The Bible of the history of mathematics is Morris Kline's *[Mathematical Thought From Ancient To Modern Times][1]*, but this is really for mathematics students. I think it'd be hard to teach a course from it to non-mathematics majors. 

  To be honest, I think it'd be really hard to teach such a course to non-mathematics majors PERIOD: How would you explain why Weierstrass's non-differentiable function is important to students who don't know calculus? Even worse, why would such students CARE? 

  If I was really gung ho to teach such a course I'd take Kline, Stillwell, Bell's *[Men Of Mathematics][2]* and 3 or 4 other texts and use them to write a set of lecture notes for my students. That's how I'D do it. 

  


  [1]: http://books.google.com/books/about/Mathematical_thought_from_ancient_to_mod.html?id=8YaBuGcmLb0C
  [2]: http://books.google.com/books/about/Men_of_mathematics.html?id=BLFL3coT5i4C