Jean H Gallier's Books

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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760

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World Scientific

Published Date

ISBN 10

981129173X

ISBN 13

9789811291739

Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

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Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

Volume 2 applies the linear algebra concepts presented in Volume 1 to optimization problems which frequently occur throughout machine learning. This book blends theory with practice by not only carefully discussing the mathematical under pinnings of each optimization technique but by applying these techniques to linear programming, support vector machines (SVM), principal component analysis (PCA), and ridge regression. Volume 2 begins by discussing preliminary concepts of optimization theory such as metric spaces, derivatives, and the Lagrange multiplier technique for finding extrema of real valued functions. The focus then shifts to the special case of optimizing a linear function over a region determined by affine constraints, namely linear programming. Highlights include careful derivations and applications of the simplex algorithm, the dual-simplex algorithm, and the primal-dual algorithm. The theoretical heart of this book is the mathematically rigorous presentation of various nonlinear optimization methods, including but not limited to gradient decent, the Karush-Kuhn-Tucker (KKT) conditions, Lagrangian duality, alternating direction method of multipliers (ADMM), and the kernel method. These methods are carefully applied to hard margin SVM, soft margin SVM, kernel PCA, ridge regression, lasso regression, and elastic-net regression. Matlab programs implementing these methods are included.

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896

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World Scientific

Published Date

ISBN 10

9811216584

ISBN 13

9789811216589

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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594

Publisher

Springer Science & Business Media

Published Date

ISBN 10

0387950443

ISBN 13

9780387950440

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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799

Publisher

World Scientific

Published Date

ISBN 10

9811245045

ISBN 13

9789811245046

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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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

Differential Geometry and Lie Groups

A Second Course

By: Jean Gallier,Jocelyn Quaintance

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Differential Geometry and Lie Groups

A Second Course

By: Jean Gallier,Jocelyn Quaintance

This textbook explores advanced topics in differential geometry, chosen for their particular relevance to modern geometry processing. Analytic and algebraic perspectives augment core topics, with the authors taking care to motivate each new concept. Whether working toward theoretical or applied questions, readers will appreciate this accessible exploration of the mathematical concepts behind many modern applications. Beginning with an in-depth study of tensors and differential forms, the authors go on to explore a selection of topics that showcase these tools. An analytic theme unites the early chapters, which cover distributions, integration on manifolds and Lie groups, spherical harmonics, and operators on Riemannian manifolds. An exploration of bundles follows, from definitions to connections and curvature in vector bundles, culminating in a glimpse of Pontrjagin and Chern classes. The final chapter on Clifford algebras and Clifford groups draws the book to an algebraic conclusion, which can be seen as a generalized viewpoint of the quaternions. Differential Geometry and Lie Groups: A Second Course captures the mathematical theory needed for advanced study in differential geometry with a view to furthering geometry processing capabilities. Suited to classroom use or independent study, the text will appeal to students and professionals alike. A first course in differential geometry is assumed; the authors’ companion volume Differential Geometry and Lie Groups: A Computational Perspective provides the ideal preparation.

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Page Count

627

Publisher

Springer Nature

Published Date

ISBN 10

3030460479

ISBN 13

9783030460471

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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532

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Courier Dover Publications

Published Date

ISBN 10

0486805085

ISBN 13

9780486805085

Differential Geometry and Lie Groups

A Computational Perspective

By: Jean Gallier,Jocelyn Quaintance

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Differential Geometry and Lie Groups

A Computational Perspective

By: Jean Gallier,Jocelyn Quaintance

This textbook offers an introduction to differential geometry designed for readers interested in modern geometry processing. Working from basic undergraduate prerequisites, the authors 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 many modern applications. Starting with the matrix exponential, the text begins with an introduction to Lie groups and group actions. Manifolds, tangent spaces, and cotangent spaces follow; a chapter on the construction of manifolds from gluing data is particularly relevant to the reconstruction of surfaces from 3D meshes. Vector fields and basic point-set topology bridge into the second part of the book, which focuses on Riemannian geometry. Chapters on Riemannian manifolds encompass Riemannian metrics, geodesics, and curvature. Topics that follow include submersions, curvature on Lie groups, and the Log-Euclidean framework. The final chapter highlights naturally reductive homogeneous manifolds and symmetric spaces, revealing the machinery needed to generalize important optimization techniques to Riemannian manifolds. Exercises are included throughout, along with optional sections that delve into more theoretical topics. Differential Geometry and Lie Groups: A Computational Perspective offers a uniquely accessible perspective on differential geometry for those interested in the theory behind modern computing applications. Equally suited to classroom use or independent study, the text will appeal to students and professionals alike; only a background in calculus and linear algebra is assumed. Readers looking to continue on to more advanced topics will appreciate the authors’ companion volume Differential Geometry and Lie Groups: A Second Course.

