This blog offers a concise overview of several algebraic structures commonly encountered in theoretical computer science and graduate-level mathematics. It is intended as a convenient reference for essential definitions, while also providing insight into the relationships among these structures.

“A drunk man will find his way home, but a drunk bird may get lost forever”- Shizuo Kakutani. This blog explains why the mathematician, Shizuo Kakutani, said so through amazing interactive visuals simulating random walk.

Can one implement Fourier transform on a quantum computer? Can this help us decompose our music into fundamental frequencies even faster? What if I say the answer to the former is ‘yes’ but latter is ‘no’. Read this blog post to know why and how.

Is the Discrete Fourier Transform (DFT) the most efficient classical approach? Can we find a faster algorithm for computing the Fourier transform? And what if I told you this also leads to a quicker way to multiply polynomials? This blog dives deep into these questions and more!

Have you ever wondered how noise cancellation in earphones works or how music editors remove unwanted overtones from a composition? This blog post introduces fast discrete transform.

As ingenious as RSA is, Shor’s Algorithm is equally remarkable—with the potential to break it and disrupt modern secure systems. This blog post offers a detailed and engaging introduction to Shor’s Algorithm, exploring its implications for cryptography.

Have you wondered how security is ensured in communication channels? When we use Instagram or chat with a friend in WhatsApp, it says end-to-end encrypted. How is this achieved? This blog post gives an introduction to one of the most widely used cryptographic systems, the RSA.

Given any problem, is it always possible to develop better or faster methods to solve it? Is there such a thing as the best method for solving a problem? If so, how can one determine which method is the best? And finally, when should one decide to stop searching for an even better or faster way to get to the solution?

This blog offers an intuitive and engaging introduction to various algorithmic lower-bounding techniques, presented in a playful and interactive manner that anyone—even without a mathematical background—can grasp. The follow-up post will delve into the mathematics behind elegant lower-bounding techniques.

An Intimidating puzzle, which leads to exploring projective geometry…

How can we mathematically describe a quantum algorithm? Can quantum advantage help reduce the query complexity to a significant level? What is a quantum oracle? In this blog, I will address these and many other questions about Quantum Query Complexity.

Like many other models of computation, can we add the power of randomization to decision trees? Can this reduce the number of queries? How can we define randomized query complexity? This blog post answers these questions and discusses randomized query algorithm, introducing it from two different lenses.

This is a introduction to Query Complexity Model (also known as Black Box Model). This blog will specifically focus on deterministic algorithms in query model.

What is computation? In loose terms, computation is making a physical device (a computer) do some task for us. Things that are hard for humans can be easily done on a computer. So, can computers do anything and everything? Are there things that are hard even for computers? If so, how do we quantify the hardness? Computational complexity theory tries to answer these and even more interesting questions. I would like to give a short bird’s eye view of the field in this blog post.

This is a note on a powerful algorithmic technique called Dynamic Programming

A problem from the textbook Sanjoy Dasgupta, Christos H. Papadimitriou, and Umesh Vazirani. 2006. Algorithms (1st. ed.). McGraw-Hill, Inc., USA.; Chapter 6, problem 6.5. I have rephrased the problem and provided an elaborate solution.