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  • Kenn Velasquez 10:04 am on June 8, 2017 Permalink | Reply  

    Synthesis 

    a. The topic that mostly impacted me is the topic about vectors. Since vectors can be used almost everywhere in the real life, then it can be applied to almost everything in life. From real world physics to language, vectors can be applied.

    b. If I can summarize the subject into one word, then I can say that the word is enlightening. It enlightened me to the various applications of theories to real life. And I can say that it is quite stunning as well as exciting.

    c. My parting message to this class is to never give up and have fun. CS 130 is a fun subject, so you can enjoy it as much as you want to. Just remember to not leave the learning part just because of the fun that you experience.

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  • Kenn Velasquez 10:03 am on June 8, 2017 Permalink | Reply  

    Week 4: Laplace and Fourier Transformations 

    Laplace and Fourier transform are usually used for converting signals from digital to analog and vice versa. Since we are talking about signals, it might also be able to deduce the mixed signals given by women. If you will graph the mixed signals given by women into a sinusoidal signal, and apply Laplace transform (since mixed signals are unstable) so you will be able to determine whether the signal is a yes or a no to easily deduce what she means.

     
  • Kenn Velasquez 10:02 am on June 8, 2017 Permalink | Reply  

    Week 3: Symmetry and Structural Integrity 

    Symmetry is present in many things. This was observed in nature and in the environment since the ancient times. From the pyramids in Egypt, to the shells of some mollusks, symmetry is present and ever useful.

    Symmetry can help in structural integrity in buildings. Usually, symmetric buildings are easier to balance because their center of gravity is easy to find. That is why a lot of buildings are symmetric in construction when looked at in a certain perspective. Structural integrity is not only applicable to buildings, but to cakes as well, since the baker needs to find the place where to put the cake that they will not cause each other to collapse and fall

     
  • Kenn Velasquez 10:01 am on June 8, 2017 Permalink | Reply  

    Week 2: Vectors and Thermodynamics 

    Vectors can be applied to various fields. Vectors are  useful for determining directions, image modification, data analytics and more. It can even be used in thermodynamics combined with calculus.

    Vectors can be used for predicting the movement of fires, based on the oxygen levels of the space where the fire occurred. For example, if the fire occurred in an area where the oxygen comes from a single direction. Using the calculations for the flux of vector fields, we can calculate the direction the fire will spread, using the levels of oxygen as the values for the vector fields.

     
  • Michelle Dela Rosa 3:16 pm on May 29, 2017 Permalink | Reply
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    Love your mother 

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

    Row Echelon Form and Reduced Row Echelon Form! Kasi pag sinasabi yung ~*ECHELON*~ sobrang sosyal pakinggan ang saya :^D Pero ok serious, may sense of achievement kapag nakapagtransform ng matrix to its RREF ❤ Yung effort sa pagsusulat at pagsosolve ang worth it haha!

    Plus Basis kasi medyo may bias(is) ako sa topic namin sa video tutorial ❤

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

    “Challenging and at the same time, inspiring. Every meeting was an adventure.” — J.K. Rowling

    What would be your parting message to the class?

    Stay strong! And see you around 🙂

     
  • karen alarcon 2:47 pm on May 29, 2017 Permalink | Reply
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    Synthesis 

    1. Which topic/s in class made an impact to you? Why? RREF because I had a hard time reducing the matrix noong exam 3. I always end up getting stocked up at some point because I get the wrong combinations of scalar multiples. Ughh. I need some practice.
    2. If you can summarize this course in one word or sentence, what would it be? It was fun! 🙂 .. Although di ako masyado close sa mga classmates ko, but because ung harmony na nabuild sa class makes it totally worth it. I admit, nakakapressure minsan kasi madaming magagaling na students and i feel like im left behind, pero, overall nag enjoy pa rin ako kasi this is my first math class na sobrang fun ung class.
    3. What would be your parting message to the class? Well, of course, first, I’d like to thank Sir Paul.. kasi he made this course interesting, challenging and fun.. I can feel na gusto nya lahat makapasa kasi dito sa class na to nafeel ung word na “CHANCE”. hahaha.. Di ko kasi malilimutan ung time na nag pm sakin si Sir and gave me some references that will greatly help me prepare for the course. So thank you so much Sir for that. Secondly, gusto mag thank you sa kagrupo ko during quizzes and sa final project, shoutout kila Gen, Lois and Mark. 🙂 They served as my inspiration to pursue this course kasi go lang sila ng go so ayun. hahaha.. and lastly of course I’d like to thank the whole class kasi the experience wouldn’t perfect without each everyone who made this class so enjoyable. Yun lang po. 🙂 Thank you so much guys! God Bless sating lahat! See you around. 😀

     
  • Gabby Torres 1:56 pm on May 29, 2017 Permalink | Reply
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    ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°) ( ͡° ͜ʖ ͡°) 

    • Share your thoughts on the following questions:
      • Which topic/s in class made an impact to you? Why? Vectors (?) since they’re a pretty huge deal with 130 and you’d fail if you forget anything about it. :))
      • If you can summarize this course in one word or sentence, what would it be? Fun 🙂 I enjoyed learning about it since it was taught so well in class. I know it’s hard but I guess the class made it worth it.
      • What would be your parting message to the class? YAY THANK YOU. Seniors always told me this would be a tough class and us enjoying it already says a lot about how the class was handled. 🙂 Thank you po for making me meet new friends and letting me communicate with people even though I’m terribly bad at it. Definitely a highlight for this semester. ❤
     
  • Nathan Paglinawan 1:56 pm on May 29, 2017 Permalink | Reply
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    Symmetry (Repost)

    Pwede siya sa earphones haha dapat symmetric yung earphones mo para pantay sila sa tenga mo. 🙂

    ########
    # #
    # #
    ### ###
    ### ###

     
  • Nathan Paglinawan 1:54 pm on May 29, 2017 Permalink | Reply
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    Force

    If you pull upon an object in an upward and rightward direction, then you are exerting an influence upon the object in two separate directions – an upward direction and a rightward direction. The vector sum of these two components is always equal to the force at the given angle.

    References:
    Independence of Perpendicular Components of Motion, http://www.physicsclassroom.com/Class/vectors/u3l1g.cfm

     
  • Nathan Paglinawan 1:53 pm on May 29, 2017 Permalink | Reply
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    Hello! (Repost)

    What’s your name?
    Nathan Dale S Paglinawan. Just call me Nathan.

    What were your thoughts when you enrolled in this course?
    MATH

    How comfortable are you with math?
    I’m not good in math pero naaral naman siya so okay lang.

    What’s your dominant feeling right now?
    Sleepy

     
  • JD Laborada 12:33 am on May 25, 2017 Permalink | Reply
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    Fourier Transform – Image Compression 

    Fourier transform is useful for image compression. If you save the individual pixel colors less accurately, the image will look far from the original image. But if you save the spectrum less accurately, the picture just gets slightly blurry (better).

    By doing a sophisticated analysis of the way the human brain processes image data, you can estimate which frequencies in a given image are “the most important”, and store those with high precision, while throwing away any “less important” frequencies.

     
  • Paulo Santiago 12:36 pm on May 24, 2017 Permalink | Reply
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    Bye 130 

    1. Matrix. Most of the topics in the class involved matrix and it really made me understand the topic more than I ever did. I also learned about its applications that I didn’t thought of.
    2. Happy 🙂 After a stressful day of classes all day, i’m thankful it ends with CS 130. Masayang may surprise games and interactive learning before and even in the lecture tapos very welcoming ang atmosphere sa class. Lagi rin nagtatawanan kahit lecture at isa sa pinakamagandang paraan to learn while having fun.
    3. Thank you sir Paul!! Thank you rin sa mga seatmates/groupmates ko. It was fun. SIR 131 naman!!! 🙂

     
  • Gerard Montemayor 5:04 am on May 24, 2017 Permalink | Reply
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    131 naman 

    1. Matrix/Vectors. It made me look into math in a different perspective.
    2. Puzzles
    3. Thank you sir! Next sem ulit 131 naman HAHAHA. Sorry din kasi puro late ako sa submissions HAHAHA including this one :)) Thank you din sa mga groupmates ko na bumuhat sakin sa quizzes. Mas narealize ko na tama nga na nag shift out ako sa Math :))

     
  • Camille Comia 4:23 am on May 24, 2017 Permalink | Reply
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    fin. 

    Which topic/s in class made an impact to you? Why?
    Matrices, we live in a magical world of ~*matrices*~. The Matrix never really made sense to me until I learned what matrices really represent haha

    If you can summarize this course in one word or sentence, what would it be?
    Pick-me-up. Although hindi halata yung energy ko in class, this is the one class this semester that I really looked forward to every time without fail. It wasn’t a course that I was afraid of but rather the class that I really wanted to learn something from.

    What would be your parting message to the class?
    Thank you sa mga naging ka-group ko and ofc, kay Sir Paul. Is it safe to say we passed? *knocks on wood* haha. See you around, hopefully 🙂

     

     
  • Daine Daling 6:30 pm on May 23, 2017 Permalink | Reply
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    Symmetry in Physics 

    Symmetry is quite beautiful in its applications. From photographs to paintings to music, a sense of symmetry gives a sense of balance and therefore is comfortable to look at. In the same way, symmetry in physics also yields beautiful results. According to Feynman, symmetry is when “if there is something we can do to it so that after we have done it, it looks the same as it did before”. Indeed, symmetry has multiple deep applications in theoretical physics. In Electrodynamics, for example, symmetry helps to make calculations easier, removing the need for complex integrals. In quantum mechanics, the applications of symmetry are massive.

    And of course, who could forget one of the more recent and memorable applications of symmetry:

     
  • Daine Daling 6:08 pm on May 23, 2017 Permalink | Reply
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    Synthesis 

    I think the topic that had the most impact for me would be Eigenvectors and Eigenvalues. When I first encountered these last year in a Math 114 class, I didn’t really see too much in it and shrugged it off as a minor tool in mathematics (probably because I barely attended the lectures in that class, lol). However, CS 130 has really brought it to light. Now I appreciate them more than ever, seeing many of their applications, especially those in matrix/image transformations.

    This may sound cliche but I really think the course, in my opinion, is best described as fun. Yes, fun. Sir Paul’s pre-class group activities and his humor definitely made the class feel lighter, despite the mental workload of studying mathematical methods. I don’t think any other class I’ve been in has better ice-breakers and an overall fun vibe than this one.

    I was never good at parting messages because I usually revolve around one point that I keep reiterating and it ends up being annoying in the end lol. Besides, I’m not really too close with much of the class so I will take this opportunity to say goodbye and best of luck to all your future endeavors. Also, support local independent (the actual independent, DIY artists, not those that pose as “indie” merely to market themselves) music!

     
  • Daine Daling 5:57 pm on May 23, 2017 Permalink | Reply
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    Fourier in Quantum Mechanics 

    Fourier transforms are used extensively in areas such as signal processing and electronics. However, Fourier analysis is also useful in quantum mechanics and quantum field theory. Because it is used in solving partial differential equations, it is useful in solving Schrodinger’s equation, as detailed here . Of course, the many applications of Schrodinger’s equations and quantum mechanics follow.

     
  • Daine Daling 5:25 pm on May 23, 2017 Permalink | Reply
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    An (un)timely Introduction 

    I know this is quite late. Okay, who am I kidding, this is way overdue, but you know what they say (old as it may seem), better late than never (is it really?)

