Maths on Zymacs

Binomial theorem

Thu, 18 Jun 2026 08:09:50 +0300

Given the math problem (a+b)^2. You are required to expand it to its terms. There's different ways to go about this. One way is to multiply (a+b) into (a+b). That would give us a(a) + a(b) + b(a) + b(b) which would result in a^2 + ab + ba + b^2 which essentially is a^2 + 2ab + b^2. But what if we replace the power 2 with some bigger number, say, 4. It becomes an impractical task solving this with rudimentary expansion.

What is a combination

Thu, 18 Jun 2026 07:09:50 +0300

In previous posts I defined a permutation and a factorial. A combination is somewhat similar to a permutation. With a permutation, the order of arrangements matters. Which isn't the case with combinations. A combination 121 is the same as the combination 211 and 112. But those are three different permutations.

In some problems , the order of elements in an arrangement makes sense while in others it does not. Permutations matter for passwords. But if we are dealing with food mixtures, meat, chicken and beans would make up the same mixture as chicken, meat and beans.

What is a permutation

Thu, 18 Jun 2026 06:09:50 +0300

In a previous post I wrote about what a factorial is. Its the number of ways n distinct positions can be filled. Or, the number of ways n distinct elements can be arranged in n distinct positions.

Now the permutation. The number of elements is more than the number of positions to be filled or vice versa. If given 6 distinct elements, we need to find out how many ways we can fill up 4 distinct positions, that is a permutation.

What is a logarithm

Wed, 17 Jun 2026 15:09:36 +0300

This one will be simple. A logarithm is how many times you have to repeatedly divide some number by the denominator until the quotient is a one.

You have a number a that you divide by b and use the quotient as the next division operation's numerator. Carry on with the pattern till you get to a quotient which when divided by b you get one. The number of division operations is the logarithm to the base b of the number a.