One also has to learn to neglect things when they are not important and consider them when they are.
Oooh yeah, your comment makes a lot of sense for different reasons. These days, I'm brushing up my Physics and Maths and among the books I'm reading, there are Soviet Era books (MIR Publishers). Some of them I have from my older brothers and sisters, but anyway, I found it fascinating that there are
many things Soviet books stressed from the beginning that I haven't found in books written elsewhere where they just take things for granted.
For instance, Belikov's "General Approach to Solving Physics Problems" introduces
interactions (strong, electromagnetic, weak, gravitational) as soon as page 12. A lot of other books also introduce
interactions and
concepts of physics (example: Irodov's "
Fundamental Laws of Mechanics" , Landau & Lifschitz's books, or Matveev's "
Electricity and Magnetism"). You don't find this in most books.
My point is that they put a lot of stress on the fact that to study a problem, you can't take *everything* into account and you must simplify, sometimes idealize things, etc., in order to be able to solve the problem.. It'd be insanely hard not to. Something such as Newton's second law is introduced in a complete different manner, talking about the conditions of applicability of the law (inertial reference frame, etc). My courses in college were similar (momentum was introduced not as it's introduced in most books written in English 'mv', but included the "speed of light in vaccum" part (most books don't, and if they do, don't mention "in vaccum"), and then we're told that the particle moves much slower than photons, and the mass is constant (again, taken for granted in many books), so we can extirpate the mass from the derivation of the momentum, and the fraction of squared velociy/c is approximated to 0, which gives m.
γ . ).
They are rigorous enough to tell you that sometimes you must not be too rigorous. Which is different from not being aware of the latitude you're taking simplifying a problem. This is a similar approach to the saying (I think Picasso's) :"Learn the rules like a pro so you can break them like an artist". These books are *soooooo* good, they make the other 99.99% of the books appear as "X for dummies".