Linear Algebra: Introduction to Abstract Math by Isaiah Lankham
Linear Algebra: Introduction to Abstract Math - Table of Contents
1. What is Linear Algebra?
2. Introduction to Complex Numbers
3. The Fundamental Theorem of Algebra and Factoring Polynomials
4. Vector Spaces
5. Span and Bases
6. Linear Maps
7. Eigenvalues and Eigenvectors
8. Permutations and the Determinant of a Square Matrix
9. Inner Product Spaces
10. Change of Bases
11. The Spectral Theorem for Normal Linear Maps
A. Supplementary Notes on Matrices and Linear Systems
B. The Language of Sets and Functions
C. Summary of Algebraic Structures Encountered
D. Some Common Math Symbols and Abbreviations
E. Summary of Notation Used
F. Movie Scripts
What You Will Learn in Linear Algebra: Introduction to Abstract Math
"Linear Algebra: An Introduction to Abstract Mathematics" by Isaiah Lankham, Bruno Nachtergaele, and Anne Schilling is a clear and rigorous textbook designed to introduce students to "abstract mathematics", "linear algebra", and "proof-writing". Unlike traditional computational texts, this book emphasizes understanding the theory behind familiar operations, helping learners build a strong foundation for advanced mathematics. It is ideal for upper-level undergraduates or beginning graduate students who want to connect practical computations with theoretical concepts.
The book covers essential topics such as "vector spaces", "linear transformations", "eigenvalues", and "inner product spaces", providing detailed explanations and examples. Students are guided through abstract reasoning, developing their ability to construct and understand proofs. Each chapter introduces definitions and theorems carefully, with exercises that encourage logical thinking and deep comprehension rather than rote calculation. This approach bridges the gap between applied linear algebra and more theoretical mathematics courses.
Overall, the text is both rigorous and accessible, combining "mathematical rigor" with clear exposition and illustrative examples. By focusing on theory, logic, and abstract structures, the book prepares readers for advanced studies in algebra, analysis, geometry, and other branches of mathematics. It is a valuable resource for anyone aiming to gain a deep and lasting understanding of linear algebra beyond computation.
Book Details & Specifications
Title:
Linear Algebra: Introduction to Abstract Math by Isaiah Lankham
Publisher:
University of California, Davis
Year:
2015
Pages:
256
Type:
PDF
Language:
English
ISBN-10 #:
9814723770
ISBN-13 #:
978-9814723770
License:
CC BY-SA 4.0
Amazon:
Amazon
About the Author: Isaiah Lankham, Bruno Nachtergaele, and Anne Schilling
The author
Isaiah Lankham, Bruno Nachtergaele, and Anne Schilling
are mathematicians and educators known for their work in "linear algebra", "abstract mathematics", "algebra", "mathematical reasoning", and "proof-writing". They combine teaching expertise with deep research experience to help students grasp complex mathematical ideas. Their textbook, "Linear Algebra: An Introduction to Abstract Mathematics", reflects this approach by emphasizing theory, logical thinking, and rigorous reasoning. The authors focus on making "vector spaces", "linear transformations", and eigenvalue concepts accessible, preparing students for advanced mathematics while strengthening their conceptual understanding and problem-solving skills.
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