‘Standard*’ university classes (like linear algebra, electromagnetism, computer architecture) start by motivating you with applications and grind it down to the mechanics on solving textbook problems. Even if you aced the class, chances are you’ve forgotten what the course was about 5 years down the line if you don’t have a chance to use it.
Teachers have trouble helping ideas stick with students for years to come because they don’t
- make sure each student’s prerequisites are tightly knit (e.g. properties of complex numbers)
- narrow the class down to a few simple major intuitions (e.g. express any reasonable signal in terms of sinusoids), ‘things explainer‘ style.
- list frequently used example objects (e.g. sinusoidal inputs) and tricks (e.g. coordinate transformation)
- use jargon (e.g. sifting) effectively to compress a complex idea into one word to remember.
Hard work ALONE will get you:
- Routine solution approaches
Smarts ALONE will get you
- Tricks such as exploiting symmetry, nice round numbers.
Which is good enough for acing the class and NOT remembering anything afterwards. Some professors choose to teach you the basics, solve a few straightforward (potentially long-winded) problems, and leave you to struggle with the essence and intuition presented in the exams and learn it the painful way.
What goes on in those ‘smart but tough’ exams, characterized by “either you see it or you don’t” kind of questions (i.e. it’s a easy, one-liner kind of solutions but many hard-working students won’t get it), tests if you
- downplayed the seemingly trivial basics they taught at the beginning (e.g. superposition)
- are comfortable with the commonly used ‘objects’ (e.g. impulse inputs, sinusoids)
- know what the course or the major themes presented are truly about (e.g. represent arbitrary signals by sinusoids)
In ‘Ideas Oversimplified‘ Series, I aim to capture only the essence and carefully order the prerequisite knowledge so you don’t learn something the hard way. Nonetheless, it’s not supposed to be self-contained (unless I think it’s a topic most students would have glossed over when they should have paid attention to). If I used a term that you don’t know what it means right away, go back to your textbook.
This series covers only the ‘secrets of the trade’ which your professor conveniently (or intentionally) didn’t teach in class (so he can quiz you on it). It’s meant to gloss over knowledge that you can quickly synthesize in your head after you firmly grasped the ideas. If I am successful in organizing the materials the ‘Ideas Oversimplified‘ approach, you’d be able to attack many problems you’ve never seen before instead of pattern matching solution approaches.
As for jargon, I will selectively underline important keywords that serves as anchors to help you retain the ideas. Don’t glance over anything. If it’s not super-important, I won’t put it in, unless it’s a footnote.
I wrote this series so I can swap what I’ve learned out of my L1 and L2 cache to make space for new topics, and quickly become the ‘expert’ I used to be in a short time by reviewing it. A good organization of the materials is just as important for me to quickly relearn the stuff as well as beginners and professionals alike, so I wrote it as if it was meant for a broad audience.
It’s done in a blog page format for now and constantly updated as I find better ways to organize the information. I’ll turn it into a short PDF book once I’ve written enough materials for it.
* Non-standard classes usually don’t have a standard textbook (like Boyce for differential equations) associated with it and the materials vary a lot depending on the professors. Survey courses and advanced topics courses doesn’t have a predictable theme, commonly used tools and focus, so you are on your own for those.