## Synthesis

Which topic/s in class made an impact to you? Why?

• Matrices. A lot of topics revolved around this and it had a lot of practical applications in the field of Computer Science.

If you can summarize this course in one word or sentence, what would it be?

• Mathakit sa ulo. Kidding. If I were to summarize this course in a sentence, it would be: mathututo ka talaga, hindi lang ng Math kundi pati ng applications nya in real life. I just love how sir taught CS 130 because it made me appreciate the Mathematical concepts we learn in class. We were shown not only the concepts and practices in this class but also how it is related to solving real-world problems.

What would be your parting message to the class

• Thank you Sir Paul for making the topics relatively easier to learn and thank you for making the class fun and insightful.
• Thank you ebribadi u dabest. Kapit lang. I believe in you.
• HORAY!

• #### Lois Velasco 2:09 pm on May 12, 2017 Permalink | Reply Tags: Transform ( 55 )

Fourier Transform in Microscopy

In electron microscopy a lens can be placed behind a sample. Incident electron waves hit the sample and it creates scattering. Constructive interference and wave fronts are produced all over the sample (the lines on the picture). The lens gets parallel illumination and focuses it at a particular spot behind the lens. Other rays also hit the lens and each are focused at a particular spot behind the lens (the dot where intersection of lines can be seen). The spots on the back focal plane is the Fourier transform of the sample density (diffraction pattern). This will spread out again and it will interfere with other waves. Each ray represents a particular sine wave of a particular frequency; scattering at a different angle represents another. It will carry through and it will produce an image on the image plane. After it does Fourier transform, it will perform inverse Fourier transform (Fourier synthesis) wherein it will take each sine waves and add it up to reproduce the replica of the density sample. This copy can can be larger than the original sample.

• #### Lois Velasco 12:52 pm on February 17, 2017 Permalink | Reply Tags: Vector ( 70 )

Vectors are also used in economics. One example of this is the use of vectors in predicting the consumption demand of a system. It uses an input-output matrix to show how goods from one industry are consumed in other industries.

The rows represent the producing sector of the economy and the columns represent the consuming sector of the economy. The total internal demand for the economy is equal to the sum of the entries per row in the input-output matrix and it can be represented as:

The image below shows an example and the result of the computation.

This shows the flow of goods between industries.

Now, if we get relative size of industries with respect to currency, we construct a diagonal matrix where the each entry is the price of the goods that the corresponding industry produces then multiply it to the input-output matrix we obtained before to have the value input-output matrix. We’ll then arrive at the internal demand vector with respect to currency when we get the sum of each rows.

Source:

http://kurser.math.su.se/pluginfile.php/30620/mod_resource/content/0/matrix-ex%20leontif.pdf

• #### Paul Rossener 6:48 am on May 3, 2017 Permalink | Reply

Hi Lois, this topic was already taken by Kyle Rosales (collision detection).

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## Molecool

There are molecular structures that have symmetry. Once certain transformation in three-dimensional space is carried out (symmetry operations), the molecules will look indistinguishable from its initial orientation. These operations may be performed along a line, a plane or a point (symmetry elements).

Reflection (σ) – Symmetric in the plane

Rotation (Cn) – Symmetric along an n-fold symmetry axis

Inversion (i) – Symmetric through the inversion center

Improper Rotation (Sn) – Symmetric through an improper axis ; Rotate 360/n degrees and reflect through the plane perpendicular to the axis

Symmetry of molecules is helpful in group theory and this has some applications in chemistry. Isn’t it interesting to see that even small particles like these have symmetry?

See the link below to see the animation of certain molecules:
http://symmetry.otterbein.edu/tutorial/index.html

## Hello, it’s me

Hello! My name is Lois Alexis Velasco. You may call me Lois (Lo-wis).

What were your thoughts when you enrolled in this course?
“I need to review past math lessons; baka nakalimutan ko na.”
“Sana pumasa ako. Kailangan ko mag-aral nang mabuti. :))”
“Si Sir Paul yung prof. Yey! =)”

How comfortable are you with math?
I’m a bit comfortable with math (but I’m not that good with calculus). I find math REALLY interesting and useful. As long as the topics were explained well (and it makes sense to me), I’d probably be fine with it. :))

What’s your dominant feeling right now?
Sleepy~~

• #### Paul Rossener 4:16 pm on February 22, 2017 Permalink | Reply

Nice meeting you, Lois!

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