A Gentle Introduction to Tensors (2014) [pdf]
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A Gentle Introduction to Tensors (2014) [pdf]
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Re: A Gentle Introduction to Tensors (2014) [pdf]
#2I have always hated when tensors are defined as something whose coordinates are transformed in a certain way. I just find it inherently unfriendly and un-geometric. No matter how much talk is given about simpler cases such as scalars, vectors, covectors, etc., the final defining formula would still look to me as daunting as always. (There is nothing “gentle” about the formulas on page 14.) Surprisingly or not, the whole thing clicked for me when I eventually learned about tensors in a more abstract algebraic setting, where they are defined as multilinear forms. The coordinate transformation laws were very easy to understand and remember after that.
But if you want to learn about tensors from how their coordinates transform, here’s a treat:
Re: A Gentle Introduction to Tensors (2014) [pdf]
#3[deleted]
Re: A Gentle Introduction to Tensors (2014) [pdf]
#4The author is clearly more comfortable with deploying beautifully laid out mathematics than prose. The introduction or "Opening Remarks" is lovely and well written but is nearly a wall of text. There is one long first paragraph followed by some staccato afterthoughts.
The author wavers between I and we. Am I your friend, guiding you through the maze or are we lecturing you on something? The author needs to settle on either one identity or spell out when they become one or another.
Sometimes, you might wish to appear as a friend hovering over the shoulder and provide hints as to the right direction to follow and at other times you might deploy something that will give LaTeX a headache and pull out the Vox Dei stop on the 250 ton Organ and destroy nearby eardrums.
I love the paper and it is saved locally.
Re: A Gentle Introduction to Tensors (2014) [pdf]
#5The author is clearly more comfortable with deploying beautifully laid out mathematics than prose. The introduction or "Opening Remarks" is lovely and well written but is nearly a wall of text. There is one long first paragraph followed by some staccato afterthoughts. The author wavers between I and we. Am I your friend, guiding you through the maze or are we lecturing you on something? The author needs to settle on…
I've always thought of it as a journey that we're going on together, where we may do something, expect something, find something, or conclude something - together!
Perhaps I'm finding camaraderie where there is none. How disappointing.
Re: A Gentle Introduction to Tensors (2014) [pdf]
#6I never studied tensors, but for a very first ultra basic understanding of tensors I really liked Dan Fleisch's video:
https://www.youtube.com/watch?v=f5liqUk0ZTw&t=3s
He also has some great "Student's Guide" books about tensors and other subjects.
Re: A Gentle Introduction to Tensors (2014) [pdf]
#7Yet to see a "Gentle Introduction to" that didn't freely and accurately translate to poorly written, impenetrable prose whose purpose is to gratify the ego of the author in demonstrating how they are unbelievably more clever than any reader who could conceivably require any kind of "introduction"
Is that bad luck on my part? (I've given up on thinking I'm particularly or especially dense - while making no claims to be some species of super-genius) Or is that the generally accepted genre?
Re: A Gentle Introduction to Tensors (2014) [pdf]
#8Yet to see a "Gentle Introduction to" that didn't freely and accurately translate to poorly written, impenetrable prose whose purpose is to gratify the ego of the author in demonstrating how they are unbelievably more clever than any reader who could conceivably require any kind of "introduction" Is that bad luck on my part? (I've given up on thinking I'm particularly or especially dense - while making no claims to b…
Many of the scientific treatises of today are formulated in a half-mystical language, as though to impress the reader with the uncomfortable feeling that he is in the permanent presence of a superman.
Cornelius Lanczos
Re: A Gentle Introduction to Tensors (2014) [pdf]
#9Yet to see a "Gentle Introduction to" that didn't freely and accurately translate to poorly written, impenetrable prose whose purpose is to gratify the ego of the author in demonstrating how they are unbelievably more clever than any reader who could conceivably require any kind of "introduction" Is that bad luck on my part? (I've given up on thinking I'm particularly or especially dense - while making no claims to b…
After having had difficult topics explained remarkably well by a few math teachers, I'm convinced that the "gentle introductions" you're talking about are meant to be confusing. Or perhaps, in some cases, they don't grasp the material as well as they let on.
edit: For anyone who wants examples of good introductions, check out 3Blue1Brown's YouTube channel.
Re: A Gentle Introduction to Tensors (2014) [pdf]
#10Yet to see a "Gentle Introduction to" that didn't freely and accurately translate to poorly written, impenetrable prose whose purpose is to gratify the ego of the author in demonstrating how they are unbelievably more clever than any reader who could conceivably require any kind of "introduction" Is that bad luck on my part? (I've given up on thinking I'm particularly or especially dense - while making no claims to b…
After having had difficult topics explained remarkably well by a few math teachers, I'm convinced that the "gentle introductions" you're talking about are meant to be confusing. Or perhaps, in some cases, they don't grasp the material as well as they let on. edit: For anyone who wants examples of good introductions, check out 3Blue1Brown's YouTube channel.
Or, the infamous Curse of Knowledge?