The Should I Become a Mathematician? Thread
I am glad to see Matt is chipping in. Courtigrad, I think Apostol is outstanding and probably more than sufficient for training in any future direction, but at intervals I suggest going back and reconsidering Courant. I also did not like it as a student, but appreciate it more now.
One thing a friend/student of mine said about his career in applied mathematics may be useful: he said it was primarily the difficulty of the pure mathematics he studied that readied him for applied mathematics work, not the specific knowledge. Having had to learn algebraic topology taught him how to learn something hard, and he had a big advantage over others in his field when he needed something new. He knew how to learn.