<p>I'm having summer off and I haven't made any plans yet except for working part-time. I'm looking for something valuable that I can self-study, preferably math/engineering/cs. I like studying by myself more than going to lecture, it's more effective for me.</p>
<p>Some background:
Right now I'm at a Community College but I finished most of the standard math (Calc, DiffEq, Linear Algebra, taking discrete math next semester). I'm a Computer Engineering major. I'm trying to transfer to Berkeley (EECS) next year.</p>
<p>What was the most valuable math class you took? Is there a something that you wish you would've taken earlier which has made other things easier for you?</p>
<p>I think linear algebra was the math class that really mattered to me in engineering. You may want to take whatever your school calls "numerical methods" as well, but it might not be offered through the math department so I don't consider it a math course.</p>
<p>Linear algebra for me. (chemE). Calculus/DiffEq is second. But normally, "real" engineering problems can't be solved analytically and cleanly with just calculus solutions. So numeric techniques are quite often used which is founded in linear algebra to some extent.</p>
<p>And any actual integral or derivative you would need to do, it will be most likely be pretty complex and in interest of time you would need math software tools like Matlab or Mathematica for solutions.</p>
<p>The basic math courses, or in any department for that matter, end up being most important along the road. Make sure to really understand the fundamentals</p>
<p>I'd say make sure you that you have a mastery of Calculus and Diffeqs. Calculus is obviously used heavily in engineering and I find that understanding the fundamental proofs/theories make other classes such as Fluids or Heat Transfer quite intuitive. Another reason is that many engineers forget the derivatives/integral formulas and just rely on the almighty TI-89 or charts--I'm not saying that this is wrong but it's nice to rely on yourself rather than reference materials. DiffEQs will dominate your coursework as well and make the basis of control theory--KNOW your Laplace transformations.</p>
<p>Finally, understanding Probability/Statistics isn't pivotal but is really helpful in higher level classes.</p>
<p>Of course in the real world, much of you education isn't taken advantage of. My point is that a sound understanding of mathematics will really help with your upper division courses. </p>
<p>For example, I skipped over ODEs and nearly died during a Control class, since I wasn't really used to Laplace transformations. Also in thermo, its nice to know how to manipulate any of the state equations to a new equation based on a constraint (constant volume or etc). I remember at times when the proff was like "Now simply take a surface integral of this equation an you get..." and I was like what?</p>
<p>Numerical Analysis and Partial Differential Equations. I don't know how many times I've dealt with PDEs in engineering problems and always using Separation of Variable,s Eigenfunction Expansion, Bessel Functions, etc...</p>
<p>Another thing to keep in mind is that a vast majority of the math you learn in the engineering degree will rarely be used in the real world. There are typically commercial grade software or charts that you use to circumvent conventional calculations.</p>
<p>However, I found an increasing trend of professors to simply gloss over the mathematics during equation deriving for the sake of brevity and divert the student to a textbook to see the proof. In lower level classes this might be okay but in upper divison classes where the professors "dummy" down subjects such as bessel functions, I find it harder to simply accept the formula and plug and chug.</p>
<p>Graduate school on the other hand, is VERY math intensive.</p>
<p>It isn't really math, but there is one class that I was really suprised to be using at the internship I've been working for 3+ weeks now. Engineering Statistics. It seemed so stupid and pointless the whole time I was in there, but I'm doing some work with the process improvement group here and being able to analyze the data in a really meaningful way has been insanely helpful. My professor may as well have not existed he was so terrible so I suppose you could try and learn it on your own.</p>