    Hi, I’m Daine Rhythm Daling

    When I first checked the course syllabus on the first day, I immediately recounted my experiences in the past courses I had back in EEE. Math 114 was our linear algebra course, and I quite enjoyed it except for the hellhole that is matrices. Nonetheless, the linear algebra part got me excited. For the latter parts, I was pretty excited to meet my good old friends Pierre-Simon Laplace and Joseph Fourier. Exactly a year ago they nearly beat me to death in my Signal Processing class, notoriously known as EEE 35. While I did fail that class, I was however excited to take another shot.

    I would actually consider myself pretty comfortable with math. Shifting into Computer Science, I was deeply motivated by the theoretical aspect more than the part where people make cool websites and video games. I knew math and logic would be the heart of it all, two fields I would not consider myself a stranger to.

    At the time, my dominant feeling was that of excitement. I could not wait to brush up on my linear algebra and get another chance to face Laplace transformations and the Fourier series.

     
  • Daine Daling 5:23 pm on May 23, 2017 Permalink | Reply
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    I know this is quite late. Okay, who am I kidding, this is way overdue, but you know what they say, old as it may be, better late than never (is it really?)

    Hi, I’m Daine Rhythm Daling

    When I first checked the course syllabus on the first day, I immediately recounted my experiences in the past courses I had back in EEE. Math 114 was our linear algebra course, and I quite enjoyed it except for the hellhole that is matrices. Nonetheless, the linear algebra part got me excited. For the latter parts, I was pretty excited to meet my good old friends Pierre-Simon Laplace and Joseph Fourier. Exactly a year ago they nearly beat me to death in my Signal Processing class, notoriously known as EEE 35. While I did fail that class, I was however excited to take another shot.

    I would actually consider myself pretty comfortable with math. Shifting into Computer Science, I was deeply motivated by the theoretical aspect more than the part where people make cool websites and video games. I knew math and logic would be the heart of it all, two fields I would not consider myself a stranger to.

    At the time, my dominant feeling was that of excitement. I could not wait to brush up on my linear algebra and get another chance to face Laplace transformations and the Fourier series.

     
  • abcorwynd 4:52 pm on May 23, 2017 Permalink | Reply
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    Week 5: Synthesis 

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

    • The topic that stuck to me most is the the topic of transformations especially the part where sir Paul showed us how you can actually transform a specific image to look more readable or pleasant to the eye. It stuck to me since I didn’t know that things like this were actually done via the manipulation of vectors. It came as a surprise to me and something I didn’t really expect.

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

    • If I could summarize this course in one sentence I’d say … “This would’ve been difficult to understand if it wasn’t Sir Paul teaching.”

    What would be your parting message to the class?

    • Thanks for the great semester to Sir Paul, thanks for the fun group works during class and the efforts you guys put. So grateful. ^_^
     
  • abcorwynd 4:46 pm on May 23, 2017 Permalink | Reply
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    Week 4: Laplace and Fourier Transform 

    In real life, we can apply Fourier Transform in for creating terrain data in 3D manipulation that can be used for graphics in different kinds of software like gaming or mapping. Fourier Transform works by smoothening out rigid terrain to make it look more like real life terrain. As seen in these examples:

     
  • abcorwynd 4:45 pm on May 23, 2017 Permalink | Reply  

     
  • Joshua Buslig 4:19 pm on May 23, 2017 Permalink | Reply
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    Tapos na 

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

    -Sa totoo lang matrices, parang yun yung laging gagamitin eh. 😀

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

    -Ayos!!! (kahit ayaw ko ng math)

    What would be your parting message to the class?

    -Thank you. Enjoy tong klase. Laban lang 😀 HAHAHAHA

     
  • Edrich Chua 3:48 pm on May 23, 2017 Permalink | Reply
    Tags: synthesus   

    Cute padin ako 

    Pinaka may impact…. transformation. wala lang ang cool kasi yung mga nangyayari ang trippy.

    summary: ang saya. how 2 make class fun? ask sir paul

    parting message: bye fam auq na sana pumasa ako pls team B parin dabest your welcome team A for letting us share our points. thank you for adding another deep word to my crappy deep words: eigenvectors and eigenvalues.

     
    • Justo Balderas 5:13 pm on May 23, 2017 Permalink | Reply

      Onga palaaaaaaaaaaa! ❤ ❤ ❤ sobrang #blessedt nga pala that day dahil sa Team B! Napaka competitive nung una (ang yayabang, Hmmmp!), pero sa bandang huli pinashare nyo pa kami ng bonus points (as in akala namin magta-tie tayo sa bonus points, yun pala paghahatian 🤣 ). Woooooo. Thanks Edrich! Thanks team B! :))

      Like

  • Edrich Chua 3:43 pm on May 23, 2017 Permalink | Reply
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    HOW DO I DELETE THIS I’M PANICKING

     
  • Lois Velasco 3:42 pm on May 23, 2017 Permalink | Reply
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    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!
     
  • Mark Asiddao 2:39 pm on May 23, 2017 Permalink | Reply
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    CS 650: At last we part ways 

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

    • The first topic for me was the most impactful, because I never really knew that complex numbers can visually be represented in a 2-dimensional (or possibly 3-dimensional) space. Also, it was the first time I’ve encountered the lesson.

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

    • Application-learning!

    What would be your parting message to the class?
    Hello there 🙂
    First of all, I probably am the most excited person in the whole class that CS 130 has finally come to an end (believe me, it took me 2.5 years) but at the same time, I fear as well for the upcoming CS 131 :))
    Sir Paul made the class fun to learn (while adjusting the pace of the course to best fit how fast we all learn and comprehend topics), something that I really don’t see much in many CS courses. Some lower-batch students fail to see real-world applications of Computer Science concepts, making them demotivated in pursuing what’s left the course has to offer. I believe Sir Paul best fits what a good teacher is, not just an instructor following university standards. I really hope to see Sir Paul teaching after earning his masters degree.
    As for everyone in the class, I’m sure we’re all thankful for this CS 130 🙂

    Thanks for a wonderful sem!

     
  • Jairus Garcia 2:33 pm on May 23, 2017 Permalink | Reply
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    Fourier Transform in Making Noise-less Appliances 

    Most electric appliances such as washing machines, refigerators, and dishwashers make noise and vibrations when on use. Manufacturers are trying to eliminate this problem. However, it is necessary to know the natural frequencies of vibrated system in order to make measures to reduce the vibrations. One way to accomplish this is recording sound to a digital file and transforming the data by the Fast Fourier Transformation.

    This is expounded in this paper: http://www.sciencedirect.com/science/article/pii/S1877705812045687

     
  • Eunice Angel Cruz 2:28 pm on May 23, 2017 Permalink | Reply
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    "Uy, huling 'bye, sir' ko na pala ito…" 

    I said that after the last meeting but Sir replied with “hala, magkikita pa ulit tayo di pa ito ang last day.”

    Weeks after, the “this is not yet the last day” day turned out to be the last for real.
    Pizza is gone for good. HAHAHAHAHA JUST KIDDING (mas nasad pa over pizza joke lang sir hehe)

    RREF had the most impact para sa akin. I think I won’t be able to forget it for at least the next academic year hahahahaha I spent a lot of time, a lot of paper, and a lot of patience while practicing it. *reminisces* aaah good old times…

    All in all, I think CS 130 was the “subject na pwede ka mag feeling confident pagpasok sa class dahil alam mong hindi ka papasok sa pressure cooker kundi sa isang happy place” hahahaha

    To Sir,
    Thank you very much po! You give me confidence even if I am just starting to learn or to get a feel of a concept in ways like group works, ice breakers, other fun activities, Running Man!!! Hahaha

    On a more serious note, CS 130 was hard but I appreciate your effort po of helping us understand topics kahit hindi nagdadive ng malalim on each one. I like how you are hands on, thank you for that, Sir – kayo lang yung hands on na hindi nakakapressure but nakaka encourage pa nga na prof ko so far. Sir nood ka lang ng Running Man para happy lagi char hahahaha pantanggal streeess ganern.

    To my classmates,
    Thank you for attending classes with me, for talking to me and answering my questions kahit hindi naman tayo formally friends, for having fun on activities with me, for understanding me and my side comments na napapalakas minsan (baka naingayan na kayo hahahahuhu)… let’s be friends! 😀

    Thankful ako for this course. I hope, and I know, na hindi lang ako ang nag enjoy sa class! Woohoo!!!

    Eunice Angel D. Cruz
    CS 130 1617B 🙂

    P.S. random pictures taken sa class hahaha yas pabida jk hahaha sir gusto ko lang po makita niyo self niyo kapag nagtuturo tulad ng pagcapture niyo ng exam moments namin, char

    P.P.S. Sir, nawa po ay checkan ninyo ang aking mga journal entry huhu thank you po :’D

    This slideshow requires JavaScript.

     

    ((I told u I’m so confident… ang hirap makibaka sa mabagal na internet halp))

     
  • Paul Sason 2:02 pm on May 23, 2017 Permalink | Reply
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    Comrades 

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

    • I’m gonna have to join the M A T R I X train here. Almost everything in the semester revolved around matrices and its applications, and I feel like it’s going to stick to me for quite some time; or at the very least, until after CS 131.
    • I guess I can mention Complex Field here too, in regards to the final project. ^^

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

    • Refreshing
    • I can’t really put it any other way. The fact that a course that’s essentially filled with math was presented in the way this course was handled was really refreshing to me.

    What would be your parting message to the class?

    • I really enjoyed this course in a way I didn’t really think of. Sir Paul’s classes have always stood out to me as different from the norm, in a good way. I like the lesson organization, the motivational activities, and the fact that I don’t feel very overwhelmed by the lessons at all. I found myself looking forward to the lessons, and even though I believe some topics sort of lacked a little more practical application, I was overall satisfied with the way it was executed. Thanks Sir!
    • The main takeaway for me was the video-making project. Who would really have thought we would be making videos in a math class? I’m quite art-inclined myself, so it was something that I enjoyed taking part in. Thanks to my groupmates!
    • So yeah. Congratulations to everyone for living through it, and let’s see each other next time. Don’t let your dreams be dreams. Byebye~
     
  • Jairus Garcia 1:59 pm on May 23, 2017 Permalink | Reply
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    Week 5: Synthesis 

    Which topic/s in class made an impact to you? Why?
    Matrix! Because I have encountered this on a lot of my previous subjects and to be honest, I had no freaking idea what they where talking about; but not anymore! Thanks to this class. 🙂

    If you can summarize this course in one word or sentence, what would it be?
    F U N
    because, as the great Spongebob has once sung,
    “F is for Friends who do stuff together. (shoutout to my Intro Bois, u da best groupmates I ever had in mah layf)
    U is for you and me. Hi @sirprrr (best prof ever!!!)
    N is for anywhere and anytime at all. (because there is CS130 everywhere)”

    What would be your parting message to the class?
    Enjoy your break (if thy exist) and good luck in life!

     
  • Patriz Cajaljal 1:49 pm on May 23, 2017 Permalink | Reply
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    Week 5: Synthesis 

    Which topic/s in class made an impact to you? Why?
    Determinants! It is our topic sa project, and I think I will always remember how to compute for the determinant of a matrix. 🙂

    If you can summarize this course in one word or sentence, what would it be?
    The best class of my semester! 🙂

    What would be your parting message to the class?
    Thanks to everyone for making the class very enjoyable and informative, esp. to my groupmates sa proj and quizzes, and also kay Sir Paul! 🙂

     
  • Gerald Roy Campanano 1:47 pm on May 23, 2017 Permalink | Reply
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    Which topic/s in class made an impact to you? Why?
    Vectors, because I am planning to create games this coming midyear, and reviewing/re-learning vectors is very essential to the type of games that I’m planning to create.

