Mugwort · HackerTrans

7 лет назадdiscuss

Always. Robin Hartshorne's "Geometry: Euclid and Beyond" is the best book of its kind. It does Euclidean geometry with Hilbert's axioms and cleans up some of the loose ends of Euclid's classical treatment. Hartshorns book also covered the 5th postulate very thoroughly and non-Euclidean geometry. Hyperbolic geometry is treated axiomatically. He also has a nice treatment of axiomatic projective geometry which you can download for free. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.475...

Mugwort

7 лет назадdiscuss

It's a very good start. From there I think the most productive thing anyone could do is make a very thorough study of Classical Mechanics. People underestimate how much a thorough knowledge will help them. Start with an easy book and work your way up. Goldstein and Laundau are excellent intermediate level choices. For a beginner I think Jakob Schwichtenbergs "No Nonsense Classical Mechanics" could work or Leonard Susskind's "Theoretical Minimum Classical Mechanics" . Personally, I really liked Jakob's book. You'll need a friend or a study group online to help you when you get stuck. Classical mechanics is very serious physics and I regard a thorough foundation in say Hamiltonian Mechanics as a solid achievement. a sure sign someone could go on and learn E&M, Statistical mechanics, Quantum mechanics, Relativity and Gauge theories. For a semi advanced book if you know some advanced maths try Spivak's Classical Mechanics and anything by V. Arnold.

Mugwort

7 лет назадdiscuss

Agreed. Hard for some people to appreciate but so true.

Mugwort

7 лет назадdiscuss

There are some really good suggestions here. I would like to add that learning calculus properly is of the utmost importance. It's no exaggeration when I say that this is unquestionably the single best, most profitable action you can take. Any one of these books can change your life.

1. Spivak Calculus

2. Apostol Calculus vol. I and II

3. Courant and Johns, Introduction to Calculus and Analysis vol. I, IIA and IIB

For the more casual computer science or physics major, I'd go with choice 3 which resembles the Feynmann lectures the most. All the rigour of the other two is there but in a more digestible form. It's hard for someone not accustomed to hard maths to digest long proofs, it could give you a bad case of indigestion. It's more a function of patience. Courant and Johns get to the point much more quickly while Spivak and Apostol take their time to do everything thoroughly. Courant and Johns does do everything thoroughly but they are kinder to the reader and delay lengthy rigoourous proofs as long as possible while giving plenty of motivation and intuition.

Also I strongly recommend any books by Ray Smullyan particularly his introduction to mathematical logic. "A Beginner's Guide to Mathematical Logic"

Mugwort

7 лет назадdiscuss

Javascript is still missing simplicity, consistency and a unified core set of ideas. It will always be that way too. Javascript will always be something grudgingly accepted or used with some misgiving. ES6 has some very nice features and the good parts of javascript stand out as much as the unfortunate inconsistencies lurking inside the language. People know how to use it. Some use it quite well but I always get the feeling I have to step around carefully and not make a dumb mistake in js which is easier to do than almost any other language except say PHP. Web assembly should open up some badly needed possibilities. All we really need is a consistent API. A world without js? I hope so.

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