The Bible of the history of mathematics is Morris Kline's Mathematical Thought From Ancient To Modern TimesMathematical Thought From Ancient To Modern Times,but but this is really for mathematics students.I I think it'd be hard to teach a course from it to non-mathematics majors.
To be honest,I I think it'd be really hard to teach such a course to non-mathematics majors PERIOD:How How would you explain why Wierstrauss' nondifferentiableWeierstrass's non-differentiable function is important to sudentsstudents who don't know calculus?Even Even worse-why, why would such students CARE?
If I was really gung ho to teach such a course-I'd I'd take Kline,Stillwell Stillwell,Bell's Bell's Men Of MathematicsMen Of Mathematics and 3 or 4 other texts and use them to write a set of lecture notes for my students.That's That's how I'D do it.