Imagine!

WELCOME TO THE WORLD OF

Md Faiyaz Siddiquee Taaroop

Taaroop (তরূপ), originally an archaic Bangla word, means "the best version of oneself".

I hope everyone will benefit from this comprehensive digital repository of my original published research papers, expository notes, unique problem formulations and solutions, and lecture videos with accompanying notes in Mathematics, Physics, Astrophysics, and Computing. The platform is completely open-access, disseminating my ideas and approaches as an enthusiast in the mathematical and physical sciences across borders.

All educational resources here are and will be free for all, in hopes of inspiring everyone to entertain the philosophy of science and be the best version of themselves.

Additionally, the platform contains some of my musical performances and original compositions on the piano and guitar, which I hope you will enjoy.

Feel free to reach out if you have any queries.

Hello there! I am Md Faiyaz Siddiquee Taaroop, a 12th-grader interested in Mathematics, Physics, Astrophysics, and Programming. Throughout most of high school, I have dedicated a significant part of my time to exploring concepts and solving problems that I found intriguing in my fields of interest. I have been enthusiastically participating in various National and International Olympiads in Math, Physics, Astronomy, and Programming, securing merit positions in many of them. Additionally, I love working on research problems within my grasp and pondering about the possibilities of learning much beyond what the classroom offers.

Publications

Encompasses all of my publications to date, be it my book 'A Quest for Clarity', my math research papers, conference presentations, or competition submissions.

Mathematics

This is probably the page closest to my heart on this website and has been so since its inception. The expository notes in their finalised forms encapsulate not only the countless hours spent behind them, but also my interpretations and synthesis of the concepts I learn (read this for my motivation behind how and why to do math for fun). One particular instance I can recall was when I finished my 20-page-long exposition and derivation of the function describing the Gaussian distribution days before my IGCSE secondary board exams! Ranging from explaining my visual understanding of integrals of inverse functions to deriving the exponential forms of the hyperbolic trig functions (which I wished popular textbooks included), this page is where you will find a good sample of my true self for the past 4 years. And, before you leave, don't forget to amuse yourself with an 'integral' limerick!

Physics

Contains unique problem ideas (many with solutions); some of the problems are computer problems, requiring the construction of an algorithm. Expository notes range from intriguing ideas I gathered from my Olympiad experiences, like finding the tipping point of an egg, to more self-driven explorations such as deriving an expression for g from an infinitely bouncing ball.