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On the idea of "mechanics 101 for smart people" - can anyone recommend good books that are the analogs of SICP for other subjects? I'd love to know ones for, sa

by tgb 13y ago

On the idea of "mechanics 101 for smart people" - can anyone recommend good books that are the analogs of SICP for other subjects? I'd love to know ones for, say, genetics or evolution as well as stats. I can say that Hubbard + Hubbard "Vector Calculus, Linear Algebra, and Differential Equations" does a good job of being that for vector calculus specifically and for exposure to theoretical mathematics.

fancyketchup 13y ago
I'm currently preparing for a course based around The Theoretical Minimum by Leonard Susskind, which (so far) seems like exactly what you're looking for. The beginning has a very quick recap of state spaces, vectors, calculus, etc. It goes over Lagrangian mechanics and conservation laws in the middle before finishing with Poisson brackets. The table of contents also claims a chapter on E&M, but I haven't looked at that yet.
cconroy 13y ago
Almost finished Vol I of Feynman Lectures On Physics. So far, Im picking up on the same enthusiasm and joy. A real pleasure to read. Euclid's Elements too for geometry is fantastic. (I think reading "from the horses mouth" is necessary but not sufficient. With guys like Newton especially, since there are no translation barriers (for us English speakers), and they are quite relatable.) I have noticed that excursions? in history of a topic; its people, places, culture, enhance the quality of the book. Feynman goes on historical asides, as does say, Apostol (in his calculus texts), and it has been a while but I believe SICP does too. I think the teaching of something should be coupled with its history. In this same vein, I'm too am interested in a book covering evolution and biology, but I have not found one, or heard of one, so if anybody knows I would greatly appreciate it. Two good bio books I have read are The Selfish Gene, and The Machinery Of Life (Goodsell), but they're more auxiliary.
nextos 13y ago
I'm quite fond of Watson's Molecular Biology of the Gene (not to be confused with Molecular Biology of the Cell). In the stats camp, Jaynes is fantastic, alas a bit difficult. But the prerequisites are very modest. It's self-contained. Hoel, Port & Stone's volume is a great introduction to basic (w/o measure theory) probability.
deleted 13y ago
[deleted]
CurtMonash 13y ago
On a more elementary level, Michael Spivak's Calculus is an amazing book on first-year calculus. He also wrote Calculus on Manifolds and a 5-volume series on Differential Geometry. Those, to put it mildly, were rougher going. I actually once got a crush on a dorm-mate in large part because I saw Calculus on Manifolds on her bookshelf. It wasn't reciprocal, however. Later in life, she went on to run the Bureau of Labor Statistics.
- ics 13y ago
  > I actually once got a crush on a dorm-mate in large part because I saw Calculus on Manifolds on her bookshelf. It wasn't reciprocal, however. Later in life, she went on to run the Bureau of Labor Statistics. I had someone I'd never met before see my copy which happened to be the international edition (in Chinese, with English in the back) and then assume I spoke fluent Mandarin. Your story's a lot better :)
  - CurtMonash 13y ago
    I lived 3 years in a Harvard grad school dormitory. One meets a variety of interesting people in such a place. E.g., I once pitched a foreign policy maven dorm-mate on caring more about Africa ... and it was http://en.wikipedia.org/wiki/Paula_Dobriansky http://en.wikipedia.org/wiki/Paula_Dobriansky, who 25 years later had a very major role in combating AIDS. But http://en.wikipedia.org/wiki/Daniel_Pipes http://en.wikipedia.org/wiki/Daniel_Pipes was a jerk who couldn't stomach losing to a math student at Scrabble. :)
- tgb 13y ago
  Yeah Hubbard & Hubbard that I recommended is a more approachable take on Calculus on Manifolds (which it is based on or inspired by). It's still not simple, but it's probably a bit easier-going for the modern student than Spivak.
- mrcactu5 13y ago
  I remember being disappointed with Calculus on Manifolds, since it was very abstract. I was looking for something with more explicit calculations. To this end, I was quite happy with Edwards "Advanced Calculus" http://www.amazon.com/Advanced-Calculus-David-V-Widder/dp/0486661032 http://www.amazon.com/Advanced-Calculus-David-V-Widder/dp/04... http://www.amazon.com/Advanced-Calculus-Several-Variables-Mathematics/dp/0486683362 http://www.amazon.com/Advanced-Calculus-Several-Variables-Ma...
santaclaus 13y ago
I'm a big fan Landau and Lifshitz's "Mechanics." Starting from nothing they hit the major results in classical mechanics in 224 pages. Short. Sweet. Elegant.
tMcGrath 13y ago
For statistics I can really recommend 'All of Statistics' by Larry Wasserman (http://www.stat.cmu.edu/~larry/all-of-statistics/ http://www.stat.cmu.edu/~larry/all-of-statistics/) It runs through a lot of important topics, particularly in inference, without being either as turgid as most stats texts for people without a maths background or as dry as more 'pure' books (no measure theory required). For biology I'd recommend 'Physical Biology of the Cell' (http://microsite.garlandscience.com/pboc2/ http://microsite.garlandscience.com/pboc2/) if you like to think quantitatively. About evolution specifically I find Schrodinger's 'What is Life?' thought-provoking if you already know the basics.
aufreak3 13y ago
"A course in mathematics for students of physics" (volumes 1 and 2) by Paul Bamberg and Schlomo Sternberg. [1] [2] I loved both the books! I replaced my course textbooks with these and am eternally thankful I did that. Volume 2, in particular, is really cool where you get introduced to the exterior calculus formulation of circuit theory, leading to Maxwell's equations. [1] http://www.amazon.com/Course-Mathematics-Students-Physics/dp/0521406498 http://www.amazon.com/Course-Mathematics-Students-Physics/dp... [2] http://www.amazon.com/Course-Mathematics-Students-Physics-Volume/dp/0521406501 http://www.amazon.com/Course-Mathematics-Students-Physics-Vo...
mrcactu5 13y ago
Doesn't Feynman Lectures do that? http://feynmanlectures.caltech.edu/I_toc.html http://feynmanlectures.caltech.edu/I_toc.html

