A Statement of Purpose (SOP) can be referred to as a document including all the blanket statements about an applicant’s life story. In other words, an SOP encompasses every relevant positives-and-negatives of the applicant’s academic life. An SOP, otherwise known as the Statement of Intent or Academic Statement, can be one, two, or three pages in length. The page-limit, ultimately, depends on the university or grad school that you are applying to; the lower the limit, the more concise and succinct your SOP has to be to cover all relevant minutiae in a single page. On the contrary, the longer…


Why do we need to create tables using commands and environments in LaTeX when someone already took the toll to generate the built-in functions that give out a beautiful user-interface (UI) to create tables to our satisfaction, like in Microsoft Word?

Literally, we are just a few clicks away from creating our own tables. Well, it is not always about coding, at times, it is about creating with one’s own satisfaction; also, sometimes complex tables, which make our MS word document fall apart all of a sudden, need special attention to not let the document go full bizarre. Although it…


So to initiate, we need to declare the type of document we want to have our project printed in; that is, whether we want an article or a book-type document.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}

Then, we need some packages to help the LaTeX compiler understand the lines we are going to write. \usepackage{amsmath}- this is the package we need to use some commands, such as double integral, triple integral, and many more. AMS stands for American Mathematical Society.

There are 2 ways to write mathematical expressions in LaTeX: 1. In-line Mode: $ . . . . . $ or…


(Prologue: In order to understand how mathematical formalism in Quantum Mechanics works, we have to get a good grasp on the Hilbert Space, and for that, we need to know what Space is in terms of mathematics before jumping onto the Hilbert Space. Although this is a detour chapter that mostly ignores the charming word ‘Quantum’, this will not fail to mesmerize you, for sure.)

Space is what we see around us. In a general context, space means some kind of distance; this can be verified when your fiance says, “I need some space. Don’t call or text me.” Jokes…


Quantum Mechanics- a hard nut to crack? Let’s break it down to its root words- Quantum and Mechanics. Let’s start with Mechanics; this is related to the mathematical formalism of things- from a grain of sand to the moon and so on- with which the whole universe can be described. Quantum basically refers to the smallest discrete unit of any physical property, such as energy or matter. So, a combination of these two words results in something that describes how everything in this world works; it is like a panacea for everything in this universe. In other words, QM describes…


HAL/S (High-order Assembly Language/Shuttle) is a programming language developed for NASA in the early 1970s by Intermetrics. HAL/S is regarded as one of the then real-time, high-level programming languages for onboard programs of Spaceflights. Almost 85% of the programs used in the Space Shuttle programs were written in HAL/S.

At the time of the emergence of HAL/S, almost every program of onboard spacecraft was written either in assembly languages or in interpreted languages. But the slowness of interpreted languages and the difficulty of writing programs in assembly languages made NASA come up with a new high-order language that can be…


Constants in big O notations are usually ignored because they don’t add much to the complexity when the input size is very large. But, they do have significant meaning when the input is small or when we want to make a comparison between different algorithms. Let’s discuss these two scenarios in this short-but-somewhat-useful treatise.

In my previous write-up, Big O Notation, I tried to present big O notations in a fathomable way. When we determine O( ) for an algorithm, we tend to ignore constants since when the input is very large, these constants don’t matter much.

Constants matter for the following cases:

Small Input Size:

Let’s take T(n)…


When we write an algorithm to get something done, the compiler takes up some resources from our computer to execute the code. These resources are not limitless and they should be checked so that minimal resources are taken within each execution. In this short article, we are going to traverse through the beautiful concepts of how we can speed up our algorithms if the input size is large for which the compilation takes a significant amount of time.

There’s a caveat here; we are not dealing with improving our code’s runtime, rather we are more concerned with how our code’s…


Think about a box comprised of people from a conservative cultural background that has been undergoing some changes due to the advent of external stimuli, such as, but not limited to, a foreign norm. Well, those people will start disseminating their own opinion on this new culture; some will accept and some not. This can hamper personal relationships among people within the community. For example, many will move from one social group or circle to another only to justify their stance. Don’t be so skeptical, it’s just a metaphor. …


We all know that one couch-potato who advertently does not tend to move out from the couch because of his exigency to binge-watch some trendy Netflix show. That’s fine, and I oftentimes make myself turn into this potato to absorb those fancies as well. Well, you know how to kickstart that person (assuming you are not the couch-potato).

So, you are applying Newton’s laws of motion, although it sounds enormously weir, to make someone move. Duh? Classical Mechanics!! You are kicking the atoms and molecules to move to a new position. They don’t move as much as they should’ve been…

Afnan Mostafa

Science-savvy

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