The links to the appropriate PDF files of my ongoing research projects are highlighted. I'm typing each one of them. Every project on this list is changing and being updated on a daily basis. Return often to find out more about the situation. I'll finish them all by the end of September, and I have at least 250 more pages to typeset in Latex, per my discussion with my research director and mentor Yaashaa Golovanov. 

Major Directed Reading Projects -

• Study of Topological and Abstract Algebraic Structures [165 pp and last updated on January/02/2025]. 

• Problems and Solutions in Fields [25 pp and last updated on January/02/2025]. 

• A copy of handout on Group theory and Rubik's cube [6 pp, updated January/02/2025]

• My handout on the Axiom of Choice, its various equivalences and application across the spectrum of mathematics - like, Baire Category theorem, existence of maximal subgroup, maximal ideal, right inverse for a surjective map, basis for every vector spaces, well ordering theorem, Zorn's lemma. [6 pp, updated January/02/2025]

• Abel's Theorem through problems and solutions - Lectures of V. I. Arnold. This is basically understanding of lectures that were delivered in Moscow by one of greatest mathematician of last century, Vladimir Arnold. I solved 198 problems of this book. 

• Access copy of my solution to exercise of "Category Theory - Paolo Aluffi's  "ALGEBRA - Chapter 0", Graduate studies in Mathematics, AMS. I am yet to type solution of the section 'universal properties' though I have written them in my notebook. 

• "Rigorous Analysis in Euclidean Spaces" from textbook of Terence Tao, Georgi Shilov, J.J. Duistermaat, and Lynn H Loomis & Shlomo Sternberg. -  Participant - Me, Tisya Rawat (Freshman @Caltech), Adelina (Sophomore at U. of Toronto) and Rama Chunduri (A third year student at the UCSD).  

• Study of "Matrix Group for Undergraduates" - Reading project & typing solutions to exercises given in this book with the same title. 

• Enumeration via Group Action & Burnside Lemma - a project that unifies 3 important topics. The project is evolving however, current updates can be read here. 

Publications in Mathematical Reflection - a prestigious journal of Recreational Mathematics. 

• In July and September Issue of this journal, I published solutions to eighteen problems. The solution file is here. 

Solutions to Power round of team contest CMM'24(Caltech), BMT'24 (Berkeley) and PUMAC'24(Princeton). 

• Solution to Power round of Berkeley Math Tournament'24. The subject of this team tournament was Origametry. The team members were Medha Shrivastava, Prasanna Pawar, Kaushik Kashyap, Nihad Hashimov, and myself. 

• Solution to the Power round of Princeton University Mathematics Tournament. The subject of this team tournament was Measure Theory and Fractals. The team members were Medha Shrivastava, Prasanna Pawar, Nihad Hashimov, Kaushik Kashyap, and myself. 

• n January 2024, AMMOC Team, with Darsan (my classmate at AMMOC Math Circle) as registered leader participated in Caltech Math Meet. There were six members and I was senior most among them. The syllabus was too advanced drawing contents from UG & Upper UG courses like Character & representation Theory, Groups, Vector spaces etc.  There were total 6 chapters. However, despite I putting efforts and discussing lot with my team mates, they found it difficult to understand 58 pages paper. So, I worked chapter 2, 3, 4 all myself and chapter 1 was Collaboration between me & Medha (a 10th grade mentee of AMMOC Circle), however, it was largely done by Medha Shrivastava. We attempted total 145 marks out of 343 and were credited 111/343 won TOP three rank worldwide. However, for next round we could not participate as it was a physical exam, thanks to virtual first round & 3 weeks time to do the task . Despite missing physical round, we stood overall top 12 in the world ! I consider this is most important mathematical contest that I have ever written ! 

• My hand written solution which we submitted on behalf of AMMOC team towards CMM paper are here Chapter 2, Chapter 3, and Chapter 4. Chapter 1 was done by my fellow math circler Medha Shrivastava of AMMOC. I have collaborated with her on other tournaments as well and most notably Stanford Math Tournament.