I finally finished the edX version of MIT’s 6.002 Circuits and Electronics course. It’s a second year course there designed as a first introduction to digital and analogue circuits.

Course format

The course consists of short video lectures, online quizzes using some kind of software that accepts numeric, textual, or algebraic input (and works well), suggested readings, and tutorial videos. There are also online homeworks, three final exams (the full 6.002 course is split into three pieces on edX, scheduled to take 4+4+6 weeks), and weekly online labs using their browser-based circuit simulator. You have to pay them quite a lot of money if you want access to the homeworks, final exams, and labs, but I didn’t: instead I worked through the contemporary OCW problem sheets and used qucs for occasional circuit simulations. I missed the labs though. The edX version of the course is over 10 years old and the circuit simulator didn’t work for me in Chrome, but it was OK in firefox.

The lectures are given by Anant Agarwal - almost always they consist of him writing on pre-prepared slides using a graphics tablet, but there are some practical demo videos taken from actual MIT lectures. These worked fairly well, though they were hard to read sometimes. There’s a scrolling transcript next to the youtube player which is very helpful if like me you prefer watching the videos slightly speeded-up and pausing them when you need to think (you can enable something similar for some videos on the youtube website by clicking the three dots beneath the player and selecting “Open transcript”). Agrawal is a fantastic lecturer: it feels like he’s talking to you rather than reading a script, which makes the videos very engaging, he’s full of enthusiasm and confidence in how interesting the material is, and he puts in the right amount of humour so that it lightens the tone without getting annoying (obviously this is a matter of taste - I usually find jokes in lectures irritating so there can’t have been that many).

The online quizzes were good - with maybe one exception they were challenging but fair. The technology is fairly basic (unsurprising given the age) in that you only get told whether you are wrong or right, but you can click through to worked solutions.

Impressions

I loved taking 6.002, it was the best educational experience I’ve had in years and I learned a great deal from it. It took a lot of time and commitment - I worked on it nearly every day for 14 weeks - but it never felt like a drag. Splitting the content into weeks puts you under time pressure: this was extremely helpful in keeping me on track, but if you couldn’t devote as much time as I did it would have been a big problem. I didn’t mind not having solutions to the problem sets.

Here my favourite thing from 6.002: complex impedance. Circuits with resistors and sources only are relatively easy to solve because they are linear: the transfer function for a resistor is Ohm’s law, ideal sources just produce a constant voltage or current, so everything that happens in the circuit is an affine linear function.

This seems to go wrong when you introduce inductors and capacitors: the element laws are \(v_L = L \frac{di_L}{dt}\) and \(i_C = C \frac{dv_C}{dt}\) where \(v_L\) and \(v_C\) are the voltages across the devices and \(i_L\) and \(i_C\) are the currents through them. Now we have a time variable, and the solutions to the DEs that govern the circuit won’t usually be linear.

Suppose however that what you care about is the response to a sinusoidal input. Introduce \(V_C = V_c e^{j\omega t}\) whose real part is the input you want. The current through the capacitor is then (the real part of) \(I_C = Cj\omega t V_C e^{j\omega t} = j\omega C V_C\), that is, the capacitor behaves just like a \(1/(j\omega C)\) resistor. Similarly the inductor behaves like a \(j\omega L\) resistor. You’ve got linearity back!

Takeaways

  • the lecturer’s style and attitude makes a huge difference to how well the video lectures work.
  • short video lectures are much better than long ones. The live transcript (not just subtitles - a complete autoscrolling transcript with the current line highlighted) was very helpful.
  • having the online problems sequenced with the lectures was crucial.
  • it must have been an enormous amount of work to put 6.002x together, no wonder they still want money for it.
  • having material split into week-sized chunks was invaluable in getting me through the course.

One of the most striking things I got from 6.002 and from watching a few of the 6.004 and 6.0001 videos on youtube is how much MIT institutionally cares about undergraduate teaching. For example, I’ve never seen a UK university that comes within a hundred miles of them in terms of the investment in AV facilities and educational technology. (Of course they say they care about this stuff, but this is exactly like when employers say they care about their staff’s mental health - you can judge how much they mean it by what they do about material conditions. The only time I’ve ever seen a UK university with a decent facility for giving maths lectures using slides is when a member of staff threatened them with disability law to get it).