<p>Hello I was just accepted to the MIT class of 2017 on EA! I am ecstatic at the opportunity. My only fear is that I am slightly disadvantaged by my school's opportunities in engineering and I am afraid that I will be behind entering the class, especially compared to students who had the opportunity to compete in first, Mu Alpha Theta events, and so on. This is not to say that I am scientifically challenged. I have competed and ranked at ISEF, but in chemistry, something that I feel is much more easily self taught (resources are not as limiting). I have dabbled with Arduino, and speak a few programming languages but in the long run I want to Major in Electrical Engineering. My knowledge of circuitry is extremely limited (how to manipulate voltage, amperage, how to wire and work with more complex components, etc). Is there a place, or a summer program (for the senior summer of coarse) where I can become more experienced so I can hit the ground running at MIT? Thank you so much for your help.</p>
<p><a href=“https://www.edx.org/courses/MITx/6.002x/2013_Spring/about[/url]”>https://www.edx.org/courses/MITx/6.002x/2013_Spring/about</a></p>
<p>That’s for the spring, not summer. Still free, though.</p>
<p>Congrats. </p>
<p>A few things you can do that I think would help</p>
<p>1) Buy Strang’s Linear Algebra book and work through it. There are also his OCW lectures. For some reason that escaped me 30 years ago and still escapes me today, Linear Algebra is not a required part of the MIT EE curriculum. It was and still is the most useful course I ever took. I guess they figure that you’ll see so much of it and absorb it anyway. Had I learned it earlier than my senior year when I took it, it would have made much of the earlier course work much easier and manageable. </p>
<p>2) I assume you learned calculus really well. Make sure that you really understand Taylor series. It’s so important yet when you are learning it, it seems so abstract. Basically, one way to deal with anything non-linear is to compute a linear approximation about some operating point. The size of the quadratic term often tells you how good your approximation is, or a range of values for which the approximation is good. This is especially true in dealing with electronics like transistors and amplifiers, but is also useful for using circuit elements to model what really goes on when you connect physical components together that are really approximations to the ideal circuit elements that you studied. It’s also used in control and many other areas. Basically, make sure you know how to compute a linear approximation of a function about a point, and know how to determine the remaining error in the approximation. If I recall, 18.01 has some notes that discuss this in greater detail than most textbooks. I believe that 18.02 (multivariable) also has similar notes treating Taylor series in multiple dimensions. This is also much easier to understand and retain if you understand linear algebra because the idea of a tangent plane (the multidimensional extetion of a tangent line), and projections makes more sense. </p>
<p>3) Make sure you are comfortable manipulating complex numbers and trig identities. There is stuff that you learned in precalculus that at the time seemed useless and bizarre, like exp(iw) = cos(w) + i sin(w). Complex numbers are among your best friend and if you know them like you know 2+2=4, then you will be ahead of the game. </p>
<p>4) Another book they made us read, and I don’t know if they still do is Div, Grad, Curl and All That. It reads like a novel. Very useful. </p>
<p>That’s what I would look at. As you can see, it’s all related to math, but as you’ll see, math is really your toolbox. Once you have that down, the rest isn’t too difficult.</p>