For programmers interested in classical mechanics, "The Structure and Interpretation of Classical Mechanics" is a highly unique - and outstanding - introduction to Lagrangian and Hamiltonian mechanics. Available free online:
The idea behind the book is to make the "mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer." Since Sussman is involved, that means that they (and you, when you do the problems) write scheme programs.
In a more traditional vein, _Mechanics_ by Landau and Lifshitz is (in my view) among the 2 or 3 best physics textbooks available. It's a great supplement for two reasons: (1) it takes a somewhat different approach to the material than most other textbooks (emphasizing the consequences of symmetries from the very beginning) (2) it's quite short, which I find to be very helpful when self-learning.
Cool book. That's from where I learnt the Euler-Lagrange equations first.
Sussman also wrote a book, in his characteristic style, on Differential Geometry, that doubles as a possible introduction to special relativity, and bridge to the general theory.
I've read some of it, and it's not even in the same sport, much less league. SIQM has no code and uses all the handwavy notation you could read in better books (Landau, probably; or Feynmann, for an intro). It struck me as the Ford Fiesta to Sussman's 911. In fact, after that read, I was pissed at the author from riding the coat-tails of the Structure and Interpretation series.
The Landau chapter (2nd on the "Mechanics book) demonstrating how conservation laws derive from symmetries (eg Energy conservation due to homogeneity of time) was really mind-blowing for me when I was starting out in college. I don't understand why I haven't seen this idea presented in other textbooks and I can't recommend it enough for anyone with an interest in physics or science.
It's also in the Feynman lectures (proved only for quantum mechanics) and Feynman's popularization The Character of Physical Law (proof sketch for classical mechanics). (I suppose the latter is also in the online videos for the lectures that book was made from -- IIRC the Messenger lectures. http://research.microsoft.com/apps/tools/tuva/)
It's funny you mention these two books in the same comment, since I always assumed Landau was one of the targets of Sussman and Wisdom's comment, "It is surprisingly easy to get the right answer with unclear and informal symbol manipulation." (See their paper, Functional differential geometry.) Sussman/Wisdom's book is, from a brief look, not 'rigorous' either, but the 'symbol manipulations' in Landau/Lifschitz's series are sometimes borderline insane!
This is perfect for me! As a physics/CS student I prefer to learn my physics from a computational perspective. It allows me to solve more interesting/complex problems as traditional problems tend to go for cookie cutter analytical solutions that are very restricted.
Thanks!
Comments
For programmers interested in classical mechanics, "The Structure and Interpretation of Classical Mechanics" is a highly unique - and outstanding - introduction to Lagrangian and Hamiltonian mechanics. Available free online:
http://mitpress.mit.edu/sites/default/files/titles/content/s...
The idea behind the book is to make the "mathematical notations be explicit and precise enough that they can be interpreted automatically, as by a computer." Since Sussman is involved, that means that they (and you, when you do the problems) write scheme programs.
In a more traditional vein, _Mechanics_ by Landau and Lifshitz is (in my view) among the 2 or 3 best physics textbooks available. It's a great supplement for two reasons: (1) it takes a somewhat different approach to the material than most other textbooks (emphasizing the consequences of symmetries from the very beginning) (2) it's quite short, which I find to be very helpful when self-learning.
Cool book. That's from where I learnt the Euler-Lagrange equations first.
Sussman also wrote a book, in his characteristic style, on Differential Geometry, that doubles as a possible introduction to special relativity, and bridge to the general theory.
http://groups.csail.mit.edu/mac/users/gjs/6946/calculus-inde...
And one on quantum mechanics, though by a different author: http://www.amazon.com/The-Structure-Interpretation-Quantum-M...
I've read some of it, and it's not even in the same sport, much less league. SIQM has no code and uses all the handwavy notation you could read in better books (Landau, probably; or Feynmann, for an intro). It struck me as the Ford Fiesta to Sussman's 911. In fact, after that read, I was pissed at the author from riding the coat-tails of the Structure and Interpretation series.
This differential geometry book is convenient. If only someone could port this book into Python.
The Landau chapter (2nd on the "Mechanics book) demonstrating how conservation laws derive from symmetries (eg Energy conservation due to homogeneity of time) was really mind-blowing for me when I was starting out in college. I don't understand why I haven't seen this idea presented in other textbooks and I can't recommend it enough for anyone with an interest in physics or science.
Online: http://archive.org/stream/Mechanics_541/LandauLifshitz-Mecha...
It's also in the Feynman lectures (proved only for quantum mechanics) and Feynman's popularization The Character of Physical Law (proof sketch for classical mechanics). (I suppose the latter is also in the online videos for the lectures that book was made from -- IIRC the Messenger lectures. http://research.microsoft.com/apps/tools/tuva/)
It's funny you mention these two books in the same comment, since I always assumed Landau was one of the targets of Sussman and Wisdom's comment, "It is surprisingly easy to get the right answer with unclear and informal symbol manipulation." (See their paper, Functional differential geometry.) Sussman/Wisdom's book is, from a brief look, not 'rigorous' either, but the 'symbol manipulations' in Landau/Lifschitz's series are sometimes borderline insane!
This is perfect for me! As a physics/CS student I prefer to learn my physics from a computational perspective. It allows me to solve more interesting/complex problems as traditional problems tend to go for cookie cutter analytical solutions that are very restricted. Thanks!
Thanks for the Landau recommendation. I'm finding I'm not progressing with Goldstein's Mechanics.