    If you can summarize this course in one word or sentence, what would it be?
    This CS 130 is fun and awesome.

    What would be your parting message to the class?
    I will never forget the fun times we had in class, I will cherish my memories with my classmates, sir, and especially my groupmates forever.

     
  • Gerald Roy Campanano 1:36 pm on May 23, 2017 Permalink | Reply
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    Chemical Kinetics and Laplace Transform

    Chemical kinetics is the quantitative study of chemical systems that are
    changing with time. (Thermodynamics, another of the major branches of
    physical chemistry, applies to systems at equilibrium—those that do not
    change with time.)[1]

    Laplace Transforms can be used to handle moderately complicated chemical systems. But these techniques work only for linear (1st-order) systems. This can be used in handling mixed order reaction equations, such as “mixed second order” reactions.

    References:
    [1] http://faculty.gvsu.edu/mcbaneg/chm358wi02.pdf
    [2] https://math.stackexchange.com/questions/1248834/chemical-kinetics-using-laplace-transformation/1248849
    [3] http://www.biokin.com/tools/pdf/Koro11-Kinetics-Maple-Chap2.pdf

     
  • Justo Balderas 1:27 pm on May 23, 2017 Permalink | Reply
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    Dibs 

    Dibs pa? Ahaha

    Week 5: Synthesis


    • 1] Vectors dahil sa “you are a vector” thing sa post na “we are vectors”.
      2] Matrices dahil sa quote ni Margot Gerritsen, at dahil narin sa movie na The Matrix.
      3] Symmetry dahil shinare ko yung fractal music video sa kakilala kong grad ng music. Nalaman ko sa kanya na ganun daw yung music noong kapanahunan pa nila Bach, nakasulat lang. Wala pang recording, kaya para mapakinggan, kailangang tugtugin. Kaya yung mga demographic daw ni Bach, na-aappreciate yung patterns na ginawa niya kasi binabasa daw talaga nila.
      4] Change of basis dahil dun sa skewed/distorted picture thing ala photoshop.
    • Relationship.
      :)) Mema/meta nalang eh noh.
    • Yes naman, sipag magbasa oh. Salamat sa mga contributions nyo sa applications nung wk. 2, 3, & 4. Marami akong natutunan at narealize ko, dapat pala inaraw araw ko yung pagche-check ng post, hindi yung isahan lang at ‘at the end of the sem’ pa, kasi nakakamotivate nga talaga to learn kapag nakikita mo yung mga application.
     
  • Kyle Rosales 1:12 pm on May 23, 2017 Permalink | Reply
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    WALANG FOREVER (Week 5: Synthesis) 

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

    Siguro yung Fourier Transform kasi natutunan kong pwede parin kayong magkaintindihan kahit na puro mixed signals natatanggap mo, hahaha jk.

    It’s not really on the topic but I guess it’s on the teaching style as a whole. In the first post I mentioned that I like math but I don’t like it in a classroom setting. Well in this class it didn’t feel like a typical classroom setting. I liked how there was an “appreciation” for every lesson and we don’t just learn them because we have to but because the topics have an importance in real life.

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

    Appreciating math in computer  science.

    What would be your parting message to the class?

    I think everyone had fun, it was a great ride. Good luck to everyone and I hope we have a great future ahead of us. I’ll leave with a favorite quote from an anime I’ve started watching recently.

    Go beyond! PLUS ULTRA!

    (All Might, Boku No Hero Academia)

     
  • elkingmorado 1:08 pm on May 23, 2017 Permalink | Reply
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    Which topic/s in class made an impact to you? Why?
    Matrices and matrix operations. In bioinformatics (my field of interest), there’s a process called SNP calling/analysis, or Single Nucleotide Polymorphism Analysis, where different sequences of different organisms are being compared, and the single change in base (Single Nucleotide Polymorphism) can cause a lot of difference in the biology of the organisms (from simple coat color to life vs death). The problem is, we deal with organism vs nucleotide position table, which can span from 1000 x 1000 to 10,000 to hundreds of thousands– very big matrices. Though I haven’t tried it yet, there can be a lot of ways I can use my newly acquired knowledge about matrices and matrix operations on SNP analysis.

    If you can summarize this course in one word or sentence, what would it be?
    Math can be enjoyable and fun!

    What would be your parting message to the class?
    This CS 130 class proved that you can enjoy while learning, and you don’t have to stress out your students with a lot of requirements weekly,and make them sacrifice their health and social life for them to learn. 🙂

     
  • Miguel Sesdoyro 12:32 pm on May 23, 2017 Permalink | Reply
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    synthesis – vectors and vector transforms 

    vectors and vector transforms made the biggest impact on me, mostly because I work with game engines like Unreal 4 and Unity as a hobby and have to use vectors and vector transforms on a regular basis to represent physics

    CS130 in summarized in one word is “math”

    my parting message to the class is I hope that everyone enjoys CS 131

     
  • Levi De Guia 11:37 am on May 23, 2017 Permalink | Reply
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    FIN. 

    The topic that made an impact to me in class is vector. It was such a simple concept when I was introduced to it on my Physics classes but this course made me appreciate it more that vector is not just simply a Physics-Mathematics lesson and applied in Physics-related concepts such as force, weight, etc. Vectors are basically everywhere and the journal entries of my classmates somewhat prove that with various interesting real life applications of vectors. I liked Gaussian Elimination and Gauss-Jordan too although the experience solving it on the second exam was … UGH.

    If I can summarize this course in one word, it would be eigen. Because the course (and the professor too (: ) is a class of its own.

    Thank you sa mga naging groupmates ko sa quizzes! Thank you Sir for making each of your class session light and enjoyable. Good luck sa future endeavors.

     
  • Ryan Rivera 11:21 am on May 23, 2017 Permalink | Reply
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    Which topic/s in class made an impact to you? Why?
    Vectors. I think if not for Vectors, I would not be able to understand most of the topics in CS130. For me, Vectors served as the stepping-stone to greater things both in CS130 and in life.

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

    What would be your parting message to the class?
    I think that the song I’ll Make A Man Out Of You from Mulan (1998) perfectly depicts the class with Sir Paul as Captain Li Shang and the rest of us as Mulan, training and teaching the class with patience and determination with the goal of making true Iskolars ng Bayan out of his students. Thank you for not giving up on us, Sir Paul!

     
  • Arthur Yiu 11:19 am on May 23, 2017 Permalink | Reply
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    RREF was the most impactful topic for me because I really hard a time time learning it and doing it properly. It felt so satisfying to be able to answer RREF problems since I studied hard how to do it and I could see that it paid off.

    FUN. CS130 was a class that I always looked forward to attend. It was fun not only for the games before the start of the class, but also for the discussions. The discussions weren’t dull which made it easier to learn the topics.

    Hope to see everyone in CS131!

     
  • Aira Pega 10:54 am on May 23, 2017 Permalink | Reply
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    (5) Synthesis 

    I appreciated Linear Transformations the most because of its applications: RGB values, compressing images, digital media processing. Honestly, it’s hard to appreciate math kung puro solve lang but because of its applications, it’s easier and much more fulfilling to absorb the lessons kasi may kwenta pala yung ginagawa natin, ganun. I also enjoyed Gauss-Jordan elimination because it’s very useful and it really makes solving (systems of equation, inverse) easier. Feel ko isa ito sa mga topic na matatandaan ko pa rin n years from now kasi ang dami kong ginamit na papel for this hahaha.

    Running man will always remind me of CS 130. Simula nung pinapanood ni sir sa class, nagstart na rin ako manood and super nakahelp siya sa stressful sem na ‘to. Plus, yung mga games na ginawa sa class (!!!) and just like RM, pangpaalis din ng stress ang 130 dahil ang positive and fun ng class.

    Thank you and good luck sa remaining requirements!! Woo

     
  • Dana Redeña 9:58 am on May 23, 2017 Permalink | Reply
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    Thank you :) 

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

    • I will always remember one of the first classes we had where Sir told us that the applications of CS 130 are practically everywhere. As a person who is not really fond of doing math, those applications gave my a new perspective for mathematics. As for a “math” topic, I really enjoy transforming matrices into their Reduced Row Echelon Forms. I don’t know why I’m specifically fond of this but maybe because it just feels so satisfying once you get to have the final RREF matrix.

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

    • “A Paradigm Shift”

    This class has gave me a new pair of eyes in the way I look at mathematics and a CS student. For mathematics, I’ve learned to appreciate it more by knowing how much mathematics is all around us. For UP students, I’ve further appreciated how each CS student has a different skillset. I’m amazed on how much each of us has a different skill to offer for this class, and I’m very thankful that this is a kind of class that is open for that. Even though I’ve always questioned on how much further I can survive in CS because I’m not really great in math but now I’ve learned to appreciate the skills that I’m good at even more and to use these skills in order to still do my part in this CS journey.

    What would be your parting message to the class?

    • To everyone, congratulations for surviving this semester. It was difficult but our feats (no matter how small) are all moments of triumph that would remind us that we’ve made it and we we’ll make it again in the next stage. To Sir Paul, thank you for your passion and service for teaching and congrats for completing your thesis! We’re proud of you as you’ve believed are we’re proud of us first. Thank you 🙂
     
  • Mikayla Lopez 9:50 am on May 23, 2017 Permalink | Reply
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    auf Wiedersehen ✨ 

    Which topic/s in class made an impact to you? Why?
    Matrices, vectors, and linear transformations. It’s amazing to think how even the simplest things we encounter on a daily basis involve and embody these. (The colors and images that we see on-screen are alone basically a collection of vectors and matrices.) RREF is another thing. I find it difficult to reduce matrices to RREF and I have spent a heck ton of paper studying this, repeatedly going over just a single matrix on about three sheets of paper. I don’t like it, but I could never hate doing it. I wonder why, but I guess it’s the challenge in the trial and error that keeps me going whenever I tried solving this.
    If you can summarize this course in one word or sentence, what would it be?
    ~Symbolism~
    Another word that came to my mind is firetruck, because of the firetruck problem, so, I guess that, too. :))

    What would be your parting message to the class?
    See you around~

     
  • Sig Encarnacion 8:11 am on May 23, 2017 Permalink | Reply
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    Which topic/s in class made an impact to you? Why?
    On Fourier and Laplace transform: Sir, interesting ung gadget na nag-s-scan ng brain waves na dinemo niyo sa class. Iniisip ko tuloy kung pwede ba siyang gamitin as a means to know if a person is filtering out all criticism and is processing feedback only when it is positive i.e. praise.

    If you can summarize this course in one word or sentence, what would it be?
    It was enjoyable, but I honestly wish for a more in-depth discussion of each of the topics.

    What would be your parting message to the class?
    Keep on learning.

     
  • Paul Sason 7:54 am on May 23, 2017 Permalink | Reply
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    Body Buddy 

    Give a useful application of symmetry in real-life.

