11/08/2017
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Ever since school, we are fighting a never ending battle with mathematics. We Despise it . Loathe it . Want to get rid of it . But that just seems impossible . Well , let me tell you a matrix joke(assuming you at least heard about linear algebra) . And here I quote
βWe can only understanding matrix when we learn it without using any matricesβ
Our college professors obscure even the basic math . Why you may ask . In my case, our professor came to be a college professor because he couldnβt get any decent job elsewhere .Without any delay , lets get right into business and try to uncover the delight of various areas of math .I not only want to give you practical insight of math but also show you way to implement these math in Programming.
for now ,Letβs discuss these two important fields of Math (considering how heavily they are applied in Machine learning and Neural Networks)
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I donβt know where to start describing about how miraculous linear algebra actually is . Wanna listen to a Algebra pun ? .I am going to say it anyways .
βRelationships are like algebra . You look at your X and wonder Yβ
Lets see its applications :
-Computer Graphics heavily deploy linear transformations .Ever wondered the mechanics of movement of game characters . If your game involves the position of an on-screen button, the direction of a camera, or the velocity of a race car, you will have to use vectors. The better you understand linear algebra, the more control you will have over the behavior of these vectors.
-Algorithms implementation : Although it sounds out of context , its really isnβt. For computer, everything is numbers . Linear algebra helps to manipulate large numbers as vectors(1D arrays) ,matrices and tensors . If it were not for matrix multiplication, we can literally forget faster implementations of sophisticated algorithms .
-Digital Image Processing/Computer Vision : Now I mentioned matrices, Image processing is likely to come. Image is just and 2 dimensional array of numbers .Videos are sequence of images displayed in a second . Ever wondered how Snapchat puts those ridiculous filters , or , Facebook detects your photos automatically . Believe it or not , If it were not for linear algebra (and statistics), that would not be possible.
If you want to learn linear algebra intuitively, I suggest you to watch these VIDEOS before reading and books and getting bored with looking βnumbers inside boxesβ.
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For anyone who get overwhelmed by calculus, I have just one word . If you fully grasp the concept of graph plotting , nothing will make more sense than calculus.
Lets get over its applications in real life :
We have the ability to find the effects of changing conditions on a system. By studying these, you can learn how to control a system to make it do what you want it to do. Because of the ability to model and control systems, calculus gives us extraordinary power over the material world. It has wide application in Physics,Geology,space Science etc. but for now , lets see how it appends to computer science.
Long story short , understanding basic calculus algorithms opens doors to others branches of mathematics like optimization/minimization.We minimize a cost function and get the best possible solution. Thatβs how YouTube suggest us with videos, Amazon suggest us books etc.
In a nutshell, itβs all about that PREDICTION!!!. No trouble .
itβs all about that PREDICTION!!! . No Troubleβ¦β¦PUN INTENDED
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If you donβt get this, donβt worry. This article intent was just to give you glimpse of mathematics . Just remember this. Everything with Machine Learning , Deep learning and stuffs that are todayβs buzz words requires intuitively getting linear algebra,calculus,probability( I donβt think i should overwhelm you with Bayesian Theory, I plan to have a separate blog for that ) and Curve-fittings.
Whatβs so fascinating with Mathematics? Ever since school, we are fighting a never ending battle with mathematics. We Despise it . Loathe it . Want to get rid of it . But that just seems impoβ¦
