Numerical analysis is my favorite topic so I am a bit biased. To me it is one the most interesting and useful topics when mixing computers and mathematics. However one does need to be very comfortable with linear algebra and calculus to understand it AS LONG as the approach to the topic is algorithmic. Biggest problem with such a course is that a lot of math professors view numerical analysis as nothing more than the study of error. This in my opinion, while is important and sheds a lot of light on some things, is often very unintuitive. Its not very illuminating to approximate some error through algebraical means of some polynomial interpolation that has a factor of Nth derivative; you cant really visualize it and it just feels fucking bad and hand-wavy. Anyway a lot of this shit is taught in a very dry and dull manner because most mathematicians dont want to understand the fucking topic. To me numerical analysis seems more than studying error. It is the fun of algorithms but is solving the continuous instead of discrete which requires a more interesting mathematical thought, one dealing with the infinite instead of finite.
TL;DR your professor sucked dick.
As an example of what i tried to ramble on about, and since I mentioned it before in this thread, when i learn a new language, I do it by implementing linear algebra routines, using efficient and not efficient methods, one finds in any scientific library (a library that is usually calling on some god awful Fortran written 50 years ago). My favorite, probably because its simple and intuitive, is implementing least squares solution using Householder Transformations. Basically you take a mathematical fact, proven by fairly basic proof, and apply it algorithmically to solve a problem. Its cute, its fun and it shows the power of mathematical truth when applied to a problem.
More TL;DR Something...something, school good, professors bad.
Take a look at Numerical Linear Algebra by Trefethen or Matrix Computations by Golub to see an example of interesting presentation of Numerical Analysis + Optimization. For a more mathematically heavy approach, and one that requires a bit of basic analysis, I would recommend Michelle Schatzman's book.