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exercises/approximating-pi.md

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### Question - Approximating Pi
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### Theoretical - Approximating Pi
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The number π (pi) is a mathematical constant defined as the ratio of a circle's circumference to its diameter. This magical number appears in many formulas in all areas of mathematics and physics.
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Write a program which approximates the value of π
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### Answer - Approximating Pi
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### Practical - Approximating Pi
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There are a couple different ways of estimating π. I will use **[Monte Carlo Method](http://mathworld.wolfram.com/MonteCarloMethod.html)** with C programming.
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exercises/caesar-cipher.md

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### Question - Caesar Cipher
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### Theoretical - Caesar Cipher
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**Caesar Cipher** is one of the simplest and most widely known encryption techniques. It is a type of substitution cipher in which each letter in the text is replaced by a letter some fixed number of positions down the alphabet.
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You can watch this _[Khan Academy Video](https://www.khanacademy.org/computing/computer-science/cryptography/crypt/v/caesar-cipher)_ and read this _[article](http://www.cs.trincoll.edu/~crypto/historical/caesar.html)_ for more information.
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### Answer - Caesar Cipher
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### Practical - Caesar Cipher
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We read every character one by one using for loop in Python. Instead of using alphabet string I used Python's two build-in functions for shifting. ```ord()``` function converts character to its _[ascii code](https://theasciicode.com.ar)_ and the ```chr()``` function works vice-versa. Firstly we get the ascii number of the character, then add that shift value.
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exercises/fibonacci-finder.md

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### Question - Fibonacci Finder
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### Theoretical - Fibonacci Finder
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The Fibonacci sequence is one of the most famous formulas in mathematics. Each number in the sequence is the sum of the two numbers that precede it. So, the sequence goes: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, and so on.
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For more information check out _[this](http://mathworld.wolfram.com/FibonacciNumber.html)_ website and *[wikipedia](https://en.wikipedia.org/wiki/Fibonacci_number)* page.
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### Answer - Fibonacci Finder
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### Practical - Fibonacci Finder
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Here is a function which returns the index of the input number in fibonacci sequence. If input value is not a member of fibonacci sequence it gives -1.
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exercises/image-kernels.md

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### Question - Image Kernels
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### Theoretical - Image Kernels
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An **image kernel** is a small matrix used to apply effects such as blurring, sharpening, and edge detection. They are like ancestors of modern image processing techniques and even used today in machine learning for _feature extraction_, a technique for determining the most important portions of an image.
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If you want to learn more about image kernels, you can check *[wikipedia](https://bit.ly/2yfaapD)* page and _[this documentation](https://docs.gimp.org/en/gimp-filter-convolution-matrix.html)_ from gimp, also I certainly suggest you to look at _[this website](http://setosa.io/ev/image-kernels/)_ for visually explanation of image kernels.
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### Answer - Image Kernels
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### Practical - Image Kernels
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I will use Python for this solution. Before coding, we need to import _[numpy](https://docs.scipy.org/doc/numpy/user/whatisnumpy.html)_ and _[matplotlib](https://matplotlib.org/)_ modules to our program. Numpy enables us to perform fast operations on matrices. Of course we can write our program without using numpy but it would be much harder. Matplotlib actually a plotting library for python but we need it just for showing our filtered image.
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exercises/inverse-factorial.md

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### Question - Inverse Factorial
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### Theoretical - Inverse Factorial
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In mathematics, the **factorial** of a integer n, denoted by n!, is the product of all positive integers less than or equal to n.
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```
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### Answer - Inverse Factorial
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### Practical - Inverse Factorial
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We create a loop counting from one to infinite. And in every loop we check that if number can be divided without remainder and multiply the products until we reach to input value.
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exercises/linear-regression.md

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### Question - Linear Regression
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### Theoretical - Linear Regression
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todo
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### Answer - Linear Regression
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### Practical - Linear Regression
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```python
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import random

exercises/mass-spring-damper-simulation.md

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### Question - Mass Spring Damper Simulation
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### Theoretical - Mass Spring Damper Simulation
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todo
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### Answer - Mass Spring Damper Simulation
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### Practical - Mass Spring Damper Simulation
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```python
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import numpy as np

exercises/perlin-noise.md

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### Question - Perlin Noise
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### Theoretical - Perlin Noise
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[Perlin noise](https://en.wikipedia.org/wiki/Perlin_noise) is a random sequence generator producing a more natural, harmonic succession of numbers than that of the standard ```random()``` function. It was developed by Ken Perlin in the 1980s and has been used in graphical applications to generate procedural textures, shapes, terrains, and other seemingly organic forms.
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- [Working with Simplex Noise](https://cmaher.github.io/posts/working-with-simplex-noise/)
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- [Simplex Noise Demystified](http://staffwww.itn.liu.se/~stegu/simplexnoise/simplexnoise.pdf)
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### Answer - Perlin Noise
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### Practical - Perlin Noise
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[Here](https://gist.github.com/eevee/26f547457522755cb1fb8739d0ea89a1) is a Python implementation of Perlin Noise. You can examine that but for simplicity I will use [OpenSimplex](https://pypi.org/project/opensimplex/) package. Using this package, we can generate 2D, 3D and 4D simplex noise in Python.
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