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Simpson Rule for Definite Integrals Simpson Rule for Definite Integrals
Simpson's rules are numerous approximations for definite integrals in numerical analysis, named after English mathematician Thomas Simpson (1710−1761). In calculus, basically, there are two ways to approximate the value of an integral, Reimann sums and Trapezoidal sums. However, calculating the value of an integral, we need to compute the areas of a zillion rectangles or more to get a better result. Therefore, we use Simpson's Rule, which is a way to approximate integrals without having to deal with lots of narrow rectangles.
2021-06-09 Mathematics
Numerical Analysis Integrals
Develop Strategy for Tic-Tac-Toe Develop Strategy for Tic-Tac-Toe
Tic-tac-toe is a paper-and-pencil game for two players, X and O, who take turns marking the spaces in a 3×3 grid. The player who succeeds in placing three of their marks in a diagonal, horizontal, or vertical row is the winner. It is a solved game with a forced draw assuming best play from both players. In this article, I want to discuss whether there's a must-win strategy for this game.
2021-04-01 Mathematics
JavaScript Mathematics Strategy
Cube Root of 9 Digit Number in Your Head Cube Root of 9 Digit Number in Your Head
In this article, I will show you how to find the cube root of 9 digit number. This is a very effective way of finding cube root of such high numbers. If you practise rigorously, you can do it in 10 seconds!
2021-03-24 Mathematics
Mathematics Mental Arithmetic
Tower of Hanoi Puzzle Tower of Hanoi Puzzle
Tower of Hanoi is a mathematical puzzle where we have three rods and n disks. The objective is to move the entire stack to another rod, and follow some simple rules.
2021-03-23 Mathematics
Python JavaScript Mathematics
Python Sudoku Solver Python Sudoku Solver
Sudoku is a logic-based, combinatorial number-placement puzzle. In classic sudoku, the objective is to fill a 9×9 grid with digits so that each column, each row, and each of the nine 3×3 subgrids that compose the grid (also called "boxes", "blocks", or "regions") contain all of the digits from 1 to 9. The puzzle setter provides a partially completed grid, which for a well-posed puzzle has a single solution.
2021-03-19 Mathematics
Python Javascript Algorithm
A Proof that e is Irrational A Proof that e is Irrational
In this article, I'll try and show that e, sometimes called Euler's number, is an irrational number 2.718281828459045.... Euler's number is a fantastic number, and it plays a role in just about every aspect of physics, maths, and statistics. There are many ways of calculating the value of e, but none of them ever give a totally exact answer, because e is irrational and its digits go on forever without repeating.
2021-03-17 Mathematics
Mathematics Euler's Number
Eigenvectors from Eigenvalues Eigenvectors from Eigenvalues
This article is about implementing "Eigenvectors from eigenvalues" of Terence Tao's paper using Python and R. It's a amazing work and mathematics contribution from Terence Tao. It is an elegant non-evident result, which makes me so excited about it!
2021-03-15 Mathematics
Python R Linear Algebra
Estimate π on π Day Estimate π on π Day
Happy π Day 2021! In this article I'll estimate the digits of π with random numbers and the probability of two integers being co-prime. What is the probability of two random integers being coprime? Euclidean Algorithm can be used to estimate π!
2021-03-14 Mathematics
Python Linear Algebra Probability
Demystify Matrix Decomposition Demystify Matrix Decomposition
The most important application for decomposition is in data fitting. The following discussion is mostly presented in terms of different methods of decomposition for linear function.
2021-01-29 Mathematics
Python MATLAB Linear Algebra
Laplace Expansion and Chiò Condensation Laplace Expansion and Chiò Condensation
Determinants are mathematical objects which have applications in engineering mathematics. For example, they can be used in the solution of simultaneous equations, and to evaluate vector products. Determinants can also be used to see if a system of $n$ linear equations in $n$ variables has a unique solution. There are several ways to calculate determinant, however, today I'm going to introduce another way of computing determinants Chio Identity.
2021-01-28 Mathematics
Python Linear Algebra
Missionaries and Cannibals Problem Missionaries and Cannibals Problem
This is actually one of my project when I was in college during my "Mathematical Programming" class. I used R programming language to solve missionaries and cannibals problem with matrix analysis and graph theory.
2021-01-27 Mathematics
R Linear Algebra
Quality of Search Engine - PageRank Quality of Search Engine - PageRank
Web search engines such as Google.com distinguish themselves by the qualtiy of their returns to search queries. I will discuss a rough approximation of Google's method for judging the qualtiy of web pages by using PageRank.
2021-01-26 Mathematics
MATLAB PageRank