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777

Publisher

Springer Nature

Published Date

ISBN 10

3030460401

ISBN 13

9783030460402

Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

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Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

By: Jean H Gallier,Jocelyn Quaintance

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896

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World Scientific

Published Date

ISBN 10

9811216584

ISBN 13

9789811216589

Geometric Methods and Applications

For Computer Science and Engineering

By: Jean Gallier

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Geometric Methods and Applications

For Computer Science and Engineering

By: Jean Gallier

This book is an introduction to the fundamental concepts and tools needed for solving problems of a geometric nature using a computer. It attempts to fill the gap between standard geometry books, which are primarily theoretical, and applied books on computer graphics, computer vision, robotics, or machine learning. This book covers the following topics: affine geometry, projective geometry, Euclidean geometry, convex sets, SVD and principal component analysis, manifolds and Lie groups, quadratic optimization, basics of differential geometry, and a glimpse of computational geometry (Voronoi diagrams and Delaunay triangulations). Some practical applications of the concepts presented in this book include computer vision, more specifically contour grouping, motion interpolation, and robot kinematics. In this extensively updated second edition, more material on convex sets, Farkas’s lemma, quadratic optimization and the Schur complement have been added. The chapter on SVD has been greatly expanded and now includes a presentation of PCA. The book is well illustrated and has chapter summaries and a large number of exercises throughout. It will be of interest to a wide audience including computer scientists, mathematicians, and engineers. Reviews of first edition: "Gallier's book will be a useful source for anyone interested in applications of geometrical methods to solve problems that arise in various branches of engineering. It may help to develop the sophisticated concepts from the more advanced parts of geometry into useful tools for applications." (Mathematical Reviews, 2001) "...it will be useful as a reference book for postgraduates wishing to find the connection between their current problem and the underlying geometry." (The Australian Mathematical Society, 2001)

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Page Count

696

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1441999612

ISBN 13

9781441999610

Linear Algebra and Optimization with Applications to Machine Learning

Volume II: Fundamentals of Optimization Theory with Applications to Machine Learning

By: Jean Gallier,Jocelyn Quaintance

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Linear Algebra and Optimization with Applications to Machine Learning

Volume II: Fundamentals of Optimization Theory with Applications to Machine Learning

By: Jean Gallier,Jocelyn Quaintance

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895

Publisher

World Scientific Publishing Company

Published Date

ISBN 10

9811216568

ISBN 13

9789811216565

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

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Page Count

512

Publisher

Morgan Kaufmann

Published Date

ISBN 10

1558605991

ISBN 13

9781558605992

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

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760

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World Scientific

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ISBN 10

981129173X

ISBN 13

9789811291739

A Guide to the Classification Theorem for Compact Surfaces

By: Jean Gallier,Dianna Xu

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A Guide to the Classification Theorem for Compact Surfaces

By: Jean Gallier,Dianna Xu

This welcome boon for students of algebraic topology cuts a much-needed central path between other texts whose treatment of the classification theorem for compact surfaces is either too formalized and complex for those without detailed background knowledge, or too informal to afford students a comprehensive insight into the subject. Its dedicated, student-centred approach details a near-complete proof of this theorem, widely admired for its efficacy and formal beauty. The authors present the technical tools needed to deploy the method effectively as well as demonstrating their use in a clearly structured, worked example. Ideal for students whose mastery of algebraic topology may be a work-in-progress, the text introduces key notions such as fundamental groups, homology groups, and the Euler-Poincaré characteristic. These prerequisites are the subject of detailed appendices that enable focused, discrete learning where it is required, without interrupting the carefully planned structure of the core exposition. Gently guiding readers through the principles, theory, and applications of the classification theorem, the authors aim to foster genuine confidence in its use and in so doing encourage readers to move on to a deeper exploration of the versatile and valuable techniques available in algebraic topology.

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184

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Springer Science & Business Media

Published Date

ISBN 10

3642343643

ISBN 13

9783642343643

Book's by Jean H Gallier

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

Geometric Methods and Applications

Geometric Methods and Applications

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

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

Differential Geometry and Lie Groups

Differential Geometry and Lie Groups

Logic for Computer Science

Logic for Computer Science

Differential Geometry and Lie Groups

Differential Geometry and Lie Groups

Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

Linear Algebra And Optimization With Applications To Machine Learning - Volume Ii: Fundamentals Of Optimization Theory With Applications To Machine Learning

Geometric Methods and Applications

Geometric Methods and Applications

Linear Algebra and Optimization with Applications to Machine Learning

Linear Algebra and Optimization with Applications to Machine Learning

Curves and Surfaces in Geometric Modeling

Curves and Surfaces in Geometric Modeling

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

Aspects Of Harmonic Analysis On Locally Compact Abelian Groups

A Guide to the Classification Theorem for Compact Surfaces

A Guide to the Classification Theorem for Compact Surfaces

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