I'm interested in studying philosophy as a framework for thinking about engineering. I have a background in science. Who are some interesting thinkers for science, engineering and math? More specifically, are there some defining philosophical ideas that make those fields different? I'm trying to answer the question of how traditional engineering is different from scientific study.
I will fix on your last sentence since it defines your main concern. Try the following :
Sunny Y. Auyang, 'Knowledge in Science and Engineering', Synthese, Vol. 168, No. 3 (Jun., 2009), pp. 319-331.
Edwin T. Layton, Jr., 'American Ideologies of Science and Engineering', Technology and Culture, Vol. 17, No. 4 (Oct., 1976), pp. 688-701. (Johns Hopkins publication.)
Leo Young, 'Science and Engineering', Science, New Series, Vol. 209, No. 4464 (Sep. 26, 1980), p. 1475.
These are all reflective pieces, looking at the nature and conceptual relationship between science and engineering. I think they will provide you with ideas to work on.
I will take a stab at your last question: 'how traditional engineering is different from scientific study.'
It's very hard to define exactly what science is (this is the problem of demarcation), but it's sometimes loosely defined as the empirical branch of knowledge, other times it's described as a method--but the important part is that science is an activity (or branch of knowledge) that is concerned with understanding how the world is.
Engineering, on the other hand, is not concerned with how the world is, but rather how to solve technological problems (or advance technology).
Sometimes the distinction is not obvious. For example, it's possible to have two people doing the exact same thing but one is trying to solve an engineering problem, while the other is trying to answer a fundamental question about nature. Thus the agent's intentions may be required to properly classify an activity. Furthermore, there is also a symbiotic relationship between science and technology, which sometimes causes people to confuse the two: science often leads directly to advances in technology and technology often leads directly to advances science.