What books should I read to fill my knowledge gap in tensor analysis?

[Fantini]

I had a badly taught Advanced Linear Algebra course and it covered tensor algebra, resulting in a knowledge gap. What books would you recommend, if any? Exterior algebra, exterior calculus, Clifford and Grassmann algebras included wouldn't be bad ideas as well.

 

[Sudharaka]

I had a badly taught Advanced Linear Algebra course and it covered tensor algebra, resulting in a knowledge gap. What books would you recommend, if any? Exterior algebra, exterior calculus, Clifford and Grassmann algebras included wouldn't be bad ideas as well.

Hi Fantini,

For a basic idea about tensors I referred, Schaum's Outlines Vector Analysis (And An Introduction to Tensor Analysis) Once I did a General Relativity course and I found A Brief on Tensor Analysis (Undergraduate Texts in Mathematics) quite good, although I didn't read it apart from the first few chapters.

 

[math771]

I'm sorry to hear that you had a bad experience with your Advanced Linear Algebra course. It's definitely frustrating when a course doesn't cover all the necessary material or doesn't teach it well. Here are some books that I would recommend for filling in the knowledge gap and learning about tensor algebra, exterior algebra, exterior calculus, and Clifford and Grassmann algebras:

1. "Tensor Algebra and Tensor Analysis for Engineers" by Mikhail Itskov: This book provides a clear and concise introduction to tensor algebra and tensor analysis, with plenty of examples and exercises to help you practice.

2. "Exterior Algebra" by Peter Lax: This book covers the basics of exterior algebra and its applications in geometry and physics. It's a great resource for understanding the fundamentals of this subject.

3. "A Geometric Approach to Differential Forms" by David Bachman: This book introduces exterior calculus and differential forms in a geometric way, making it easier to understand the concepts and their applications.

4. "Clifford Algebras and Spinors" by Pertti Lounesto: This book provides a thorough introduction to Clifford algebras and their applications in physics and geometry.

5. "Grassmann Algebra: Exploring Extended Vector Space" by John Browne: This book covers the basics of Grassmann algebra and its applications in geometry, physics, and computer science.

I hope these recommendations help you in filling the gaps in your knowledge and expanding your understanding of these important topics. Best of luck in your studies!