Modern mathematics and applications in computer

This book presents a concise exposition of modern mathematical concepts, models and methods with applications in computer graphics, vision and machine learning. The compendium is organized in four parts Algebra, Geometry, Topology, and Applications. One of the features is a unique treatment of tensor and manifold topics to make them easier for the students. All proofs are omitted to give an emphasis on the exposition of the concepts. Effort is made to help students to build intuition and avoid parrot-like learning.There is minimal inter-chapter dependency. Each chapter can be used as an independent crash course and the reader can start reading from any chapter almost. This book is intended for upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision, pattern recognition and machine learning. It can be used as a reference book, or a textbook for a selected topics course with the instructors choice of any of the topics.Contents:Mathematical StructuresAlgebra:Linear AlgebraTensor AlgebraExterior AlgebraGeometric AlgebraGeometry:Projective GeometryDifferential GeometryNon-Euclidean GeometryTopology and More:General TopologyManifoldsHilbert SpacesMeasure Spaces and Probability SpacesApplications:Color SpacesPerspective Analysis of ImagesQuaternions and 3-D RotationsSupport Vector Machines and Reproducing Kernel Hilbert SpacesManifold Learning in Machine LearningReadership: Upper level undergraduate students, graduate students and researchers in computer graphics, geometric modeling, computer vision and machine learning.