    • We’re all familiar on how our bodies are quite symmetrical if you When drawing the human body, it is usually recommended to use a basic anatomy framework as a starting point to learn how body proportions generally work, like this (check out dem circles). It helps in picking up proper habits if you know how it looks like in its simplest form. But the standard front-view pose like that is too static and doesn’t look natural at all, so you’d want to draw at an angle with varied poses for something that evokes more emotion. You’ll find that this stage is full of asymmetric parts and shapes, because perspective does a lot to its original form of the body. However, by remembering the basics from the symmetric front-view anatomy bare bones (and maybe with some help from reference images), visualizing how these body parts would look like at all sorts of angles would be easier.
     
  • JD Laborada 7:44 am on May 23, 2017 Permalink | Reply
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    Synthesis 

    Share your thoughts on the following questions:

    • Which topic/s in class made an impact to you? Why?
      • Change of basis – cool stuff, it was something that I never new was possible. Kala ko sa spy movies lang.
    • If you can summarize this course in one word or sentence, what would it be?
      • The only class I looked forward to attend.
    • What would be your parting message to the class?
      • Sorry sa classmates ko kung maingay ako HAHAHAHA. I laborada u sir Paul! CONGRATZZ
     
  • robbasilona 7:34 am on May 23, 2017 Permalink | Reply  

    Synthesis 

    Share your thoughts on the following questions:

    • Which topic/s in class made an impact to you? Why?
      • Anything related to matrices – it basically gave me an avenue to see that realistic things could be represented in matrices, or numbers in general.
    • If you can summarize this course in one word or sentence, what would it be?
      • Comeback
    • What would be your parting message to the class?
      • IT WAS FUN. Number are fun. Thank you, Sir Paul!!!! 😀
     
  • Foo 7:31 am on May 23, 2017 Permalink | Reply
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    ( ͡° ͜ʖ ͡°)

    • Which topic/s in class made an impact to you? Why?
      – The topic that made an impact to me was changing of basis. Its application in real life (changing/shifting perspectives in images) seemed really useful and interesting. I find it fascinating because vectors and the math we think is useless in real life actually matters in this application.
    • If you can summarize this course in one word or sentence, what would it be?
      – Besides from learning a lot, it was a fun class to attend to and there came a point where CS 130 was the only class I wanted to attend because of the interesting activities we had before the class started.
    • What would be your parting message to the class?
      – Yay walang hardcore proving nyahaha! and ty Sir Paul for the dp! Jk for the learning and experience! Ty classmates 4 bullying me, i’ll never forget the day you all wanted keel me because you thought i was the werewolf TWICE, not once, TWICE. Jk ty for being coolios. pizawt
     
  • Aliya Miranda 6:52 am on May 23, 2017 Permalink | Reply
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    Finale 

    • Which topic/s in class made an impact to you? Why?
      • I think I got interested the most when there was a video shown in class about repeating patterns in music but with different instruments and timing thus creating a melody
      • also the fire truck problem
    • If you can summarize this course in one word or sentence, what would it be?
      • tons of activities/colorful
    • What would be your parting message to the class?
      • TAPOS NA ANG SEM YEEEEEEEEY
      • Thank you for a fun class 🙂 Lez do our best sa next majors~
     
  • Eliza Tan 6:10 am on May 23, 2017 Permalink | Reply
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    Synthesis 

    Which topic/s in class made an impact to you? Why?
    Yung mga related sa matrices(halos lahat pala) lalo na yung operations tapos RREF kasi sobrang nahirapan ako pero noong medyo na-gets ko na sobrang fulfilling. hehe. nag-enjoy rin ako kasi ang dami pala nilang applications :O parang everytime magpapakita ng example ng applications sa class napapanganga ako tapos lumalaki mata ko (kahit d halata)

    If you can summarize this course in one word or sentence, what would it be?
    This course is….challenging but very interesting. (Kung iisipin mo lang yung concepts siguro mahirap tapos boring pero dahil tinuro rin sa amin yung applications nila in real life, naging interesting)

    What would be your parting message to the class?
    Thank you for the fun semester! See you around 🙂

     
  • Ethan Tan 7:49 pm on May 22, 2017 Permalink | Reply
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    Eigenvectors and change of basis are relatable to… 

    Eigenvectors and change of basis are relatable to image transformations.

    Interactive.

    Good luck.

     
  • Ethan Tan 7:41 pm on May 22, 2017 Permalink | Reply
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    Fourier Transform Piano 

    Each key of a piano corresponds to a discrete wave form of sound. By the simple act of pressing down multiple keys simultaneously, the sound produced becomes a combination of different waves.

     
    • Paul Rossener 5:38 am on May 23, 2017 Permalink | Reply

      Please explain further the application of Fourier transform (e.g. why do we want to get the FT of the waves).

      Like

  • JC Sun 5:16 pm on May 22, 2017 Permalink | Reply
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    Goodbye, CS 130 

    Transcript of my Final Interview for CS 130

    Interviewer: Please reintroduce yourself to the audience.
    Me: *faces audience* Hi. I’m [NAME REDACTED]. I’m a Computer Science student.

    Interviewer: What were your thoughts when you enrolled in this course?
    Me: Totoo naman yung sinabi ko before na natuwa ako na si Sir Paul prof, marami kasi ako naririnig na nag-enjoy yung friends ko sa classes niya. Yung tipong nag-enjoy sila sa classes na hindi ko naman na-enjoy. Kaya ayun, nag-expect talaga ako na maging enjoyable yung CS 130. Tapos ayun. Masaya nga! 🙂

    Interviewer: How comfortable are you with math?
    Me: Hindi ako comfortable talaga sa math, or siguro tamad lang talaga ako as a person. Pero ngayon looking back sa sem na ‘to, medyo naging comfortable din ako nang onti sa CS 130. 🙂

    Interviewer: What’s your dominant feeling right now?
    Me: Wala, eto bida bida nag-susulat ng mahabang journal entry. Jk. I don’t feel any pressure right now – tapos na rin kasi yung sem kaya medyo chill na. Kaya sinusulit ko na rin yung journal entry kasi baka di na ako magsulat ulit ng ganito haha.

    Interviewer: Which topic/s in class made an impact to you? Why?
    Me: Hindi ko na talaga maalala yung titles ng topics, sorry. Pero siguro nagkaroon ng impact sa akin yung isang day na may pinarinig si Sir sa amin na audio file na nagloloop forever *ata*. Yung maraming sound waves na iba’t ibang kulay tas nagooverlap yung tunog nila. Siguro kasi parang sabi nila lagi di ba “bakit ako nag-aaral nito hindi naman ‘to magagamit”, eh mahilig ako sa music. So parang naisip ko, may gamit din pala ‘to sa something that I like or something that I experience everyday. 😮

    Interviewer: If you can summarize this course in one word or sentence, what would it be?
    Me: Aircon! Malamig kasi sa room. Sobra. Tapos sa lahat ng math related course na naexperience ko sa UP siguro ito yung pinaka-chill. Tapos cool pa yung prof! Oh, di ba? Wittyyyy.

    Interviewer: What would be your parting message to the class?
    Me: *takes a moment to wipe tears and asks for a bottle of water* Ayun, sana nag-enjoy din kayo as much as nag-enjoy ako sa CS 130. *drinks tubig* Salamat pala sa libreng tubig.

    Anyway, thank you classmates kasi ang fun niyo kasama tas ang funny ng mga ganap sa games lagi. Masaya dahil may games (Thanks sir!), pero kung wala namang g na players na willing mag-enjoy, sayang lang di baaa. Kaya thank you!

    Thanks din pala sa groupmates ko, ang dami ko rin natutunan sa inyo and sana may natutunan kayo sa akin. Sorry if sabaw ako minsan. 🙂 And salamat din sa mga namigay ng food sa akin na mga nakatabi ko kilala niyo na kung sino kayo! 🙂

    Thank you rin kay Sir Paul! Sorry pala nag-cut ako nung isang beses huhu pinagsisisihan ko talaga yun. Anyway, sana na-capture nitong interview yung pasasalamat at pag-enjoy ko sa class niyo sir! 😀

    Kitakits na lang klasmeyts, and congrats sa ating lahat! ❤

     
  • Angel Furio 3:51 pm on May 22, 2017 Permalink | Reply
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    The bear, the moon, and the Big Blue House… 

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

    • Vectors. Because of its interesting application I used in my vector journal topic (bees use vectors to communicate with the other bees the location of their food source). This is just one awesome application!
    • Differentiaru Equationaru (hehehe). This video topic of our group has been a challenge to us. It is quite difficult to explain it other than saying that these equations are just normal equations that involve derivatives. But it was so fun discovering real life applications of differential equations. There are just so many…:)

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

    • CS 130 made Mathematics look fun *winkwink* 😉

    What would be your parting message to the class?

    Thank you for the super fun math adventure Sir Paul! The journals are also so helpful in exploring the applications of certain topics discussed in class. It made me search for awesome applications brought by these complicated math concepts. Thank you sir! ❤ 🙂

    “Goodbye, goodbye.. good friends goodbye
      And now, it’s time to go~
      But hey, I say, well that’s okay   
      ’cause I’ll see you very soon I know.. (very soon I know~~)

    -Goodbye song (Big Blue House)

     
  • Julius Carlo 11:27 am on May 22, 2017 Permalink | Reply
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    Week 5: Synthesis 

    Which topic/s in class made an impact to you? Why?
    The fire truck problem and finding an orthonormal basis using Gram-Schmidt process. Ang cool ng way ng pagsolve tsaka sa lahat ng problems na nasosolve ng math, dito ako naging pinaka-interesado.

    If you can summarize this course in one word or sentence, what would it be?
    Mathematical Methods in Computer Science 😀

    What would be your parting message to the class?
    Salamat po at congrats!

     
  • Berna Misa 10:27 am on May 22, 2017 Permalink | Reply
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    It’s the end where I begin 

    If you get the reference of the title without googling it, apir! Hahaha. Wala lang. 😉

    The topic about matrices made an impact on me. Kasi, at its core, it’s a simple concept. Pero yung mga applications niya, WAGAS. Hahaha. Very useful even in real life situations. 😀

    Hmm. If I were to describe this class in a sentence, it would be, “This class really is really numerical.”

    I’m not sure if having no MPs as a requirement is a good thing, or a bad thing because throughout the sem, this course got me thinking, “Pano kaya i-poprogram itong mga inaaral namin. Haha. And how to actually optimize the programming solutions.” :))

    To my (legit) classmates (1-2:30 PM),

    Thank you for being a sport whenever we play a game in class. Hahaha.
    Sa mga naging classmate ko pag nagsisit in sa ibang class time, thank you for letting me sit on your supposed chair. Hehe. 😉

    Au revoir, mes amis! 😀

     
  • Camille Comia 8:41 am on May 22, 2017 Permalink | Reply
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    Transform: Visualizing the Audio Spectrum 

    An application of Fourier transforms is an audio spectrum analyzer. A spectrum analyzer is used to view the frequencies which make up a signal, like audio sampled from a microphone. Let’s make the hardware visualize audio frequencies by changing the intensity of LEDs based on the intensity of audio at certain frequencies.

