We are Vectors

Teaching this course for the first time gave me a fresh perspective on the world of numbers, and how it affects us in real life. Although I’ve been using vectors and matrices, and differential equations in my research, this course has revealed to me several other ways that these mathematical constructs may be used.

For me, the lesson which I most enjoyed teaching would be linear transformations. It is simply beautiful to see a transformation matrix illustrated on a graph, and watch the vector subspace literally transform into another form. Surely, the next time I’ll use image editors, I’ll be thinking about what kind of transformation matrices are behind them.

As Margot Gerritsen once said, Equations define relationships. And relationships and connections are all around us. And for me, that’s what this course is all about. Matrices allow us to encode realities in our world. Images, sounds, signals: all of these can be represented by a matrix. Differential equations are relationships of change; change of force with respect to mass, or change of population with respect to time. So through this course, we learn to see the connections all around us. And by seeing these connections, we can come up with better solutions for our problems.

Finally, I’d like to leave this statement to my students: you are a vector.

As a vector, you have a magnitude, an impact to the world. You are an influencer. Whether it’s positive or negative will be all up to you. And so I hope you’ll take extra care on your actions and words.

Aside from magnitude, you also have a direction. You are going somewhere. And as long as you keep on going, you’ll reach your destination soon enough.

Sometimes you might feel like a zero vector, stuck at the origin, seemingly pointing nowhere. But remember, even the zero vector has its importance: with it, we can find the null space; and with the null space, we can find the solution to homogeneous linear systems. In short, even if you think you are a zero vector, you can still be part of the solution.

And as long as you are trying your best to improve yourselves, then you are making good use of your magnitude, and surely, you’re heading to the right direction.

I’d like to thank everyone for a wonderful semester. With that, our CS130 course ends here.

May our relationships to the each other and to the world be of high magnitude and far-reaching direction. Thank you.

Brain Signal Processing

I am currently researching on brain-computer interfaces where I recorded students brain signals and classified them into different levels of cognitive load.

In this study, I used Fourier transform (FFT) to convert the signals from time domain and frequency domain. Why is this important? You see, certain brain frequencies are correlated with activities. For example, alpha waves (8-13 Hz) are associated with alertness, while beta waves (14-30 Hz) are associated with high focus.

By using Fourier transform, we are able to access a different dimension of information that is more significant for our study.

References:

Photography Composition

In photography, symmetry is one good technique to achieve a balanced composition. A symmetrical photo exudes order, stability and perfection.

Although not everything beautiful is symmetrical, and not everything symmetrical is beautiful, there are instances when an almost-perfectly symmetrical photo surpasses a non-symmetrical one. The creators of Snap Great Photos blog provided some examples of “snapping great photos” by capturing symmetry in photos.

But as I’ve said, not all things beautiful have to be symmetric. Roberto Valenzuela shows how “breaking the symmetry” changes the story of a photo.

The symmetrical photo on the left leaves a serene, well-composed impression, but it may also be taken as static and boring. On the other hand, the photo on the right creates a tension as the subject breaks the symmetry, which leaves a more photojournalistic feel.

References:

Thought Vectors

The way I understood it, thought vectors map a word to numerous sentences that contain it. In effect, the meaning of a word can be constructed. And so it can be expected that as more sentences are linked to a word, the closer we get from the true meaning of that word [Krumins].

Thought vectors can be applied to image recognition, specifically for describing the contents of an image [Goh]:

References:
Thought vectors could revolutionize artificial intelligence, A. Krumins, https://www.extremetech.com/extreme/206521-thought-vectors-could-revolutionize-artificial-intelligence
Decoding the thought vector, G. Goh, http://gabgoh.github.io/ThoughtVectors/

Hi, I’m Paul!

Hi I’m Paul Rossener Regonia, the instructor for this course.

When I picked this course as my only course to teach this sem, I thought that this will be challenging. It’s my first time to teach 130, and I have little time to prepare for it (partly my fault).

I love math. I was part of the math club in our high school. My favorite subject back then was analytic geometry. I like shapes and graphs. And that’s why whenever I’m working on a data science project, I almost always start with visualizing the data and processes.

I only had four hours of sleep today because I stayed up all night preparing for class. So I’m a bit lightheaded. Yet excited for class!

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