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.

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