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.

> 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 :)

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, who 25 years later had a very major role in combating AIDS. But http://en.wikipedia.org/wiki/Daniel_Pipes was a jerk who couldn't stomach losing to a math student at Scrabble. :)

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/04... http://www.amazon.com/Advanced-Calculus-Several-Variables-Ma...

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.

For statistics I can really recommend 'All of Statistics' by Larry Wasserman (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/) if you like to think quantitatively. About evolution specifically I find Schrodinger's 'What is Life?' thought-provoking if you already know the basics.

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.

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.

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.

"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... [2] http://www.amazon.com/Course-Mathematics-Students-Physics-Vo...

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.

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