31–40 of 74 posts
Off topic: nice PDF rendering I wish normal PDF would be as fluent.
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Tong is good, most appropriate if you already know a little about the subject. However, it is a "fast-track" kind of resource, it is good to read some standard textbooks on the subject, i.e. Landau & Lifshitz (the most efficient book on theoretical mechanics ever) and Goldstein (broad and interesting).
Although I have immense respect for them I really don't like L&L all that much. The first one is pretty beautiful but it could use some material on the "deeper" side of things, particularly the connection with geometry and Noether's theorem. As for the others, they're just too "russian" - I like how oddly practical they are, but they're just not structured properly - StatPhys in particular just doesn't flow very well…
Do you have any recommendations for good stat mech books? I guess the two volume set by Kardar is trendy right now, but I'm always curious about other options.
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> could use some material on the "deeper" side of things The first few chapters are precisely about the extraction of concrete conserved quantities from symmetries. A sufficiently "russian" reader will be able to see immediately the general case from these very complete examples. Noether's theorem is only missing in name, not in content. > The typesetting is also a crime against humanity - they should be done similar…
I liked that section a lot but I want a jumping off point. I don't think symmetries of the action or groups are discussed, IIRC. I may have been a little vague when I said typesetting - the actual typesetting is a bit dull but the thing that is a disgrace, I should clarify, is that the fonts are terrible, and the text has that "Cheap Dover book" print quality (not far off a good typewriter).
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I liked that section a lot but I want a jumping off point. I don't think symmetries of the action or groups are discussed, IIRC. I may have been a little vague when I said typesetting - the actual typesetting is a bit dull but the thing that is a disgrace, I should clarify, is that the fonts are terrible, and the text has that "Cheap Dover book" print quality (not far off a good typewriter).
To amplify this point, all the negative Amazon reviews praise the book but excoriate the print quality.
In college I was taught Linear Algebra from the operator point of view, rather than with matrices. That way theorems are clearer and the student's understanding is deeper, but for applications it's better to study from the matrix point of view and with lots of examples. Kuttler's book was refreshing in that sense. His other books are excellent, too. If you have been studying pure math (or french-style applied math wh…
Paul Halmos "Finite-Dimensional Vector Spaces"
For instance, the way Halmos introduces the determinant of a matrix (or an operator) is the most consistent, elegant and simple way I ever encountered. OTOH, in Kenneth Kuttler's LinAlg books the determinant is pulled out of the thin air like in 1000+ other similar books.
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Classical mechanics is ultimately just masturbation compared to the "real thing", it's all a warm-up for the mind rather than teaching you how to calculate stresses on a beam - Full on symplectic geometry is niche but the basics of Noether's theorem and symmetries are central to classical and quantum field theories which are ultimately the language in which the cutting edge of fundamental physics speaks. So I sort of…
What are the titles of the two Oxford books you mentioned? I'd like to look at them.
Concepts in thermal physics
Not at the same level as L&L but they are absolute masterpieces in pedagogy and the formula should be extended to a 800page tome to cover more material. It's the way MTW should be written...
In college I was taught Linear Algebra from the operator point of view, rather than with matrices. That way theorems are clearer and the student's understanding is deeper, but for applications it's better to study from the matrix point of view and with lots of examples. Kuttler's book was refreshing in that sense. His other books are excellent, too. If you have been studying pure math (or french-style applied math wh…
The best, by far, book on Linear Algebra that elegantly teaches it from Vector Spaces and Linear Operators point of view is Paul Halmos "Finite-Dimensional Vector Spaces" For instance, the way Halmos introduces the determinant of a matrix (or an operator) is the most consistent, elegant and simple way I ever encountered. OTOH, in Kenneth Kuttler's LinAlg books the determinant is pulled out of the thin air like in 100…
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To amplify this point, all the negative Amazon reviews praise the book but excoriate the print quality.
This must concern some paperback English print? My copy in French from "Editions MIR Moscou, 1969", hardcover, masterfully typeset and in bible paper is one of the finest books that I have.
For one of the volumes, a reviewer even posted a picture of his edition with subscripts printed so faint/partially that they were basically missing, and he had to Google the proper formulas!
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Although I have immense respect for them I really don't like L&L all that much. The first one is pretty beautiful but it could use some material on the "deeper" side of things, particularly the connection with geometry and Noether's theorem. As for the others, they're just too "russian" - I like how oddly practical they are, but they're just not structured properly - StatPhys in particular just doesn't flow very well…
Yeah, I liked the mechanics and quantum volumes, but the choice of material in the stat mech books (both volumes) just seemed weird compared to what's usually done in a modern graduate course. Do you have any recommendations for good stat mech books? I guess the two volume set by Kardar is trendy right now, but I'm always curious about other options.
Beyond that the usual suspects are good enough for me, I just don't like L&L. I'm probably forgetting something.
It's not exactly statmech but I really like McComb's introductory renormalization methods book.
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The best, by far, book on Linear Algebra that elegantly teaches it from Vector Spaces and Linear Operators point of view is Paul Halmos "Finite-Dimensional Vector Spaces" For instance, the way Halmos introduces the determinant of a matrix (or an operator) is the most consistent, elegant and simple way I ever encountered. OTOH, in Kenneth Kuttler's LinAlg books the determinant is pulled out of the thin air like in 100…
Thanks, I'll look it up. The best textbook from which I studied (operators) was Elon Lima's Algebra Linear. Sadly the only physical copies are sold in Brazil.
The title is a reference to a somewhat well-known book, Linear Algebra Done Right, which avoids using determinants to develop the theory (resulting in a somewhat novel/cleaner presentation). It's unfortunately not freely available online (published by Springer – I would suspect most university students can get it freely through their library's website, however).