Jean H. Gallier's Books

Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

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Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

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.

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Page Count

823

Publisher

World Scientific

Published Date

ISBN 10

9811206414

ISBN 13

9789811206412

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

By: Jean H Gallier,Jocelyn Quaintance

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Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

By: Jean H Gallier,Jocelyn Quaintance

The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.

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Page Count

760

Publisher

World Scientific

Published Date

ISBN 10

981129173X

ISBN 13

9789811291739

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

By: Jean H Gallier,Jocelyn Quaintance

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Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

By: Jean H Gallier,Jocelyn Quaintance

For more than thirty years the senior author has been trying to learn algebraic geometry. In the process he discovered that many of the classic textbooks in algebraic geometry require substantial knowledge of cohomology, homological algebra, and sheaf theory. In an attempt to demystify these abstract concepts and facilitate understanding for a new generation of mathematicians, he along with co-author wrote this book for an audience who is familiar with basic concepts of linear and abstract algebra, but who never has had any exposure to the algebraic geometry or homological algebra. As such this book consists of two parts. The first part gives a crash-course on the homological and cohomological aspects of algebraic topology, with a bias in favor of cohomology. The second part is devoted to presheaves, sheaves, Cech cohomology, derived functors, sheaf cohomology, and spectral sequences. All important concepts are intuitively motivated and the associated proofs of the quintessential theorems are presented in detail rarely found in the standard texts.

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Page Count

799

Publisher

World Scientific

Published Date

ISBN 10

9811245045

ISBN 13

9789811245046

Geometric Methods and Applications

For Computer Science and Engineering

By: Jean H. Gallier

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Geometric Methods and Applications

For Computer Science and Engineering

By: Jean H. Gallier

An introduction to the fundamental geometric concepts and tools needed for solving problems of a geometric nature using a computer. The book offers overviews of affine, projective, Euclidian and differential geometry, exploring many of their practical applications, and providing the geometric background needed for conducting research in computer graphics, geometric modeling, computer vision and robotics.

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Page Count

594

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387950443

ISBN 13

9780387950440

Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition

By: Jean H. Gallier

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Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition

By: Jean H. Gallier

This advanced text for undergraduate and graduate students introduces mathematical logic with an emphasis on proof theory and procedures for algorithmic construction of formal proofs. The self-contained treatment is also useful for computer scientists and mathematically inclined readers interested in the formalization of proofs and basics of automatic theorem proving. Topics include propositional logic and its resolution, first-order logic, Gentzen's cut elimination theorem and applications, and Gentzen's sharpened Hauptsatz and Herbrand's theorem. Additional subjects include resolution in first-order logic; SLD-resolution, logic programming, and the foundations of PROLOG; and many-sorted first-order logic. Numerous problems appear throughout the book, and two Appendixes provide practical background information.

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Page Count

532

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486805085

ISBN 13

9780486805085

Curves and Surfaces in Geometric Modeling

Theory and Algorithms

By: Jean H. Gallier

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Curves and Surfaces in Geometric Modeling

Theory and Algorithms

By: Jean H. Gallier

Curves and Surfaces in Geometric Modeling: Theory and Algorithms offers a theoretically unifying understanding of polynomial curves and surfaces as well as an effective approach to implementation that you can apply to your own work as a graduate student, scientist, or practitioner." "The focus here is on blossoming - the process of converting a polynomial to its polar form - as a natural, purely geometric explanation of the behavior of curves and surfaces. This insight is important for more than just its theoretical elegance - the author demonstrates the value of blossoming as a practical algorithmic tool for generating and manipulating curves and surfaces that meet many different criteria. You'll learn to use this and other related techniques drawn from affine geometry for computing and adjusting control points, deriving the continuity conditions for splines, creating subdivision surfaces, and more." "It will be an essential acquisition for readers in many different areas, including computer graphics and animation, robotics, virtual reality, geometric modeling and design, medical imaging, computer vision, and motion planning."--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

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Page Count

512

Publisher

Morgan Kaufmann

Published Date

ISBN 10

1558605991

ISBN 13

9781558605992

Proof Theory and Automated Deduction

By: Jean Goubault-Larrecq,I. Mackie

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Proof Theory and Automated Deduction

By: Jean Goubault-Larrecq,I. Mackie

Interest in computer applications has led to a new attitude to applied logic in which researchers tailor a logic in the same way they define a computer language. In response to this attitude, this text for undergraduate and graduate students discusses major algorithmic methodologies, and tableaux and resolution methods. The authors focus on first-order logic, the use of proof theory, and the computer application of automated searches for proofs of mathematical propositions. Annotation copyrighted by Book News, Inc., Portland, OR

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Page Count

448

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1402003684

ISBN 13

9781402003684

Discrete Mathematics

By: Jean Gallier

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Discrete Mathematics

By: Jean Gallier

This books 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. With this logical framework firmly in place, the book describes the major axioms of set theory and introduces the natural numbers. The rest of the book is more standard. It deals with functions and relations, directed and undirected graphs, and an introduction to combinatorics. There is a section on public key cryptography and RSA, with complete proofs of Fermat's little theorem and the correctness of the RSA scheme, as well as explicit algorithms to perform modular arithmetic. The last chapter provides more graph theory. Eulerian and Hamiltonian cycles are discussed. Then, we study flows and tensions and state and prove the max flow min-cut theorem. We also discuss matchings, covering, bipartite graphs.

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Page Count

473

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441980474

ISBN 13

9781441980472

Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition

By: Jean H. Gallier

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Logic for Computer Science

Foundations of Automatic Theorem Proving, Second Edition

By: Jean H. Gallier

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Page Count

532

Publisher

Courier Dover Publications

Published Date

ISBN 10

0486805085

ISBN 13

9780486805085

Book's by Jean H. Gallier

Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

Linear Algebra And Optimization With Applications To Machine Learning - Volume I: Linear Algebra For Computer Vision, Robotics, And Machine Learning

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

Homology, Cohomology, And Sheaf Cohomology For Algebraic Topology, Algebraic Geometry, And Differential Geometry

Geometric Methods and Applications

Geometric Methods and Applications

Logic for Computer Science

Logic for Computer Science

Curves and Surfaces in Geometric Modeling

Curves and Surfaces in Geometric Modeling

Proof Theory and Automated Deduction

Proof Theory and Automated Deduction

Discrete Mathematics

Discrete Mathematics

Logic for Computer Science

Logic for Computer Science

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