepts and Simplest Properties of Convex Polyhedra -- Methods and Results -- Uniqueness of Polyhedra with Prescribed Development -- Existence of Polyhedra with Prescribed Development -- Gluing and Flexing Polyhedra with Boundary -- Congruence Conditions for Polyhedra with Parallel Faces -- Existence Theorems for Polyhedra with Prescribed Face Directions -- Relationship Between the Congr…
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…
Curvature of Contact Metric Manifolds -- A Case for Curvature: the Unit Tangent Bundle -- Convex Hypersurfaces in Hadamard Manifolds -- Contact Metric Geometry of the Unit Tangent Sphere Bundle -- Topological-antitopological Fusion Equations, Pluriharmonic Maps and Special Kähler Manifolds -- ?2 and ?-Deformation Theory for Holomorphic and Symplectic Manifolds -- Commutative Condition on the S…
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…