Rosetta Stone of Electrical Engineering
I've become a bit of a masochist when it comes to math. I didn't used to be - in high school and as an undergrad I dealt with math because I needed to for what I wanted to do (engineering). I was always fairly good at it, or at least good enough to get to where I wanted, but I didn't see the intrinsic value in it. I think partly that's due to the way math is taught (not that I know a better way to teach high school math) - it's difficult to see the value in the math itself when all you're doing is exercises to show you understand what the teacher was lecturing about. After all math is a tool - if you don't have the hard problems in front of you that can't be solved (or at least are prohibitively difficult) without the higher level math tools, how can you imagine they'd be useful?
I think the big shift in perception for me started when I first encountered a course with math I had trouble with - EE2312: Discrete Time Signal and System Analysis. I was rather shocked to discover I had trouble grasping the math - the previous course (EE2311 - Continuous Time Signal and System Analysis) was no trouble for me, but for some reason when switching over from Laplace and Fourier transforms to Z and Discrete Fourier transforms I hit a bit of a wall. Maybe I just didn't pay enough attention, or work hard enough on the homework. Anyways, it wasn't until I covered the same math in a later course (Digital Signal Processing) that I finally got the math on a mechanical level. It took going over the material again in a grad level DSP course before I could claim I understood what was happening and why in the math. Anyways - since then I've gone out of my way to attack the hard math stuff - I ended up taking the non-linear controls course for my masters instead of the standard linear controls. It helped that I had most of the linear controls material already from undergrad - but really I just wanted the hard math course.
Anyways, since I've had some free time while I'm down here on the island, I've been trying to keep my mind (somewhat) active, and mainly that means reading. One thing I stumbled upon last year, but only recently re-visited to read in-depth was a series of columns by Jack Crenshaw on Embedded.com covering a rather interesting equation he refers to as the Rosetta Stone equation. It's an equation for going back and forth between discrete time and continuous time. Anyways, the columns are fairly math intensive, and while he does a good job of talking you through it, you have to actually read it rather than just skimming over because the equations look scary. If you've done lots of controls/digital signal processing math before, this isn't much new material, but for me it was a great way to take a new look at some of the fundamental maths that make controls/DSP work.
Update: I forgot about the Two different worlds article in there.
I think the big shift in perception for me started when I first encountered a course with math I had trouble with - EE2312: Discrete Time Signal and System Analysis. I was rather shocked to discover I had trouble grasping the math - the previous course (EE2311 - Continuous Time Signal and System Analysis) was no trouble for me, but for some reason when switching over from Laplace and Fourier transforms to Z and Discrete Fourier transforms I hit a bit of a wall. Maybe I just didn't pay enough attention, or work hard enough on the homework. Anyways, it wasn't until I covered the same math in a later course (Digital Signal Processing) that I finally got the math on a mechanical level. It took going over the material again in a grad level DSP course before I could claim I understood what was happening and why in the math. Anyways - since then I've gone out of my way to attack the hard math stuff - I ended up taking the non-linear controls course for my masters instead of the standard linear controls. It helped that I had most of the linear controls material already from undergrad - but really I just wanted the hard math course.
Anyways, since I've had some free time while I'm down here on the island, I've been trying to keep my mind (somewhat) active, and mainly that means reading. One thing I stumbled upon last year, but only recently re-visited to read in-depth was a series of columns by Jack Crenshaw on Embedded.com covering a rather interesting equation he refers to as the Rosetta Stone equation. It's an equation for going back and forth between discrete time and continuous time. Anyways, the columns are fairly math intensive, and while he does a good job of talking you through it, you have to actually read it rather than just skimming over because the equations look scary. If you've done lots of controls/digital signal processing math before, this isn't much new material, but for me it was a great way to take a new look at some of the fundamental maths that make controls/DSP work.
- Rosetta Stone explained
- Decoding the Rosetta Stone
- More on the Rosetta Stone
- Two Different Worlds
- Taking the last lap around the Rosetta Stone
Update: I forgot about the Two different worlds article in there.