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 -

• 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. The file of my solutions to problems of this classic textbook is here. 

• Access copy of my solution to exercise of "Category Theory - Paolo Aluffi's  "ALGEBRA - Chapter 0", Graduate studies in Mathematics, AMS. 

• My own solutions to problems on "Honors level Abstract Algebra" textbook by Dummit and Foote" can be accessed here. 

• My own solutions to problems on "Honors level Linear Algebra" textbook by Friedberg & Spence" can be accessed here. 

• "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. 

Minor Directed Reading Projects -

• Axiom of Choice and its applications - This is an evolving projects on understanding various equivalent forms of it and application in Groups, Rings, Function Theory, Vector Spaces & Linear Maps. This is one of the most profound axioms of theoretical mathematics. Pls find my latest write up here.

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

Mathematical Reflection - a prestigious journal of Recreational Mathematics -

• In recent July Issue of this journal, I published solutions to NINE Problems. The solution file is here.

Solutions to Caltech Math Meet Paper -

• In 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.