Favorite Textbooks for introducing a subject?

Question

I'm interested in learning more about number theory, about fractal geometry, and about probability. Anyone have any good recommendations? I've taken calculus and statistics at university if that helps you gauge where I'm at.

Answer 1

Fractal's Everywhere is a great book to investigate fractals with. It's also not very expensive (the dover edition.)

Strayer's Elementary Number Theory is a good intro to number theory. As well as George Andrew's Number Theory (slightly more combinatorial in flavor).

Answer 2

I recommend Mosteller's "50 hard problems in probability," because having taken stats, you presumably already know a little probability theory. Mosteller's book helps you understand how little you know :) and teaches you some interesting new ideas as motivated by some relatively practical problems. (By the way, "Hard" is in the eye of the beholder: the first problem is something like this: a 6 inch stirring rod is falls and breaks at a random point (uniformly random along the length of the rod) into two pieces. What's the expected length of the shorter piece?)