Mathematicians have obsessed over prime numbers for centuries, and will continue to do so for the foreseeable future. Prime numbers are so enigmatic and fascinating that mathematicians just can’t stop thinking about them! Prime counting function is probably one of the most famous problems in this domain. This function simply counts the number of prime numbers less than or equal to a given number. Pretty straightforward! But why is this of such great importance? What are we going to do with this information? Continue reading

# What Is Bayesian Information Criterion?

Let’s say you have a bunch of datapoints and you want to come up with a nice model for them. We want this model to satisfy all the points in the best possible way. If we do this, then we will be able to use a mathematical formula to extract information about unknown points. At the same time, we should make sure that we don’t overfit our model to these datapoints. If we overfit our model, then it will tune itself too much to our datapoints and perform poorly on unknown data. So how we pick the best model? Where do we draw the line? Continue reading

# How To Add Swap Space On Ubuntu

Whenever you are building an application that’s memory intensive, you are bound to run into memory issues. Those out of memory errors are painful to deal with, especially when they happen during production. Before putting your code on your server, you need to make sure that it can handle the application’s memory requirements. But even if you are careful, something might still go wrong and you might end up running into memory issues. One of the easiest ways to deal with this is by adding some swap space. Now how will it help our case? How can we use it on Ubuntu? Continue reading

# Why Are They Called “Elliptic” Curves?

Have you heard of elliptic curves before? They are used extensively in number theory and cryptography. The reason elliptic curve cryptography is gaining popularity is because it’s fundamentally much stronger than the RSA algorithm, the algorithm that we all love and adore. If you don’t know what elliptic curves are, just google it and see what they look like. You are reading this sentence without googling it, aren’t you? Okay I’m going to assume that you know what elliptic curves look like. Do they look anything like ellipses? No! So why are they called “elliptic” curves? Continue reading

# What Is External Sorting?

Sorting is one of the most common things we do in programming. We are given a bunch of numbers and we want to arrange them according to some rule. Let’s say we want to arrange them in ascending order. To sort these numbers, people tend to use a sorting algorithm that takes place entirely within the memory of a computer. The memory we are talking about is the RAM. Here, we take all the numbers and store them in the memory so that we can sort them. This is possible only when the amount of data is small enough to be stored in the memory. What if we have a hundred trillion numbers to be sorted? It’s too big to be stored in the computer’s memory. How do we do it? Continue reading

# What Is A Holomorphic Function?

How do you feel when see the term “holomorphic function”? It just feels like we shouldn’t be looking further into it, right? I mean, it looks like an esoteric mathematical concept that should remain in advanced textbooks. Interestingly enough, holomorphic functions are very useful in real life. Holomorphic functions are ubiquitous in the field of complex analysis. Just to clarify, “complex analysis” doesn’t refer to an analysis that’s complex or difficult. Instead, it refers to analysis of functions of complex numbers. Alright, so let’s go ahead and see how something like this can possibly be useful in real life, shall we? Continue reading

# How Do We Know That There Are Infinitely Many Prime Numbers?

There is a very famous theorem which says that there are infinitely many prime numbers. For people who are new to this, a prime number is a number that doesn’t have any divisors except for 1 and itself. For example, 11 is a prime number because it doesn’t have any divisors apart from 1 and 11. On the other hand, 12 is not a prime number because it is divisible by 1, 2, 3, 4, 6, and 12. Now how do we know that there are infinitely many primes? As numbers get bigger, they tend to have more divisors. So may be at some point, all the numbers can possibly start being composite and they will have a lot of divisors, right? We can delve into a deep mathematical proof to prove this, but let’s take a different route. Let’s see if we can prove this with logic, shall we? Continue reading