Yaashaa Golovanov

As, it is evident that my mathematical heroes are Vladimir Igorevich Arnold and Jerrold E. Marsden. When it comes to teaching mathematics, I stick to Arnold's teaching philosophy and I practice them religiously. I agree to each and every of his views documented in Arnold's views on Teaching Mathematics. For more details on my undergraduate and graduate teaching visit this page

Directed reading project for my proteges at AMMOC (2023 – )

My teaching is either for the IMO or running graduate and undergraduate level courses as directed reading projects for my advanced highschoolers and my proteges who have joined universities. My current focus are two very devout student of pure mathematics

Sarthak Dattatray Dhobale – The most advanced high schooler that I have nurtured, taught and mentored in my life. He is an incoming student for UG in pure mathematics at Princeton on a full scholarship. You can read news about his success here.
Nihad Hashimov, a protege of AMMOC and an incoming freshman for UG in pure math at KAIST, where he has received the full scholarship.
Prasanna Mahesh Pawar, a senior in the high school who is undergoing intense training in graduate level algebra and UG level analysis.
Sergei Makarevich, an incoming highschooler at AMMOC for study of UG course on Rings and Module.
Nihad

Teaching of Graduate & UG courses (2018 – 2020)

I did conduct regular voluntary advanced mathematics seminar for courses listed below. Participants were from my alma mater NIT Allahabad and Harish Chandra Research Institute.

An Introductions to Proofs – This course, either in brief or in details, I teach to everyone whosoever participates in my seminar. This courses is completely need based and largely deals with art of proofs and applications of theorems of mathematics that have appeared in various mathematical contests – Berkley’s Problems book in Mathematics, Polya’s – How to solve it, Hungary Mathematics Contest, Stanford Mathematics Problem Book, IMO problems, University of Toronto Undergraduate Mathematics Competitions.
A rigorous foundational course in function of real variable (Participants : Dr. S. Manikandan, Samrat Kadge, Nitish Kumar, Ram Singh Yadav, Ujjwal Verma),

The list of textbooks that we read cover to cover –

Theory of continuous functions in normed linear and metric spaces (Participants : Dr. S. Manikandan, Samrat Kadge, Nitish Kumar, Yuri. R. Mikhyalov, Ujjwal Verma).

The list of textbooks that we read cover to cover –

Elementary real Analysis in Metric Spaces, textbook Shilov’s Elementary Real and Complex Analysis
Terence Tao’s Analysis II
Mathematical Analysis: Linear and Metric Structures and Continuity

Differential Calculus in Normed Linear Spaces (Participants : Dr. S. Manikandan, Ph.D and Dr. Ebtsam H. Taha)

The list of textbooks that we read cover to cover –

A classical Book Cours de calcul différentiel by french Mathematician Henri Paul Cartan
A beautiful treatise on theory of differentiation in euclidean spaces entitled Multidimensional Real Analysis (I) by Johannes Jisse (Hans) Duistermaat
Namely the chapter “differential calculus in Banach Spaces” from a beautiful book Foundation of Modern Analysis by Jean Dieudonne
A standard material on subject of Differential Calculus in Topological Linear Spaces. This note sheds lot of light upon the various problems related to definition of derivative in different types of underlying spaces. One can think how to give definition of a derivative in spaces with no notion of usual metric/distance function.
One article of interest is Various Definitions of Derivatives in Linear Topological Spaces published in Russian mathematical survey.
Two significant and perhaps first of theirs kind text are Sternberg’s & Loomis – Advanced Calculus and Steenrod, Spencer, Nickerson – Advanced Calculus. These two books shaped mathematical thought of many leading mathematicians.

An introduction to exterior algebra (Participants : Dr. S. Manikandan, Ph.D and Dr. Ebtsam H. Taha)

The list of textbooks that we read cover to cover –

First five chapters in Greub’s Multilinear Algebra
Advanced Calculus by H.K Nickerson, D.C. Spencer, N.E. Steenrod

Group Theory, Ring Theory (Using Language of Category Theory and textbook was Paolo Aluffi’s Algebra.
- Participants : Dr. S. Manikandan, Ram Singh Yadav, Ujjwal Verma. Last two participants being MSc students from NIT Allahabad)

Ordinary Differential Equation – one of the most beautiful book on subject and written by Russian mathematician and my mathematical hero V I arnold . Participants (Participants : Dr. S. Manikandan)

Manifolds, Tensor Analysis and Applications from a book with same title written by Jerrold E. Marsden, Ralph Abraham, Tudor Ratiu. Marsden is my other mathematical hero and anything that he has written and researched upon is of very close interests to my scientific teaching and research.