1-1 is implicitly required, because each element of the domain can only map to one element of the range - so to map to every element of the range you'll need a 1-1 mapping.
For what it's worth, most of the people I've encountered who call themselves theoretical physicists work in the particle physics/relativity/string theory kind of area. But I think theoretical physics is more about how you handle the subject matter than the subject matter itself. So if you...
Hi! I'm looking for recommendations of maths I can work on over my vacation to (a) keep mentally fit and (b) expand my horizons a little. To give a bit of background, I've done three of the four semesters of Calculus my university offers to undergrads (up to stuff like optimising multivariable...