    The video below shows the spectrum display listening to powerful orchestral music with a sample rate of 4000 hz, 40 minimum decibels and 60 maximum decibels. You can see the effects of instruments playing at different frequencies and how the LEDs representing those frequencies respond.

    ref:
    https://learn.adafruit.com/fft-fun-with-fourier-transforms/spectrum-analyzer

     
  • Jerico Silapan 5:14 am on May 22, 2017 Permalink | Reply
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    Unforgettable 

    The lesson I cannot forget is about RREF. First reason is that it’s really hard to reduce a matrix to it’s reduced echelon form. Second reason is, after the hardship in reducing a matrix, the output will make every other problems “easier” to solve. So I think that since we dealt with matrices almost all semester, learning how to reduce on to RREF, will surely be helpful and will make things easier.

    EXCITING. The fact that this is my class every Wednesday and Friday, the games, classmates, prof, and how the lessons are delivered stops me from being lazy to not attend the class. I’m always excited on what would be the activity for the day and what are the lessons to be discussed.

    THANK YOU EVERYONE! Thank you Sir Paul for your patience, hard work, and passion in teaching. I’m sorry if at some point, I did not give my best, yet you gave yours. I’m really sorry. I also want to thank all of my classmates for the fun experiences you all have brought. I like to give my a special gratitude to my quizmates and projectmates for the friendship and carrying me at hard times. Thank you everyone! :))

     
  • Alezon Valerio 5:11 am on May 22, 2017 Permalink | Reply
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    It’s finally time to say “farewell” 

    The topic that I appreciated the most is Determinants. I just felt like it’s the one topic I’d never forget considering it is being used by a bunch of other subjects *ahem* Stat 130 *ahem* and also by bunch of other topics. I just think that it’d be something I could use often and is the most worth taking to heart.

    It’s a “ray of hope” amidst Physics 72, CS 145, Stat 130, CS 199, and CS 180.

    Ravan guys.

     
  • Rafa Cantero 2:47 am on May 22, 2017 Permalink | Reply
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    Synthesis 

    I really enjoyed the laplace and fourier transform since I feel those topics had the most practical applications. I enjoyed having to research about these for the previous blog post.

    If I had to summarize the class in one sentence, it would be: Actually applying theory.
    Even though its not applicable for all topics, I was really happy that there were a lot of practical applications that were discussed. I came into the class expecting a lot of topics that would never help me at all in real life but I’m thankful this wasn’t the case.

    I’d just like to say thank you sir for the great experience this sem and thanks as well to the rest of the class. I really enjoyed CS 130! 😀

     
  • Justo Balderas 5:56 pm on May 21, 2017 Permalink | Reply
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    Quickly multiply two big integers via Fourier Transform 

    Week 4: Laplace and Fourier Transform


    The fastest known algorithms for the multiplication of very large integers use the “polynomial multiplication method” which uses Fourier transform. [5]

     

    Multiplying huge integers is an operation that occurs in many fields of Computational Science: Cryptography, Number theory, just to name a few. The problem is that traditional approaches to multiplication require O(n2) multiplication operations, where n is the number of digits. To see why, assume for example that we want to multiply the numbers 123 and 456. The normal way to do this is shown below.

    We see that for two integers of length 3, this multiplication requires 3 x 3 = 9 operations, hence its O(n2complexity. Executing an O(n2) algorithm for huge n is very costly, so that is why it is preferred to use more efficient algorithms when multiplying huge integers. One way to do this more efficient (in O(n log(n))), is by using FFT’s (Fast Fourier Transforms).[4]

    So how?

    “a number can indeed be divided on a decimal basis and the product of two of them is equivalent to the convolution product which on its turn can be handled fastly with FFT.”[3]

    1] Represent the integer as a polynomial

    2] Use the multiplication algorithm for polynomials using FFT

    3] O(n) carry-propagation step

    Sources:

    [1] https://www.quora.com/What-are-some-non-obvious-applications-of-the-Fourier-transform/answer/Lionel-Chiron (visited on May 21, 2017).

    [2] https://math.stackexchange.com/questions/116674/what-is-the-fastest-way-to-multiply-two-digit-numbers#comment271358_116674 (visited on May 21, 2017).

    [3] https://www.quora.com/What-are-the-major-applications-of-the-Fast-Fourier-Transform-FFT-to-algorithms-in-Computer-Science/answer/John-McGonagle (visited on May 21, 2017).

    [4] (2017). Cs.rug.nl. Retrieved 21 May 2017, from http://www.cs.rug.nl/~ando/pdfs/Ando_Emerencia_multiplying_huge_integers_using_fourier_transforms_paper.pdf

    [5] https://en.wikipedia.org/wiki/Discrete_Fourier_transform#Polynomial_multiplication (visited on May 21, 2017).
    [6] https://en.wikipedia.org/wiki/Multiplication_algorithm#Fourier_transform_methods (visited on May 21, 2017).

     
  • Justo Balderas 5:45 pm on May 21, 2017 Permalink | Reply
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    Ball Is Life 

    Week 3: Symmetric Matrices


    DIBS: Symmetry in basketball (equipment/ball)

    “I will never look at a (traditional) NBA basketball the same again” – This is just right after researching for this post. *amazed meme* *my whole life has been a lie meme*

    Ever since 7 years old, I thought basketball looks like this.

    3 plane

    expectation

    Little did I know, it is just like a tennis ball or baseball traditionally made by joining two complementary (symmetric) pieces.

    baseball

    deconstructed baseball

    In basketball, what you should see from one side is different from what you have on the other. Below’s a photo of the different flows of the leather patches in the front and rear view.

    2 different plane

    leather patches

    So the first animation (gif) should be…

    2 plane reflective symmetry

    reality (on most, if not all traditional basketball)

    Each leather patch embraces the other. Here’s an animation.

    2 plane of symmetry

    animation

     

    Here’s a real life example. Observe the 2 leather patches carefully. (sorry for the low resolution ‘.gif’, here’s the link for the video source: youtu.be/DQc8miHqdqQ?t=2m20s )

    real basketball

    NBA basketball (Spalding brand)

    Basketballs have two planes of reflective symmetry, as do tennis balls. But these balls also have a 2-fold rotational symmetry. A cube has nine planes of mirror symmetry, while some soccer balls have fifteen![2]

    sources:
    [1] https://blender.stackexchange.com/questions/41298/asymmetrical-basketball  (visited on May 21, 2017).
    [2] John Horton Conway. The Symmetries of Things, p. 12
    [3] https://math.stackexchange.com/questions/688749/number-of-reflection-symmetries-of-a-basketball (visited on May 21, 2017).

     
  • Justo Balderas 5:44 pm on May 21, 2017 Permalink | Reply
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    Real Estate 

    Week 2: Vectors


    DIBS: 3D weight matrices in modeling real estate prices

    “Vector” can be pretty much just a fancy word for “list”. Specifically, an ordered list of numbers. [1]

    For example, let’s say that you were doing some analytics about house prices, and the only features you cared about were square footage and price. You might model each house with a pair of numbers: the first indicating square footage, and the second indicating price. Since the length of this vector or list is two (a pair), this is two dimensional or 2D. [1]

    2d vector house price
    This is a very simplified way of knowing house prices in real estate. There are other factors such as amenities (parking, good view, bedrooms, etc.) or even floor level (level 1, level 2, level 3, etc.). An example would be “3D weight matrices in modeling real estate prices”.[2]

    sources:
    [1] 3Blue1Brown. Vectors, what even are they? URL: https://youtu.be/fNk_zzaMoSs (visited on May 20, 2017).

    [2] (2017). Int-arch-photogramm-remote-sens-spatial-inf-sci.net. Retrieved 20 May 2017, from http://www.int-arch-photogramm-remote-sens-spatial-inf-sci.net/XLII-2-W2/123/2016/isprs-archives-XLII-2-W2-123-2016.pdf

     
  • Haifa Gaza 4:36 pm on May 21, 2017 Permalink | Reply
    Tags:   

    Ughh… Haifa Vector 

    Which topic/s in class made an impact to you? Why?
    Baasiiiss! Hahaha it is our final project topic, and we won two awards! It was fun making the video. I learned that Michelle Scalar can’t be stopped (I’ll get back to you, buddy). Anywaayyss, yes, basis. its application is coool. Remeber that change of perspective photo? AMAZZEEENNGG!

    If you can summarize this course in one word or sentence, what would it be?
    HAAAAHHH ~(‘.’~) (~’.’)~

    What would be your parting message to the class?
    See you arouunnd mahfreennss ❤ THESISING NA NIYANN HOHOHO! Good luck sa atin! Let's enjoy the coming years, yes yes yes! \('.')/ \('.')/ \('.')/

    OMG SIR PAUL SEE YOU AROUND 🙂 CONGRAATTSSSS HIHI Very inspirational parting wooords. I'm glad I took your class!

     
  • Theo Yap 4:19 pm on May 21, 2017 Permalink | Reply
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    Photo-*chuckles*-SYNTHESIS :D heeeh? HEEEEH?! *cricket noises* 

    Well… That was fast… but OK. Definitely not an easy semester, but can’t say it wasn’t a good learning experience.

    Linear transformations and matrices made the most impact on me even if they were the ones I had a hard time understanding. These topics are used a lot in VFX, which is something I love and am very passionate about. There’s a certain bliss in learning how something you like very much works, and in a way, it gives meaning to what you do. I also liked Fourier Transform even if we just brushed over it briefly. It felt tangible, and that makes sense to me. Also, apparently you can use it to encrypt and decrypt information, and that intrigues me.

    This course has been… stressful to say the least, but I think that’s my problem since I really just have a hard time understanding these kinds of math as opposed to say AI.

    Well, my message to the class… hm… It’s no secret that I’m delayed, and most if not all of the subjects I’m taking right now are being taken by Batch 2014. To be taking 3rd year subjects with batch 2014 is humbling to say the least, but I guess the entire UP experience is humbling haha. I didn’t get to interact with you all so much except for the groups, but I had fun taking the class with all of you. And to Sir Paul, thank you for being patient with all of us (and I think especially me, I know I’m not the brightest student, and a not very easy one to teach), and thank you for making the classes more lively with your unconventional activities and teaching methods. It makes the hardcore math way more bearable. Also, congrats Sir!

    I wish everyone the best. Good luck to you all!

     
  • Abby del Castillo 4:01 pm on May 21, 2017 Permalink | Reply
    Tags:   

    Wasabi desu! (bye friends!) 

    Which topic/s in class made an impact to you? Why?
    The topic about differential equations made me more aware that math is everywhere! Also, I had to really learn the topic so that we can teach it in our video haha. Solving differential equations may be a long process but it’s actually cool when I get an answer after integrating and deriving multiple times. Even though the topic is hard, I learned to appreciate it more when we did the final project.