by tgb 13y ago

fancyketchup 13y ago

I'm currently preparing for a course based around The Theoretical Minimum by Leonard Susskind, which (so far) seems like exactly what you're looking for. The beginning has a very quick recap of state spaces, vectors, calculus, etc. It goes over Lagrangian mechanics and conservation laws in the middle before finishing with Poisson brackets. The table of contents also claims a chapter on E&M, but I haven't looked at that yet.

cconroy 13y ago

Almost finished Vol I of Feynman Lectures On Physics. So far, Im picking up on the same enthusiasm and joy. A real pleasure to read. Euclid's Elements too for geometry is fantastic. (I think reading "from the horses mouth" is necessary but not sufficient. With guys like Newton especially, since there are no translation barriers (for us English speakers), and they are quite relatable.) I have noticed that excursions? in history of a topic; its people, places, culture, enhance the quality of the book. Feynman goes on historical asides, as does say, Apostol (in his calculus texts), and it has been a while but I believe SICP does too. I think the teaching of something should be coupled with its history. In this same vein, I'm too am interested in a book covering evolution and biology, but I have not found one, or heard of one, so if anybody knows I would greatly appreciate it. Two good bio books I have read are The Selfish Gene, and The Machinery Of Life (Goodsell), but they're more auxiliary.

nextos 13y ago

I'm quite fond of Watson's Molecular Biology of the Gene (not to be confused with Molecular Biology of the Cell). In the stats camp, Jaynes is fantastic, alas a bit difficult. But the prerequisites are very modest. It's self-contained. Hoel, Port & Stone's volume is a great introduction to basic (w/o measure theory) probability.

deleted 13y ago

[deleted]

