math-for-computer-science

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Find prime numbers in a range: Sieve of Eratosthenes

The sieve of Eratosthenes is an ancient and efficient algorithm for finding all primes numbers from 2 to n. This algorithm finds all the prime numbers in a segment using O(nlog⁡log⁡n) operations.

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Check if a number is prime or not: Primality Test

Given a positive integer n, write a program to check if the number is prime or not. A number n > 1 is said to be a prime number if 1 and n are its only factors. In other words, a prime number is a number that is divisible only by two numbers itself and one.

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The Birthday Paradox

The birthday paradox is strange and counter-intuitive. It's a "paradox" because our brain find it difficult to handle the compounding power of exponents. Real-world applications for this include a cryptographic attack called the "birthday attack".

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Visual Proof: The Sum of Important Mathematical Series

The summation formulas are used to calculate the sum of the sequence. In this blog, we have discussed the visual proofs: the sum of numbers from 1 to n (arithmetic series), the sum of infinite geometric series, the sum of squares of numbers from 1 to n, etc.

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Probability Theory For Machine Learning (Part 1)

Originated from the “Games of Chance,” probability in itself is a branch of mathematics concerned about how likely it is that a proposition is true.

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Find Square Root of a Number

Given a natural number n, find the largest integer less than or equal to √n. This can be seen as a search problem where the search space S is the set {1, . . . , n}, and the number desired is the floor(√n), i.e., the largest integer that is less than or equal to √n.

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Probability Distribution Function For Machine Learning

The Probability distribution lists the probabilities of the events that happened in any given random experiment. For example rolling a dice.

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Monty Hall Problem

There are 3 doors behind which are two goats and a car. You pick door 1 hoping for the car but don’t open it right away. Monty Hall, the game show host who knows what's behind the doors, opens door 3, which has a goat. Here's the game: do you want to pick door No. 2? Is it to your advantage to switch your choice?

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Find GCD of Two Numbers: Euclidean Algorithm

Given two non-negative integers, m and n, we have to find their greatest common divisor or HCF. It is the largest number, a divisor of both m and n. The Euclidean algorithm is one of the oldest and most widely known methods for computing the GCD of two integers.

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