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

    What would be your parting message to the class?
    Thanks for the sem guys! Our final project is done woo! Congrats to all!! ❤

     
  • Camille Razal 2:15 pm on May 21, 2017 Permalink | Reply
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    SEE YOU WHEN I SEE YOUUUU 

    • Which topic/s in class made an impact to you? Why?
      • Laplace and Fourier Transform and Vectors made an impact to me in class, especially when I am researching for the journals. I realized that we are really inded use complex mathematics like these in our everyday lives. Math is around us. It can be found and used in the simplest things like when you are asking for directions and it can also be applied in complex things like MRI. After CS 130 I learned how to look for the hidden mathematical complexities of things.
    • If you can summarize this course in one word or sentence, what would it be?
      • MATHEMATICS
    • What would be your parting message to the class?
      • THANK YOU FOR EVERYTHING!!!
      • MARAMING MARAMING SALAMAT KAY SIR PAUL DAHIL FOREVER AWESOME AND KIND AND THOUGHTFUL NIYA TALAGA SA MGA STUDENTS NIYA HUHUHU Thank you very very much for being that kind of prof to us, a prof who has the heart for his students. (sobrang nafeel ko yun nung minove ni sir yung deadline nung video ❤ )
      • THANK YOU SA FUN AND CHILL KONG CLASSMATES, SEE YOU AROUND GUYS!!!!
      • sorry din pala dahil medyo butaw ako sa class na ito pero nevertheless IT WAS AN AWESOME CLAAAAAAAASSS!!!!
    • CONGRATS DIN PALA KAY SIR PAUL FOR HAVING ANOTHER SUCCESSFUL SEM OF TEACHING AAAAAAANNDDD PATAPOS NA SIYA SA THESIS NIYAAAAA ❤ ❤ ❤
     
  • Camille Razal 1:38 pm on May 21, 2017 Permalink | Reply
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    Fourier Transfrom in MRI 

    “Magnetic resonance imaging (MRI) is a test that uses a magnetic field and pulses of radio wave energy to make pictures of organs and structures inside the body. In many cases, MRI gives different information about structures in the body than can be seen with an X-ray, ultrasound, or computed tomography (CT) scan.”[1]

    The signals retrieved from a Magnetic Resonance Imaging (MRI) scan are “a combination of signals from all over the object being imaged.”[2] As we learned in class signals are composed of sine waves with different frequencies. The Fourier transform allows us to understand and interpret those frequencies and amplitudes. “It converts the signals from the time domain into the frequency domain and if we can separate out the frequencies we can say where we should plot the amplitudes on the image.”[2]

     

    Capture

    Sources:

     

    [1] http://www.webmd.com/a-to-z-guides/magnetic-resonance-imaging-mri

    [2] http://www.revisemri.com/questions/kspace/fft

    http://mriquestions.com/fourier-transform-ft.html

    photo source: https://www.quora.com/What-is-the-real-life-application-of-Fourier-transforms-and-Laplace-transforms?no_redirect=1

     
  • Jade De Guzman 11:51 am on May 21, 2017 Permalink | Reply
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    Synthesis 

    The topic that made the most impact to me is about vectors. I think in every topic in this course, vectors are involved that’s why. But the reason why it made an impact on me is because I have heard and learned things about vectors for the past years of my life. We learned about it in high school, physics, and some of our math courses in college but CS 130 gave it a new image to me. That it’s just not used in physics which is what I’ve really thought before. There are a lot of things that use vectors in our daily life and it’s just amazing, I think that this is the Computer Science major magic lol, that just knowing how things work gives something like fulfillment or feeling like you’ve achieved something for knowing these stuff.

    FUN. I think all of the courses handled by Sir Paul are fun. He was my professor in my CS 12 large class but being handled in a smaller classroom is much more comfortable. I like that there are ice breakers before class start and we were able to get to know new people and new shows to watch because of it. Honestly speaking, I really don’t know why I’m in this degree program but I really made an effort in this course. It made me feel my love for mathematics again.

    It was a fun semester, everyone. See you around!

    AND ALSO CONGRATS KAY SIR PAUL KASI GAGRADUATE NA SIYA OMG SIR LIBRE NAMAN!!! ❤

     
  • Jennie Ablog 11:03 am on May 21, 2017 Permalink | Reply
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    MATHEMAGIC: Don’t hate, appreciate. 

    The greatest topic ever that made an impact to me, is everything about vectors. And this isn’t because that is our topic for the final project, no. It’s because I think that CS130 kinda revolved around the idea of vectors. We discussed about vectors and the basic operations first. The next topics which are more complex were built upon this sort of foundation from our understanding of vectors. And I liked how this learning experience flowed smoothly. Well for me, at least. I never really had a hard time understanding it, because the class made me realize how simple it could really be!

    If I could summarize the whole class in one word, it would be “mathemagic.” Hahaha. Some of the students here might get the reference, some won’t. Idk which one is luckier. But anyway! I got this term from another professor from another subject with the number 130 (“one-three-zero”) in it too. Never really appreciated the “mathemagic” in that class. 😦 But in CS 130, I sure as heck did! My favorite part of every lecture is having to know how to apply these concepts in the real world, which made me appreciate math a whole lot more. I strongly believe that every maths class should all turn out to be a maths appreciation class, not the kind that would make math less interesting just because it is hard to do. Luckily for all of us (opinion ko po i2), CS130 is not of the latter kind!

    Honestly, I really didn’t think I would perform really well in this CS subject, let alone in any of my CS majors. Computer Science is really, really, really, really hard. But what motivates me to stay in this course is my appreciation for its real world applications, and how it could equip us with the tools, and all the mathematics, that would make us understand more deeply this world we are living in. And thus be able to actually help the field, science, and all of humanity progress. Huhuhuhuhuhu. So with that, I leave this parting message for my #klasmeyts (another reference, oops): Good job guys! Sa lahat ng nasa CS pa, laban lang!!! Kaya natin to! WOOOOHH!!!!

    PS: Let this be an appreciation post for all the great teachers that don’t make our lives a living hell and math a source of unbearable pain. Thank you Sir Paul! ❤

    PPS: This wordpress blog/journal thing has actually increased my appreciation for the subject. I am actually thinking of starting my own blog/journal to develop my appreciation on other stuff too! Thanks for the idea, Sir!

     
  • Christine Felizardo 11:01 am on May 21, 2017 Permalink | Reply
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    Avisala Meiste! 

    Which topic/s in class made an impact to you? Why?
    This might seem like I’m biased with differential equations… which I am. I’ve always been intrigued about what differential equations are and what purpose they serve in the universe, and a good portion of my questions have been answered. So many things in the world are represented by differential equations, and DEs basically give us an idea of the one thing that is constant in this world: change.

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

    What would be your parting message to the class?
    Hello reader! It’s been a very tough sem for all of us but the end is coming by soon! Hang in there! We can do it! ❤

     
  • Jade De Guzman 10:57 am on May 21, 2017 Permalink | Reply
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    Fourier Transform in NMR Spectroscopy 

    Fourier Transform is used in a lot of spectroscopy and one of this is NMR spectroscopy.

    Nuclear magnetic resonance spectroscopy or also known as NMR spectroscopy is one of the research technique that utilizes magnetic properties of some atomic nuclei. This determines the chemical and physical properties of an atom and also the molecules contained inside one.

    Fourier transform is used to extract frequency-domain spectrum from the raw-time domain FID (free induction decay).

    source: https://en.wikipedia.org/wiki/Nuclear_magnetic_resonance_spectroscopy

     
  • Roben Delos Reyes 10:34 am on May 21, 2017 Permalink | Reply
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    R5 Synthesis 

    Week 5: Synthesis

    Which topic/s in class made an impact to you? Why?
    The topic that made an impact on me was the first order ODE because I had fun learning it. It was difficult but it made me miss the Math 53 series.

    If you can summarize this course in one word or sentence, what would it be?
    If I can summarize this course in one word, it would be MATH. Although I’m already too lazy to solve math problems (as I have mentioned in the introduction), this course made me realize that I still enjoy doing it.

    What would be your parting message to the class?
    Thank you for the semester! It is finally over. Sleep well, everyone. 🙂

     
  • AF Formaran 9:29 am on May 21, 2017 Permalink | Reply
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    Life’s Reality and Imagination

    Our lives are like complex numbers. There’s the reality we live in everyday, where we bring forth ideas into something we can sense and comprehend. And there’s the imaginary, where we cower away into the deepest depths of our minds like the artists we are, thinking and manifesting.

    It all starts there. The mixture, the blending, the fusion of real and imaginary. From there roots all we have now, and what we will have in the future.

    CS 130 is like the fundamentals of something grander.

    We started off with complex numbers in CS 130, and from there, we kept on upgrading to harder and harder topics. Such is the growth of students. We first receive the simplest of tools, and using those tools, we are taught to create more complex ones.

    I guess the road of a computer science student is still a long one, but at least, we have progressed further than where we were yesterday.

     
  • JC Albano 9:26 am on May 21, 2017 Permalink | Reply
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    CS 130 Synthesis 

    I guess for me the topics that stood out were actually linear combinations and vectors. Vectors cause they’re already so familiar as having been taught in a lot of my classes and linear combinations cause of the project (I had to restart the process of recording like a million times cause my computer was slowwwww so now the topic was embedded unto my mind).

    I’d summarize the whole classroom experience into one word: “Fun”. I guess that for me is the defining factor of all of Sir Paul’s classes. It’s something that I look forward to every Wednesdays and Fridays cause it’s like we’re just having a very interesting conversation, very different from your typical classroom experience. And I don’t dread the tests as much, as reviewers are provided which for me were so helpful in actually appreciating the course itself rather than stress over if I’m gonna pass or not.

    Parting Message: Good job everyone! Especially to my final project group, and especially to Theo who tried his best to remind everyone the deadlines (and what should be done) and save the project lol

    Kudos to everyone!

     
  • Don Abril 8:14 am on May 21, 2017 Permalink | Reply
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    Matrices Everywhere 

    Yet another semester has ended to culminate in another myriad of memories to cherish.

    The lesson that made an impact on me was the one about Gauss-Jordan Elimination kasi impakto talaga yung topic na yun. But in all seriousness, I’d say the lesson held enough of my attention to make more or less of an impact on me, as I found it quite curious and annoyingly interesting that you can turn certain matrices of not-so-friendly values into ones that look so simple and friendly that they’d be puppies had they been animals.

    I’d summarize the course with one word: MATRICES. I’m willing to bet that not one of the students who took the course would deny the sheer amount of matrices that we saw over the semester. Funnily, I have been encountering matrix multiplication since my first year in college, each time having to ask how it worked because somehow the process didn’t ever get through my thick skull. However, thanks to CS 130, I don’t see myself forgetting this again.

    Final words, well well.

    I give my thanks to Sir Paul. It is commendable that you are not only an effective instructor, but also a friend among us students.

    I thank my project groupmates (most of whom also happen to be my quiz groupmates, and for which I also give thanks) for the final project, and for being some of the new friends I’ve made this semester. Special thanks to Paul Sason na nagsalba sa final project woohoo!

    Lastly, my classmates also receive my gratitude. I don’t know every one of you, but I don’t mind. We had fun.

    Cheers, and see you around! 🙂

     
  • Paul Rossener 5:48 am on May 21, 2017 Permalink | Reply
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    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.

     
  • Levi De Guia 2:35 am on May 21, 2017 Permalink | Reply
    Tags:   

    Does Laplace Have Le Place in Economics? 

    You may have only heard (and applied) Laplace Transform perhaps in your Mathematics subject or maybe in your Computer Networks subject, but did you know that it could be possible to apply this theory on certain stochastic and deterministic economic problems?

    “In a deterministic economic process the value of each function under consideration is known in advance at every future point of time.” These functions can be the cost per unit time period, the number of demanded units per unit time period, etc. For example, the maximized discounted value of a future cash flow existing during a given time interval, finite or infinite, would take a very simple form in Laplace terms[1]. The Laplace expression would be more involved if we are only to study the discounted value from a finite time interval [0, T] . The derived equations using the Laplace transform such as this one:

    130-1[1]

    would be of great use to variety of problems such as feedback controlled-production problems, inventory problems, etc.

