# The Right Wrong Way

One overarching interest of mine is to understand how problems are solved. Core to this issue is the other question: what do we mean by "understanding" itself? A problem rarely "lives" by itself - it co-exists in the neighborhood of other similar problems, some easier, some harder. To my mind, understanding a problem principally involves understanding this neighborhood, creating a rich fabric of related problems. More often than not, it is a wrong approach that leads us to the correct approach to solving a problem. At times, it is a matter of enumerating wrong approaches, while there may be more efficient ways of ruling out approaches that lead to dead ends. Spending the time on wrong approaches can also be thought of as engaging with the problem on a deeper level in order to really understand what does work for solving the problem. This blog will primarily consist of discussions of various problems/algorithms/papers equipped with wrong approaches, hopefully guiding us to the correct view of a result.

I will be organizing my writings into a couple of categories, depending on the target audience:

• Expository articles with a focus on high-school mathematics. One of my strong beliefs is that mathematics does not need to be hard - it becomes hard when it stops being play. These articles are an effort to rekindle that spirit of play that underlies exploration and search for beautiful ideas in mathematics.
• Articles on data science, machine learning and programming. As a component of understanding "understanding", it is important to tease out the simplest parts that constitute the whole of a mathematical argument, to see the interplay between the various argumental pieces. These writings are aimed towards that goal, to elucidate the underpinnings of familiar algorithms/techniques.
• Paper Discussions. This is my humble effort to engage with, and understand the papers I am going through currently. I am hoping also to accompany the discussions with code walkthroughs when appropriate.

Newest blog article: Applications of Fubini

In this short note, we discuss and dissect a program for generating all the combinations of a collection/set of $n$ characters, $r$ at a time. For $r$-combinations of $n$ objects, the program will generate all $n \choose r$ combinations.

Created 19 March 2017.

In this note, we discuss a determinantal identity and proceed to prove it. En route, we also show that the square of a number of the form $(a^3 + b^3 + c^3 - 3 a b c)$ is also of the same form.

Created 23 March 2017.

In this short note, we present and explain Simpson's paradox based on the simplest examples possible.

Created 8 June 2017.

We present and describe Fubini's principle. We also provide short (and hopefully sweet) examples/illustrations of the method.

Created 15 June 2017.

We break up the steps involved in computing the following integral: $\int e^x \sin x \, dx$.

Created 13 July 2017.

Short notes on the Pointer Net paper. Coming soon.

Short notes on the Attention is all you need paper. Coming soon.

In this note, we discuss the confluence of two of my favorite topics - submodularity and summarization as in this paper.

In this note, I present some of the underlying ideas and considerations that did not make the cut in this FSTTCS12 paper.

In this note, we describe the considerations that led to the formulation of GRUs. Coming soon.

### Articles:

The following consists of some surveys or observations in the course of reading various papers. These are more like notes on specific papers rather than surveys. These short notes are largely informal; at times they are a study of a specific part of a paper. Constructive comments (such as better ways to view a result, mistakes in understanding points of the papers) are welcome. The writing of these notes is primarily for purposes of clarification of my own understanding. At some point I would like to revisit these and clean/incorporate these in the blog above, but for now I will leave the pdfs on here.

Copyright for all of these short notes belongs solely to the author. Some of these notes were made using TeXmacs.

In this note, we show how to understand and derive Hölder's inequality via the powerful technique of Lagrangian Relaxations.

This contains notes on this seminal paper by Borodin, Linial and Saks. We end the notes by extracting a cute puzzle involving randomness from the paper.

Free-form notes on Bregman divergences and insights/intuition about the same, along with applications to the four-point inequality.

Last updated 14 June 2017.