This text gives an introduction to discrete mathematics for beginning undergraduates. One of original features of this book is that it begins with a presentation of the rules of logic as used in mathematics. Many examples of formal and informal proofs are given.

This guide offers a detailed proof of the classification theorem for compact surfaces. It presents the technical tools needed to deploy the method effectively as well as demonstrates their use in a clearly structured, worked example.

This textbook set offers both an introduction to differential geometry designed for readers interested in modern geometry processing, as well as an exploration of more advanced topics. In the first volume, the authors work from basic undergraduate prerequisites to develop manifold theory and Lie groups from scratch; fundamental topics in Riemannian geometry follow, culminating in the theory that underpins manifold optimization techniques. Students and professionals working in computer vision, robotics, and machine learning will appreciate this pathway into the mathematical concepts behind...