Jean H Gallier – författare

This book provides the mathematical fundamentals of linear algebra to practicers in computer vision, machine learning, robotics, applied mathematics, and electrical engineering. By only assuming a knowledge of calculus, the authors develop, in a rigorous yet down to earth manner, the mathematical theory behind concepts such as: vectors spaces, bases, linear maps, duality, Hermitian spaces, the spectral theorems, SVD, and the primary decomposition theorem. At all times, pertinent real-world applications are provided. This book includes the mathematical explanations for the tools used which we believe that is adequate for computer scientists, engineers and mathematicians who really want to do serious research and make significant contributions in their respective fields.

This book presents the theory of harmonic analysis for noncommutative compact groups. If G is a commutative locally compact group, there is a well-understood theory of harmonic analysis as discussed in Aspects of Harmonic Analysis on Locally Compact Abelian Groups. If G is not commutative, things are a lot tougher. In the special case of a compact group, there is a deep interplay between analysis and representation theory which was first discovered by Hermann Weyl and refined by Andre Weil. This book presents these seminal results of Weyl and Weil.Starting with the basics of representations theory, it presents the famous Peter-Weyl theorems and discusses Fourier analysis on compact groups. This book also introduces the reader to induced representations of locally compact groups, induced representations of G-bundles, and the theory of Gelfand pairs. A special feature is the chapter on equivariant convolutional neural networks (CNNs), a chapter which shows how many of the abstract concepts of representations, analysis on compact groups, Peter-Weyl theorems, Fourier transform, induced representations are used to tackle very practical, modern-day problems.

This book is an introduction to discrete mathematics with a strong emphasis on formal reasoning. Beginning with the fundamentals of propositional and predicate logic, it develops proof techniques through deduction trees, truth tables, and formal semantics. The first chapter is devoted entirely to logical reasoning, providing a foundation for the rest of the text, which covers standard topics such as sets, functions, relations, induction, and recursion, as well as more advanced material like number theory, graph theory, and discrete probability.Highlights of this book include an initial chapter that provides a gentle introduction to basic logic, including proof trees and templates, written from the perspective of a master logician. For the more advanced audience, another chapter provides a deeper look into basic logic by providing details on Gentzen-style deduction trees, first-order theories, the simply-typed λ-calculus, and Kripke models for intuitionistic logic. Other highlights include the inclusion-exclusion principle, the Möbius inversion formula, the RSA cryptosystem, and a thorough discussion on network flow problems, including the Max-Flow Min-Cut theorem and the Ford and Fulkerson algorithm. Each chapter concludes with a detailed summary and a comprehensive set of problems, making the book especially suitable for undergraduate students in mathematics and theoretical computer science.