    “In a stochastic economic process, the functions studied possess some property of giving uncertain outcomes.” This uncertainty stems from stochastic variables which have values that are unknown in advance. We also take note here the probability of these stochastic variables taking values within a certain interval which is the probability density function. If this probability function is time invariant, the process is stationary. After series of derivation and under the assumption that “using the expected value as suitable measure of the process result”, stochastic economic processes can be treated like deterministic processes.”[1] An example of a problem would be computing the expected present value of a season’s variational revenue flow using this derived equation:

    130-2[1]

    For the a detailed derivation and usage of Laplace transform in equation form, the source material is provided.

    Source:

    [1] http://ctr.maths.lu.se/matematiklth/courses/FMAF05/media/material/grub67.pdf

     
  • Arlan Uy 3:48 pm on May 20, 2017 Permalink | Reply
    Tags:   

    Symmetry in Fractals 

    Fractals lead to a new notion of symmetry. Fractal is a mathematical name used to describe the patterns of scale-self similarity which occur nearly the same at different levels. To elaborate, it is used when a specific and detailed pattern is seen to repeat itself.

    Fractals are different from other geometric figures for in fractals, even though one sees one-dimensional lengths doubled, the corresponding spatial content of the fractal scales by a power that is not necessarily double also or even an integer (this spatial content of the fractal scale is referred to in the video as mass, example given is the Sierpinski triangle). This power-exponents are called fractal dimensions or scale dimensions.

    The general consensus is that theoretical fractals are infinitely self-similar, iterative and detailed mathematical constructs having fractal dimensions. There may not be an agreed upon definition, different kinds of examples and applications about this have been formulated and studied in great depth.

    Reference: http://www.mdpi.com/journal/symmetry/special_issues/symmetry_fractals

     
  • Arlan Uy 2:41 pm on May 20, 2017 Permalink | Reply
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    Fourier Transform on measuring temperature 

    The Fourier transform converts a set of time domain data vectors into a set of frequency (or per time) domain vectors.

    To know about changes in soil temperature, we can measure the temperature of soil accordingly at different time of the day, every day for a year. We would then have a list of real numbers representing the soil temperatures.

    By plotting these readings on a line graph with the vertical y axis labelled as temperature and the horizontal x axis labelled time, we get a so called “time domain” graph. The graph that we created is then the sum of two  sinusoids or sine waves. The first sinusoid is with a frequency of one day as the temperature varies between day and night. The other sinusoid is with a frequency of one year as the temperature varies with the seasons.

    The Fourier Transform provides a means of manipulating or transforming this raw data into an alternative set of data, the magnitude of which can be plotted on a graph with differently labelled axis. Disregarding the y axis label for now, the x axis would be labelled ‘frequency’. This is in the frequency domain graph.

    This second graph looks very different than the first because it will consist of two vertical lines rising from the frequency axis, one at a frequency (or period) of one day, the other at a frequency of one year. Thus by using Fourier Transform on the raw data we have, we then extracted the most interesting facts from it – days are warmer than nights and summer is warmer than winter.

    Reference: http://nptel.ac.in/courses/117101055/cdeep%20demo%20ppt/application%20of%20fourier%20transforms.html

     
  • Nathan Paglinawan 2:03 pm on May 19, 2017 Permalink | Reply
    Tags: https://media.decathlon.in/20511/onear-sport-around-the-neck-in-ear-earphones.jpg   

    Symmetry

    Pwede siya sa earphones haha dapat symmetric yung earphones mo para pantay sila sa tenga mo. 🙂

     
  • eugenekasilag 7:04 pm on May 18, 2017 Permalink | Reply
    Tags:   

    Symmetry 

    Naapply yung symmetry sa physics, specifically sa reflection sa mirrors. Kung alam mo yung distance mo sa mirror at tumingin ka sa reflection ng isang bahay sa salamin (at alam mo yung angle), malalaman mo kung gaano kalayo yung bagay na yun mula sayo.sym

     
  • eugenekasilag 6:47 pm on May 18, 2017 Permalink | Reply
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    Vectors 

    Makakatulong yung vectors sa pagprotekta sayo mula sa init. Pwede ka pang dumamoves kay crush. Syempre itututok mo yung payong sa kung nasaan yung araw para hindi kayo masunog tapos pwede ka na rin gumawa ng rason para akbayan sya hehehe.

    12

     
  • John Ramonel Roque 6:01 am on May 18, 2017 Permalink | Reply
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    Fourier Transform — Music 

    *listen to this music while reading this article, this is Fourier transform on its finest! 🙂

    Jimmy Hendrix, Steve Vai, John Mayer, BB King, and all those musicians, ever wonder how and why they sound so good? Apart from them being virtuoso’s,  their musical equipment played a big part on their genius.

    Signal Processing and Frequency Adjustments are the core of their gadgets, from their Instruments (Electric Guitars), vibrations are being passed/received on their pickups (Guitar Pickups) and in return converts these frequencies in forms that their Effects (Distortion, Overdrive,  etc.) can manipulate through Signal Processing and then passes it to the Amplifiers which again, processes these signals into sounds that we can listen to.

    And the process mentioned above uses Fourier Transform extensively.

     
  • Eliza Tan 12:30 am on May 17, 2017 Permalink | Reply
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    Fourier Transform and Frequency Filters 

    Fourier transform allows us to smoothen or sharpen images using filters. An image is first converted from spatial to frequency domain (high components=edges; low components=smooth regions) using Fourier transform then it is multiplied with a filter function (lowpass, highpass, bandpass filter) in a pixel-by-pixel fashion, and converted back to spacial domain.
    For example, a lowpass filter will reduce high frequencies and retain low frequencies resulting to a smoother image.

    https://www.tutorialspoint.com/dip/introduction_to_frequency_domain.htm
    http://paulbourke.net/miscellaneous/imagefilter/
    http://homepages.inf.ed.ac.uk/rbf/HIPR2/freqfilt.htm

    original image

    resulting image after applying lowpass filter

     
  • JC Sun 10:31 am on May 16, 2017 Permalink | Reply
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    Topic Four (Yay!) 

    Fourier Transform in Communication Systems

    The Fourier Transform is largely used in communications theory. It is essential to understanding how signals work through channels.

    Communication systems are “systems designed to transmit and receive information”. These information are transmitted using signals, and these signals are often viewed and analyzed in the frequency domain. Using the Fourier transform we can analyze these signals and the quality of these signals. We can also convert an analog system to a digital system using the the equations essential to the Fourier Transform.

    “Fourier Transform has greatly improved the way we are sending/collecting data.” For example, “when sound is recorded digitally the strength of the sound wave itself can be recorded (this is what a “.wav” file is), but more often these days the Fourier transform is recorded instead.” Later on, the Fourier transform signal is then “turned back into regular sound signal”.

    Fourier Transform is very helpful for images and sound files, like MP3s or JPEGs. It’s nice that we have these Transforms. I couldn’t imagine my phone without all my MP3 files!

    Sources:
    http://www.ijser.org/researchpaper/Applications-of-Fourier-series-in-communication-system.pdf
    http://w.astro.berkeley.edu/~jrg/ngst/fft/comms.html
    http://www2.siit.tu.ac.th/prapun/ecs455_2011_2/ECS455_FT.pdf
    https://www.quora.com/What-are-some-applications-of-the-Fourier-Transform-of-1-t-in-real-life-problems
    https://cadcammodelling.wordpress.com/2011/04/14/fourier-transform-and-its-applications/
    http://mathworld.wolfram.com/FourierSeries.html
    http://www.askamathematician.com/2012/09/q-what-is-a-fourier-transform-what-is-it-used-for/

     
  • Haifa Gaza 7:27 am on May 16, 2017 Permalink | Reply
    Tags:   

    Fourier Transform in Painting Authentication 

    Authenticating paintings has always been a problem in the art world especially during auctions. Usually, they rely on the opinion of art historians who specialize in that artist to determine a painting’s authenticity. Now, with Fourier transform, they are able to analyze the painting with certainty. After scanning the picture for a digital image, they convert it to a Fourier transform to filter useful information that would help them identify the painting’s elements. They are able to analyze the painting’s brushstrokes and compare it to an original artwork to determine its authenticity.

    Reference: https://www.google.com/patents/WO2001082263A1?cl=en

     
  • Aliya Miranda 3:17 pm on May 15, 2017 Permalink | Reply
    Tags: ,   

    “Laplace derived the differential equations for a thin fluid on a sphere with no vertical motion, only horizontal motions, called a barotropic model. Ocean tides are caused by the horizontal gravitational force of Moon and Sun. The Earth rotates so we have Corriolis forces. A slope in the sea-surface also causes horizontal force. Bottom friction and/or lateral eddy dissipation.” Thus you can use the equation to compute for the ocean tides.

     

    Source: http://wakes.uma.pt/cimar/PartII_lecture1.pdf

     
  • Lea Cornelio 2:45 pm on May 15, 2017 Permalink | Reply
    Tags:   

    Fourier Transform in X-ray Crystallography 

    A Fourier transform is performed when a monochomatic X-ray diffracts off a crystal. When the incidence angle is varied, the complete transform is produced.

    The diffraction corresponding to a diffraction vector s and a single electron at position r multiplies the amplitude of the scattered wave by a phase factor e^(−2πirs). If ρ(r) is the electron density function in the crystal, the effect on s will sum to

    F(s)=∫crystal ρ(r)e(−2πirs) dr.

    Therefore, structure factor F(s) appears as the Fourier transform of the electron density function ρ(r).

    How a monochromatic plane wave performs Fourier analysis on the electron density distribution:

    Reference:
    http://www.ams.org/samplings/feature-column/fc-2011-10

     
  • Theo Yap 2:20 pm on May 15, 2017 Permalink | Reply
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    “I’m in. #hackerman” 

    Fourier Transform can be used in image encryption and decryption. The method in which images are encrypted and decrypted use random phase masking.

    Two random matrices are instantiated, and these will be treated as our keys. To encrypt, image is multiplied by the first random matrix then Discrete Fractional Fourier Transform (DFRFT) of order alpha is applied (this is phase masking). The result is then multiplied with the second random matrix, then DFRFT of order beta is applied. To decrypt, one simply works in reverse. You first apply DFRFT of order beta-prime on the encrypted image then  multiply the encrypted image with the inverse of the second random matrix. Then, DFRFT of order alpha-prime is applied, after which, the result is multiplied with the inverse of the first random matrix. Basically, to encrypt, you apply some procedures, then to decrypt, you apply the inverse, cancelling out the encryption.

    This works because without the proper parameters/keys, decryption result returns noise, which an image may not be inferred from.fourier

    (image is a screenshot from the work of Mr. Ashutosh; mentioned in the sources)

    Ashutosh, D.S. (2013). Robust Technique for Image Encryption and Decryption Using Discrete Fractional Fourier Transform with Random Phase Masking. Retrieved from http://www.sciencedirect.com/science/article/pii/S2212017313005756

    Hennelly, B.M. & Sheridan, J.T. (2003). Image encryption and the fractional Fourier transform. Retrieved from http://eprints.maynoothuniversity.ie/5809/1/BH-Image-Encryption.pdf

    Sharma, P. (2013). Efficient Image Encryption and Decryption Using Discrete Wavelet Transform and Fractional Fourier Transform. Retrieved from https://arxiv.org/ftp/arxiv/papers/1401/1401.6087.pdf

     
  • Theo Yap 1:24 pm on May 15, 2017 Permalink | Reply
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    "One Shot, One Kill" – US Marine Scout Sniper School 

    Vectors are used in physics to express both magnitude and direction, and almost everything runs on basic kinetic motions.

