A First Course in Optimization by Charles L. Byrne
A First Course in Optimization - Table of Contents
1. Introduction
2. Optimization Without Calculus
3. Geometric Programming
4. Convex Sets
5. Linear Programming
6. Matrix Games and Optimization
7. Differentiation
8. Convex Functions
9. Fenchel Duality
10. Convex Programming
11. Iterative Optimization
12. Quadratic Programming
13. Solving Systems of Linear Equations
14. Sequential Unconstrained Minimization Algorithms
15. Likelihood Maximization
16. Calculus of Variations
17. Operators
18. Compressed Sensing
19. Bregman-Legendre Functions
20. Constrained Linear Systems
What You Will Learn in A First Course in Optimization
"Applied and Computational Linear Algebra: A First Course" by Charles L. Byrne presents linear algebra as a "practical and computational subject", not just a theoretical one. The book is written for students who want to understand how linear algebra is actually used to solve real problems in science, engineering, and computing. Instead of focusing heavily on abstract proofs, it emphasizes "algorithms", numerical behavior, and problem-solving strategies that work well on computers.
A key strength of the book is its focus on "iterative methods" and large-scale systems of equations, which are common in modern applications such as image reconstruction, signal processing, and inverse problems. Byrne carefully connects mathematical concepts to "real-world applications", helping readers see why linear algebra matters beyond exams. Topics like least-squares problems, matrix operators, and eigenvalue methods are presented with a strong applied perspective.
Overall, this book is ideal for applied mathematics, engineering, and computational science students who want a "hands-on understanding" of linear algebra. It builds intuition, encourages computational thinking, and prepares readers to use linear algebra effectively in practical and research settings.
Book Details & Specifications
Title:
A First Course in Optimization by Charles L. Byrne
Publisher:
University of Massachusetts Lowell
Year:
2009
Pages:
301
Type:
PDF
Language:
English
ISBN-10 #:
1482226561
ISBN-13 #:
978-1482226560
License:
University Educational Resource
Amazon:
Amazon
About the Author: Charlie L Byrne
The author Charlie L Byrne
is an American applied mathematician and Professor Emeritus at the University of Massachusetts Lowell. He is best known for his work in "applied mathematics" and "computational linear algebra", where he focuses on solving large-scale mathematical problems using efficient, computer-based methods rather than abstract theory alone. Byrne’s research spans "iterative algorithms", optimization, and image reconstruction in medical imaging systems such as CT and PET. His teaching and writing emphasize clarity and real-world relevance, making complex mathematical ideas accessible and practical for students and researchers.
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