<p>My daugher was a math major, among her major courses were:
Discrete mathematics, Linear Algebra, Group Theory, Number Theory, Probability, Topology, Optimization, Probability Models & Random Processes.</p>
<p>A few of these topics I knew something about, others I'd never studied. Which surprised me, as I thought I'd had quite a lot of math in my studies of physics and engineering. But also, as others have stated, the way she studied them, in most cases, was quite proof-based rather than application based.</p>
<p>On the other hand she never even took a class in some of the areas of mathematics I studied. Not even differential equations, or calculus beyond Calc III. The overall field of mathematics has various areas of specialization, and the "applied" areas that relate most directly to science and engineering are a way to go, but not the only way.</p>
<p>Not everyone who is skilled at solving computational math problems in an engineering context would find themselves equally skilled at doing proof-based mathematics, IMO.</p>
<p>IMO, the theory I learn in a math dept class really helps me understand the techniques and apply them more flexibly. I took integral multi-variable calculus twice, one in the math dept and the other in some engineering dept. My first time in the latter boiled down somewhat to memorizing formulas; however, my second pass in the former showed me that all the multi-variable theorems (Stokes, Div, etc) were simply extensions of the fundamental theorem of calculus. The material now fits together much more coherently.</p>
<p>I'll try analysis and complex number theory next year. Maybe they won't directly help me solve problems, but I hope they'll help me grasp PDE's and signal processing better, for example.</p>
<p>Then again, I'm just a freshman so I don't know what the real world is like haha. I just think that for grad school and RD jobs more physics and math would help.</p>
<p>Groups and rings were in my algebra class. I never saw the connection of group theory to the real world until I took quantum field theory and then it all made sense. This is stuff an engineer doesn't need or use.</p>
<p>i think it's extremely important to take math classes like algebra, topology, set theory etc even as an engineer. mathematics allows you to abstract problems and create new machinery with which to solve them. in order to really create this new machinery, you need to be adept at proofs. it's quite possible there may be a very simple solution to something if you use, say, fiber bundles or something. or it may lead to new insight.</p>
<p>I think more engineering majors should take these types of courses, they really come in handy. i've solved engineering problems with stuff from these courses, which I probably couldn't have solved as well otherwise</p>
<p>I took Matrix Theory after Differential Equations. I wish I'd had more statistics as I have used a lot of that in industry. I could have used more Advanced Calculus involving PDE's. My dad was a math professor and of course he always advocated for taking more math than required simply because math is a universal language and you never know how you will apply it or when it might come in handy.</p>
<p>
[quote]
I think more engineering majors should take these types of courses, they really come in handy. i've solved engineering problems with stuff from these courses, which I probably couldn't have solved as well otherwise
[/quote]
For an average engineering student like me,rigorous proof based math courses are simply too hard and time consuming.There are always tons of required courses for an engineering major already. But I've heard that complex analysis and intro to PDE are required in some engineering schools and I think that would be fine.</p>
<p>"What is your job, DocT?" I work on research projects in the semiconductor equipment area sometimes in a project management capacity and other times in an analytical role.</p>