Visualize P formula and C formula

n:

r:

Permutation

Permutation is arrangement of a set things when the order in which they appear is important.

Taken 'r' things out of 'n' things at a time, it equals n! / (n - r)! which, in this case, is {{calculateP()}}

All permutations are: {{generatePermutations()}}

Combination

Combination is a set things where the order in which they appear is not important.

Taken 'r' things out of 'n' things at a time, it equals n! / (r! * (n - r)!) which, in this case, is {{calculateC()}}

All combinations are: {{generateCombinations()}}

Tags: Mathematical Foundations for Data Science,

Visualizing "What's Permutations" using Alphabets and JavaScript

Permutation is arrangement of a set things when the order in which they appear is important.

Taken all things at a time, it equals n! which, in this case, is

Check out all the permutations below:

Tags: Mathematical Foundations for Data Science,

Visualizing Permutation-Combination Problem Using JavaScript

Ques: Find the number of ways of distributing 8 identical balls in 3 distinct boxes so that none of the boxes is empty.

Ans: Let the number of balls in three boxes be X, Y and Z.
Below, the rounded corner rectangles are representations of boxes.

Browsers that do not support canvas show this message!

We see that X + Y + Z = 8 with X, Y, Z >= 1 and <=6.
If we put two sticks between 8 balls, is it an equivalent representation of the above scenario? 

The order (which stick you put first and which you put second) in which you select those two gaps is not important. And when the order is not important, it gives rise to "Combination". So from the above diagram, there are only 7C2 ways of doing it, that is the number of ways you can put two sticks in any of the seven gaps
between the eight balls.

You can play around with this experiment by clicking the green button.

Tags: Technology,Mathematical Foundations for Data Science,JavaScript,Web Development,

What are Hyperbolic Functions?

As Hyperbolic Function are expressions of "e", first we have to tell what "e" is:

The number e, also known as Euler's number, is a mathematical constant approximately equal to 2.71828 which can be characterized in many ways. It is the base of the natural logarithms. It is the limit of (1 + 1/n)^n as n approaches infinity, an expression that arises in the study of compound interest. It can also be calculated as the sum of the infinite series:



What are Hyperbolic Functions?

Tags: Mathematical Foundations for Data Science,

Index of Math Lessons

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Level 1

Counting

1. Counting Till 20 (Auto-reader)
2. Counting (Read it loud)
3. Counting as in Table of 10 (Auto-reader)
4. Counting Till 20 (Auto-reader) With Images
5. "Lesser Than, Greater Than" Exercise of Numbers

Addition

1. Learn Addition by Counting Sticks

Level 2

1. Learn Multi-Digit Addition by Counting Sticks
2. Detailed Solution to Upto Three Digit Subtraction

Level 7

Lowest Common Multiple

1. Lowest Common Multiple (LCM) of Two Numbers
2. Lowest Common Multiple (LCM) of Three Numbers

Highest Common Factor

1. HCF of Two Numbers Using Long-Division Method

Level 8

Rational Numbers

1. Adding two fractions using HCF

Level 11

Sets

1. Lesson 1 - Introduction to Sets (And visualization using Venn Diagrams)
2. Lesson 2 - Some more examples of Sets

Calculus

1. What are Hyperbolic Functions?
2. Derivatives of Hyperbolic Functions

Permutation and Combination

1. Visualizing Permutation-Combination Problem Using JavaScript
2. Visualizing "What's Permutations" using Alphabets and JavaScript
3. Visualize P formula and C formula

Derangement Theorem

1. Deriving Derangement Theorem
2. Problem on Derangement Theorem

Vectors

1. Cartesion and Polar Representation of 2D Vector

Level: Engineering

Matrices

1. Moore Penrose Pseudoinverse

Probability

1. Bernoulli Distribution and Binomial Distribution
2. Gaussian Distribution (or Normal Distribution)
3. Exponential Probability Distribution

Apps

1. Calculator

Tags: Mathematical Foundations for Data Science,Statistics