    The most basic of kinetic motions would be the projectile, which is affected by gravity. However, to become a sniper, one must understand more than just this. A sniper has understanding of gravity (y axis) as well as other factors that affect their shot like wind (x axis), temperature, humidity, bullet weight, muzzle velocity, and other factors that they need to control in order to guarantee or secure a shot every time.

    snipe1

    snipe2

    To sight in a target, the sniper aims their crosshairs at a target, and ideally, the crosshairs are zeroed for a specific rifle, using a specific type of bullet, and at a specific distance. When a rifle is zeroed, it means that a certain distance, given certain weather/external conditions, the rifle will always hit where its crosshairs are sighted on. However, the different external conditions affect the path of the bullet, which can make it hit higher or lower or offset to the right or left. To combat these effects, a sniper can use adjustments (the math of which I will no longer discuss) in order to compensate for the offset, or the sniper can choose to forego making the scope adjustments (to adjust the line of sight) and physically compensate for the shot themselves (raising or lowering the rifle, offset the aim to the left or right). I’d like to think of it in terms of linear combinations in which we can express the zero of a rifle at a certain distance as a zero vector [0 0]. However, external conditions added (vector addition) to the zero vector would offset our shot. So, the adjustments can be represented as coefficients to the vectors going to be added such that when all these vectors are added altogehter (c1v1 + c2v2 + c3v3… cnvn), we eventually achieve our zero vector again, thus giving us a zeroed shot.

     

    Sources:

    • years obsessing over sharpshooting
    • ROTC Military Science 1, 2, 3 (RSCT), 31, 32, 41, 42
    • US Army Field Manual 23-10: Sniper Training
     
  • Theo Yap 12:40 pm on May 15, 2017 Permalink | Reply
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    “Two Halves of a Whole” – Bruce Lee 

    Chinese martial arts are famous/infamous since more than fighting, it presents itself as an art form and even a way of life.

    One of the key aspects of Chinese martial art is finding the balance within oneself. This balance may be physical, which can be training to the point that you have found your body’s rhythm and becoming one with your movements being almost untouchable or mental and emotional, finding the patience to greet life’s challenges with hope and dignity. Of course, the goal is to achieve both.

    On a more shallow note, the movements in one of my preferred fighting styles (Wing Chun) are symmetric; meaning the moveset for one side of your body is the same and can be applied to the other side. The training method the art is known for is the “Wooden Dummy Form” consisiting of 108 strikes. That is 54 strikes to the left side of the dummy and 54 mirrored strikes to the right. Likewise, single-performed forms also feature the “left-right, left-right” scheme of movement. Even sparring seems to mirror the “balance” that symmetry brings, having two participants mirror each other’s hand movements before they begin freestyle fighting, often which, moves that counter each other can also be treated as symmetric.

    Training both sides of the body makes for a more harmonized and stable fighting style; making stance and combat “natural” should you need to switch stance. I’ve noticed the same pattern in my “Level 1” form for Shaolin Kung Fu and other styles as well.

    In general, the symmetry of the physical aspect ultimately seeks the spiritual balance within oneself to prepare for both physical and emotional challenges.

    disclaimer: Kung Fu way of life, however helpful it may be, is still not to be treated as a substitute for real medical help. If you feel you are suffering something emotional or internal, please consult your doctor.

     

    Sources:

    • years of obsessing over martial arts
    • Ip Man rare footage (all 3 forms + Wooden Dummy Form): https://www.youtube.com/watch?v=0YnEm1zaUyE
    • Wong Shun Leung – Si Lum Tao (Wing Chun Form 1): https://www.youtube.com/watch?v=crmGYEvLVcw
    • Chi Sao (“Sticking Hands”) sparring: https://www.youtube.com/watch?v=GQEiwQG7Wfc
    • Lee, B. (1997, November 15). Bruce Lee Jeet Kune Do: Bruce Lee’s Commentary on the Martial Way. Clarendon, Vermont: Tuttle
     
  • Dana Redeña 9:00 am on May 15, 2017 Permalink | Reply
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    Fourier Transform in Submarines 

    Submarines (especially the first and early version ones) use a hydrophone, which is basically a microphone to collect sound waves underwater. And just like a regular microphone there could be all sorts of sounds and noise that you could collect. The tricky part now is to be able to filter the electrical signal output of the hydrophone in order to only listen to the sounds you want to listen to. This is especially important during battle whenever the submarine looks for enemy ships. In order to focus-in to the particular signal you are looking for, the electrical signal from the hydrophone is usually passed into several filters in order to single-out the certain frequency you want to hear (usually there are certain frequencies for each ship or submarine). The mathematical process for this analysis is the Fourier Transform and with the help of the early computers, they have used the Fast Fourier Transform algorithm in order to speed up the process.

    References:
    https://cadcammodelling.wordpress.com/2011/04/14/fourier-transform-and-its-applications/
    https://fas.org/nuke/guide/usa/slbm/ssbn-secure.htm
    US Nuclear Submarines: The Fast Attack by Jim Christley https://books.google.com.ph/books?id=N1ibCwAAQBAJ&pg=PA2&source=gbs_toc_r&cad=4#v=onepage&q&f=false

     
  • Michelle Dela Rosa 9:30 pm on May 14, 2017 Permalink | Reply
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    Speech recognition with Fourier Transform 

    Speech recognition is the capability of an electronic device to understand spoken words. [1]  It can be seen in devices that have options for taking in voice commands such as Apple’s digital assistant, Siri, which is voice-controlled.

    Fourier transforms are used to process the digital signals and analyze the frequencies of the speech sounds. Its output can be used to identify phonetic features [2], which in turn could be compiled and compared with a “phonetic dictionary” to identify what has been said. [3]

    Aside from speech recognition, some have also made studies on emotional recognition (related to speech recognition) that also makes use of Fourier transforms. The transforms are analyzed for emotional classification, noting the stresses in the speech that could be used to model the emotional state of a person. [4]


    Sources:

    [1] https://techterms.com/definition/speech_recognition

    [2] http://webservices.itcs.umich.edu/mediawiki/lingwiki/index.php/Fourier_transforms

    [3] http://www.explainthatstuff.com/voicerecognition.html

    [4] http://www.sci.brooklyn.cuny.edu/~levitan/nlp-psych/papers/koolagudi12.pdf

     

    Image from http://bgr.com/

     
  • Angel Furio 5:35 pm on May 14, 2017 Permalink | Reply
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    Dancing with Fourier Transform 

    [dibs: Swing dance and fourier transform]

    Lindy Hop dance is a kind of a swing dance that originated in 1930s. Some people believed that Lindy hop is physics. And that it can be observed in the flow of energy in the dance, the changes in the linear and angular momentum, as well as the friction made with the floor. They say that:

    “Lindy is 50% Newtonian physics, 30% musicality and 20% magic.”

    Lindy Hop’s basic movements are pulse and bounce. In the video, fourier transform is used to analyze if you are pulsing enough during the dance. By measuring the acceleration and taking its fourier transform, one can now see if you are dancing with the beat!

    The top graph in the video shows the magnitude of acceleration as function of time in seconds.
    The middle graph shows the fourier transform of the last 8 seconds of acceleration in the graph above it.
    The bottom graph shows the transform of all the data up to that point in time.

    The frequency plot is measured in beats per minute and has a peak at 161 bpm, which is the tempo of the song! 🙂

    References:

    http://dnquark.com/blog/lindy-science/

     
  • Jennie Ablog 3:57 pm on May 14, 2017 Permalink | Reply
    Tags:   

    Laplace transform in astronomy 

    The Laplace transform is a really powerful tool for processing and filtering data comprising of signals. A paper called On the interpretation of continuum flux observations from thermal radio source which was published in the Monthly Notices of the Royal Astronomical Society in 1974 discusses how to deduce the distribution of surface brightness of astronomical bodies from the spectrum of its total flux density by evaluating an inverse Laplace transform.

    Read the paper here: https://academic.oup.com/mnras/article-lookup/doi/10.1093/mnras/167.3.493

     
  • karen alarcon 11:19 am on May 14, 2017 Permalink | Reply
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    Fourier Transform on Audio Mixing and Analyzing 


    photo source: http://www.audioxpress.com/assets/upload/images/0/20160112070100_Waves-Audio-eMotionLV1LiveMixerFrontWeb.jpg

    If you are dealing with frequency analysis of the audio wave “quantitatively”, one of the best tools is FFT or Fast Fourier Transform. It is an algorithm to compute the Fourier transform equivalent of a time domain. [1]

    This highly advanced technique is very simple to understand, it simply converts a time domain function into a frequency domain function. [1]

    After audio mix down (where all sound of the instruments are cohesively combined into a single wave), the song is represented as a time domain function – as we can see that the x – axis of the wave is using a time element in hours: minutes: seconds (only minutes and seconds is used realistically). [1]


    photo source: http://img.brothersoft.com/screenshots/softimage/m/mixpad_audio_mixer-50050-1318575480.jpeg

    But time domain graph of the audio wave specially used during the mastering process of the track is simply a plot of amplitude (y-axis) versus time. Obviously you cannot see the frequencies of that wave. It is why we used FFT (Fast Fourier Transform) to convert this time domain representation into a frequency domain plot. With frequency domain, you can analyze the amplitude (y-axis) versus Frequencies. [1]


    photo source: http://static.kvraudio.com/i/b/audioxplorer.jpg

    Reference:
    [1] http://www.audiorecording.me/fast-fourier-transform-to-view-audio-frequency-spectrum.html

     
  • karen alarcon 7:05 am on May 14, 2017 Permalink | Reply
    Tags:   

    Symmetry in Complex Networks 

    Many real world networks are symmetric. In the research conducted by Ben McArthur, Sanchez-Garcia and Anderson, they’ve found out that a certain degree of symmetry is also ubiquitous in complex systems. They investigated the origin and form of real-world network symmetry and its effect on network function.

    Many networks – for example the internet and the world-wide web are “growing” (that is new vertices are added to the network over time). Generally any growth process which allows for new vertices to the network one at a time generally leads to a network with locally-tree-like regions. Such locally tree-like areas are common in real-world networks and their presence is important because while majority of large graphs are assymetric, it is common for large random trees to exhibit a high degree of symmetry, deriving from presence of identical branches about the same fork. Thus, we can expect that certain degree of tree-like symmetry to be present in many real-world networks. [1]

    Reference:
    [1] http://www.sciencedirect.com/science/article/pii/S0166218X08001881

     
  • karen alarcon 6:56 am on May 14, 2017 Permalink | Reply  

    Symmetry in Complex Networks 

    Many real world networks are symmetric. In the research conducted by Ben McArthur, Sanchez-Garcia and Anderson, they’ve found out that a certain degree of symmetry is also ubiquitous in complex systems. They investigated the origin and form of real-world network symmetry and its effect on network function.

    Many networks – for example the internet and the world-wide web are “growing” (that is new vertices are added to the network over time). Generally any growth process which allows for new vertices to the network one at a time generally leads to a network with locally-tree-like regions. Such locally tree-like areas are common in real-world networks and their presence is important because while majority of large graphs are assymetric, it is common for large random trees to exhibit a high degree of symmetry, deriving from presence of identical branches about the same fork. Thus, we can expect that certain degree of tree-like symmetry to be present in many real-world networks.

     
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