CurtMonash 13y ago

On a more elementary level, Michael Spivak's Calculus is an amazing book on first-year calculus. He also wrote Calculus on Manifolds and a 5-volume series on Differential Geometry. Those, to put it mildly, were rougher going. I actually once got a crush on a dorm-mate in large part because I saw Calculus on Manifolds on her bookshelf. It wasn't reciprocal, however. Later in life, she went on to run the Bureau of Labor Statistics.

ics 13y ago
> I actually once got a crush on a dorm-mate in large part because I saw Calculus on Manifolds on her bookshelf. It wasn't reciprocal, however. Later in life, she went on to run the Bureau of Labor Statistics. I had someone I'd never met before see my copy which happened to be the international edition (in Chinese, with English in the back) and then assume I spoke fluent Mandarin. Your story's a lot better :)
- CurtMonash 13y ago
  I lived 3 years in a Harvard grad school dormitory. One meets a variety of interesting people in such a place. E.g., I once pitched a foreign policy maven dorm-mate on caring more about Africa ... and it was http://en.wikipedia.org/wiki/Paula_Dobriansky http://en.wikipedia.org/wiki/Paula_Dobriansky, who 25 years later had a very major role in combating AIDS. But http://en.wikipedia.org/wiki/Daniel_Pipes http://en.wikipedia.org/wiki/Daniel_Pipes was a jerk who couldn't stomach losing to a math student at Scrabble. :)
tgb 13y ago
Yeah Hubbard & Hubbard that I recommended is a more approachable take on Calculus on Manifolds (which it is based on or inspired by). It's still not simple, but it's probably a bit easier-going for the modern student than Spivak.
mrcactu5 13y ago
I remember being disappointed with Calculus on Manifolds, since it was very abstract. I was looking for something with more explicit calculations. To this end, I was quite happy with Edwards "Advanced Calculus" http://www.amazon.com/Advanced-Calculus-David-V-Widder/dp/0486661032 http://www.amazon.com/Advanced-Calculus-David-V-Widder/dp/04... http://www.amazon.com/Advanced-Calculus-Several-Variables-Mathematics/dp/0486683362 http://www.amazon.com/Advanced-Calculus-Several-Variables-Ma...

santaclaus 13y ago

I'm a big fan Landau and Lifshitz's "Mechanics." Starting from nothing they hit the major results in classical mechanics in 224 pages. Short. Sweet. Elegant.

tMcGrath 13y ago

For statistics I can really recommend 'All of Statistics' by Larry Wasserman (http://www.stat.cmu.edu/~larry/all-of-statistics/ http://www.stat.cmu.edu/~larry/all-of-statistics/) It runs through a lot of important topics, particularly in inference, without being either as turgid as most stats texts for people without a maths background or as dry as more 'pure' books (no measure theory required). For biology I'd recommend 'Physical Biology of the Cell' (http://microsite.garlandscience.com/pboc2/ http://microsite.garlandscience.com/pboc2/) if you like to think quantitatively. About evolution specifically I find Schrodinger's 'What is Life?' thought-provoking if you already know the basics.

aufreak3 13y ago

"A course in mathematics for students of physics" (volumes 1 and 2) by Paul Bamberg and Schlomo Sternberg. [1] [2] I loved both the books! I replaced my course textbooks with these and am eternally thankful I did that. Volume 2, in particular, is really cool where you get introduced to the exterior calculus formulation of circuit theory, leading to Maxwell's equations. [1] http://www.amazon.com/Course-Mathematics-Students-Physics/dp/0521406498 http://www.amazon.com/Course-Mathematics-Students-Physics/dp... [2] http://www.amazon.com/Course-Mathematics-Students-Physics-Volume/dp/0521406501 http://www.amazon.com/Course-Mathematics-Students-Physics-Vo...

mrcactu5 13y ago

Doesn't Feynman Lectures do that? http://feynmanlectures.caltech.edu/I_toc.html http://feynmanlectures.caltech.edu/I_toc.html