Algebra, Topology & Optimization for Machine Learning by Jean Gallier
Algebra, Topology & Optimization for Machine Learning - Table of Contents
PART I: LINEAR ALGEBRA & GEOMETRY
- 1. Introduction & Algebraic Foundations (Groups, Rings, Fields)
- 2. Vector Spaces, Bases, and Linear Maps
- 3. Haar Bases, Wavelets, and Hadamard Matrices
- 4. Gaussian Elimination, LU, Cholesky, and Norms
- 5. Euclidean Spaces and QR-Decomposition
- 6. Eigenvalues, Spectral Theorems, and Finite Element Method
- 7. Graphs, Laplacians, and Spectral Drawing
- 8. Singular Value Decomposition (SVD) & Pseudo-Inverses
- 9. Basics of Affine and Projective Geometry
- 10. Geometry of Bilinear Forms & Witt’s Theorem
PART II: ALGEBRA, TOPOLOGY & OPTIMIZATION
- 11. Polynomials, PIDs, UFDs, and Hilbert’s Basis Theorem
- 12. Tensor Algebras, Exterior Powers, and Modules
- 13. Topology, Fractals, and Differential Calculus
- 14. Extrema, Newton’s Method, and Quadratic Optimization
- 15. Schur Complements and Applications
- 16. Convex Sets, H-Polyhedra, and Linear Programs
- 17. The Simplex Algorithm and Duality
- 18. Hilbert Spaces & General Optimization Theory
What You Will Learn in Algebra, Topology & Optimization for Machine Learning
Algebra, Topology & Optimization for Machine Learning by Jean Gallier and Jocelyn Quaintance is an authoritative, mathematically rigorous textbook designed to provide computer scientists and AI researchers with the deep mathematical foundations underlying modern data science. This thorough volume guides readers through vector spaces, Haar wavelets, singular value decomposition (SVD), projective geometry, tensor algebras, general topology, differential calculus, and linear programming with exceptional analytical precision and structural clarity.
Designed for graduate students, machine learning engineers, computer vision scientists, and quantitative analysts, this foundational text bridges abstract pure mathematics and scalable learning algorithms. The authors present step-by-step mathematical derivations, structural geometry, and optimization proofs required for deep learning theory, kernel methods, and high-dimensional data geometry. Whether you are analyzing spectral graph drawing, Hilbert spaces, or non-linear optimization algorithms, this book offers an indispensable roadmap.
Recognized globally for its thoroughness and open-access pedagogy, it remains one of the best mathematical foundations books for machine learning self-study. By balancing abstract algebraic and topological concepts with practical algorithmic optimization, it serves as an essential tool for mastering machine learning mathematics with confidence.
Book Details & Specifications
Title:
Algebra, Topology & Optimization for Machine Learning by Jean Gallier
Publisher:
World Scientific Publishing Co.
Year:
2025
Pages:
2204
Type:
PDF
Language:
English
ISBN-10 #:
110845514X
ISBN-13 #:
978-1108455145
License:
University Resource
Amazon:
Amazon
About the Author: Jean Gallier
The author Jean Gallier
is a Professor Emeritus in the Department of Computer and Information Science at the University of Pennsylvania, internationally celebrated for his prolific research in theoretical computer science, automated theorem proving, differential geometry, and computational algebra. He has authored several acclaimed graduate-level texts, including Geometric Methods and Applications and Curves and Surfaces in Geometric Modeling.
Co-authored alongside Jocelyn Quaintance, a mathematician and lecturer at the University of Pennsylvania, Algebra, Topology & Optimization for Machine Learning represents their joint commitment to providing rigorous, open-access mathematical education. Their focus on explicit proofs, clear geometric intuition, and complete structural coverage makes this text a classic reference for machine learning mathematics that continues to be trusted by researchers and self-taught learners worldwide.
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