I'm studying mathematics through three books:
- Calculus: Early Transcendentals, Stewart;
- Discrete Mathematics, Kevin Ferland;
- Polynomials, Barbeau.
I have also some invitations to mathematics which present a different perspective: Some introduce mathematics through combinatorics, some introduce mathematics through set theory, etc.
Are there introductions to mathematics through physics?
The books you mentioned are not really introductions to mathematics through that topic. Rather the topic itself is a branch of mathematics; for example, calculus. Physics uses much mathematics, and much mathematics is motivated by physical problems; for example, differential equations. Some universities have undergraduate math syllabuses that cover a lot of physics; for example, Cambridge. For a good overview of undergraduate physics with lots of mathematical material, you may see The Feynman Lectures on Physics by Nobel prize winner Richard Feynman.