
In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. --from publisher description.
Mrs. Perkins's Electric Quilt: And Other Intriguing Stories of Mathematical Physics by Paul J. Nahin
It sounds like it's at about the right difficulty/knowledge level, and it has interesting stuff, isn't a boring textbook.
A Fire Upon the Deep, by Vernor Vinge
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Hyperion, by Dan Simmons
Mrs. Perkins's Electric Quilt, a fun book about some math and physics problems