Oversimplified: General Introduction

‘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:

  • Definitions
  • 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.

 

989 total views, 1 views today

2 comments

  1. Well, if you were to recommend one signals and systems book that goes to some extent with your ideas of simplifying concepts, what would you recommend?Report

  2. Hands down B.P. Lathi’s “Signals, Systems and Controls” (ISBN 0-7002-234-9). The first class I took used Oppenheim’s book; I found it too wordy and mind-numbing, so I went to the library and found this.

    It’s a very short read for covering such a huge number of concepts. It also covers 3 classes after signals & systems:
    1. DSP (Chapter 7)
    2. Classical controls (Chapter 5)
    3. Modern controls (Chapter 6)
    Once you are rock solid on “Signals and Systems”, the rest (other than modern controls) are trivial extensions. Those are giveaway classes as the materials that truly matters could be covered in one chapter each. It’s typically offered in 3 classes in universities because they wanted to give students time to catch up what they missed in the first class (“signals and systems”) as it was like drinking from a hose (under the disorganized way they taught it).

    Lathi also started Chapter 2 with a shorthand for derivative operator for differential equations so you can manipulate them like polynomials (he call it ‘p’ there). It might look dense and dry if you haven’t had the ODE class from the math department yet. Don’t fret. Just skip it and come back to it after you’ve learned Laplace Transforms. They are exactly the same thing (replace ‘p’ with ‘s’), and you actually get more detailed insights about why and when to use Laplace Transforms by reading Chapter 2 retroactively.

    Remember to ignore the flip-and-drag materials in the book (or any book). It’s a poisonous idea passed solely as a matter of legacy. Use the convolution concepts described in my tutorial/supplement instead. Lathi’s book is not the perfect treatment (that’s why I wrote the articles), but it’s the best of what you can get given the mainstream thoughts half a century ago (still propagated now).

    Note that the “vector and matrices” sections (Appendix D) is not enough for my approach. You must master inner products to get that.

    A very short “Linear Algebra with Applications” by Steven J. Leon (I used 5th edition, ISBN: 0-13-849308-1) will get you there in less than 2 weeks. If you are tight on time, you can completely glance over all the computational stuff like RRE/Gaussian Elimination in Chapter 1 and skip Chapter 2 (Determinants) without losing continuity into the juicy ideas in Chapters 3 (vector spaces), Chapter 4 (linear transformations) and Chapter 5 (orthorgonality/inner products). You can stop right after “inner product spaces” and norms (Section 5-3, page 222).

    The only enlightenment you need from Chapter 1 is on page 42 (theorem 1.3.1): every restriction (imposed properties that makes math reasonably painless) in matrix multiplication applies to signals and systems except that we ALSO get away with commutativity that’s not true for matrix multiplication. They are godsend and you’ll want to remember and exploit the properties often. Realizing matrices and systems are actually the same thing is graduate-level material.

    Keep on reading articles #2 (complex numbers) and #3 (linear algebra) in my ‘oversimplified’ series. These articles will point you to the right books and fill you in for the concepts missed by those books.Report

Leave a Reply

Your email address will not be published. Required fields are marked *