Modern mathematics and applications in computer graphics and vision / Hongyu Guo.

Includes bibliographical references and index.

0. Mathematical Structures;
Part I Algebra:
1. Linear Algebra;
2. Tensor Algebra;
3. Exterior Algebra;
4. Geometric Algebra;

Part II Geometry:
1. Projective Geometry;
2. Differential Geometry;
3. Non-Euclidean Geometry;

Part III Topology and More:
1. General Topology;
2. Manifolds;
3. Hilbert Spaces;
4. Measure Spaces and Probability Spaces;

Part IV Applications:
1. Color Spaces;
2. Perspective Analysis of Images;
3. Quaternions and 3-D Rotations;
4. Support Vector Machines and Reproducing Kernel Hilbert Spaces;
5. Manifold Learning in Machine Learning;
Bibliography;
Index.

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.