Combinatorics Combinatorics – Filling vacant spaces In the last article, we have tried to solve some combinatorics problems from our own intiuition. It’s all how you use multiplication and addition. We saw why n! gives us the number of ways to arrange n distinct objects. We also developed a notion of filling vacant spaces. This idea of filling January 2, 2020January 15, 2020

Combinatorics Introduction to Basic Combinatorics Combinatorics is a branch of mathematics which is about counting. Here we are concerned with problems which basically ask the total number of ways to do something. Combinatorics is just a fancy word for counting techniques. Combinatorial problems have attracted the attention of mathematicians since December 1, 2019January 2, 2020

Number Theory Prime Factorization using Sieve Method In the previous article, we’ve seen how we can calculate the prime factorization of a single number. Today, we’ll focus on how we can efficiently find factorization in a range . If you understand the sieve algorithm to find prime numbers, you’re good to go. In case you don’t October 17, 2019December 30, 2019

Number Theory The Unique Prime Factorization Theorem The fundamental theorem of arithmatic states that any number greater than 1 can be represented as a product of primes and this form of represenation is unique. Remember factoring integers in grade school? That’s exactly what we’re talking about. Now we’ll see two proofs which’ October 6, 2019January 2, 2020

Number Theory Sieve of Eratosthenes – Generate prime numbers In the last article about prime numbers, I discussed about different types of primilarity test and Trial division method to verify if a number is a prime. If you haven’t read that yet, here is the article, Prime numbers and basic primilarity test. In this article, we’ll focus on sieve of August 30, 2019December 30, 2019

Number Theory Prime numbers and basic primilarity test A prime number is a integer greater than 1 and has no positive divisors other than 1 and itself. 1 is neither prime nor composite. The set of positive integers can be divided into three classes, primes, composites and a unit (1). For example, 5 is prime because the only ways of writing it as August 14, 2019December 30, 2019