Learn Tensor & Topology: Self-Study Resources for Physics B.S. & CAS Fellow

M. V. Vasil'evIn summary, the conversation is about a person seeking recommendations for introductory texts on tensors and topology for self-study. They have a background in physics and are relearning vector calculus. Two recommended texts are "A Brief on Tensor Analysis" and "Tensor Geometry."
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Can anyone recommend good introductory texts for self-study? I want to teach myself about tensors and about topology.
FYI, I have a B.S. in Physics and am a Fellow of the Casualty Actuarial Society. I don't remember my vector calculus and am in the process of relearning - I'm using the book div, grad, curl, and all that
Thanks much!
 
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frank warner, foundations of differentiable manifolds(?).
 
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Try:



A Brief on Tensor Analysis (Undergraduate Texts in Mathematics)
by James G. Simmonds

and


Tensor Geometry: The Geometric Viewpoint and Its Uses (Graduate Texts in Mathematics, 130)
by Christopher T. J. Dodson, Timothy Poston
 
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1. What is Tensor & Topology and why is it important for Physics?

Tensor & Topology is a branch of mathematics that deals with the properties of geometric objects such as curves, surfaces, and higher-dimensional manifolds. It is important for Physics because it provides the necessary mathematical tools to describe and understand the behavior of physical systems in multiple dimensions.

2. Who can benefit from learning Tensor & Topology?

Tensor & Topology can benefit anyone who wants to deepen their understanding of advanced mathematics and its applications in Physics. It is particularly useful for students pursuing a degree in Physics, as well as researchers and professionals in the field.

3. What are some good self-study resources for learning Tensor & Topology?

Some good self-study resources for learning Tensor & Topology include textbooks such as "Introduction to Tensor Calculus, Relativity and Cosmology" by Derek F. Lawden and "Topology and Geometry for Physicists" by Charles Nash and Siddhartha Sen, online courses and lectures, and practice problems and exercises found in various Physics and Mathematics websites.

4. Is Tensor & Topology difficult to learn?

Tensor & Topology can be challenging for some learners due to its abstract nature and use of advanced mathematical concepts. However, with dedication, practice, and the right resources, it can be mastered by anyone with a strong foundation in mathematics and physics.

5. How can learning Tensor & Topology improve my understanding of Physics?

Tensor & Topology provides a powerful mathematical framework for understanding and describing physical phenomena in multiple dimensions. It allows for a deeper understanding of concepts such as relativity, electromagnetism, and quantum mechanics, and can help in solving complex problems in these areas. It also has applications in other fields such as engineering, computer science, and economics.

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