Appreciation of our research works
Caltech appreciates the research work of AMMOC’s proteges – Tisya Chandrashekhar Rawat – a freshman at the Caltech with full scholarship and major in mathematics, class of 2027.
A bried list of research projects for mentees of AMMOC. The pdf file elaborating upon pre-requisites for these projects is here.
Research Apprenticeship through Directed Reading Program (DRP)
Db]—writtenDb,KindsIt humbles us to say that the research works and projects of mentees of AMMOC have impressed even mathematicians at Caltech. It is a matter of honour that even top mathematicians, who were invited as speakers at the International Congress of Mathematicians, appreciate the projects and work of mentees of AMMOC.
- Protégée, Tisya Chandrashekhar Rawat, joined AMMOC in January 2021, and she has committed to UG double major in Math & Physics at CALTECH for the class of 2027. She received a full scholarship at CALTECH. She did a research project with her mentor Yaashaa Golovanov with the title “Proof of some classical theorems of number theory using Group theory.” After two weeks of her acceptance at CALTECH, she received a FedX package containing an admission letter and a praise from Caltech: “We were really impressed by your research on classical theorems, and a copy of the same is shown alongside in the left and can be accessed here.
- Sarthak Dattatray Dhobale joined AMMOC in October 2020. He has won over 50 international honors and distinctions in the prestigious international contests of the USA, Canada, Australia, and Southeast Asia. Since October 2021, his name has appeared several times on the website of the University of Waterloo for his stupendous performance in mathematical contests conducted by the University of Waterloo. In the last year he has produced a highly scholarly piece of work, Study of Topological and Abstract Algebraic Structures.
At the present, we are running directed reading courses.
- Apprenticeship in Analysis on the real line [Ca] from textbooks
- “Analysis I” by Terence Tao and
- “Analysis I” by Vladimir Zorich
- Abstract Linear Algebra from the textbooks
- “Linear Algebra” by Georgi Shilov and
- “Linear Algebra & Geometry” by Yu. I Manin
- Introduction to Modern Abstract Algebra [Cc]—Groups, Rings, and Fields from the textbooks
- “Abstrcat Algebra” by Dummit & Foote and
- “Contemporary Abstract Algebra” – Joseph Gallian.
- Metric Spaces, Continuous Function, and Uniform Convergence [Da]—Chapter I-III in Analysis II of Terence Tao.
- Multidimensional Real Analysis: Abstract Treatment of Differentiation Inverse & Implicit Function Theorem, Manifolds, and Tangent Space [Db] – written by J.J. Dieustermaat.
- Differential Geometries of Plane Curves [DC] written by Hilario Alencar.
- Basic Study of Different Kinds of Geometries: Euclidean, Projective, Spherical, Spherical, Hyperbolic [Dd]—written by A.B. Sossinsky.
- Galois Theory [De]—written by M.M. Postnikov
- Introduction to Topology [Df]—written by V.A. Vassiliev.
- Study of surfaces [Dg]: Almost everything you need to know—written by Anatole Katok.
- Study of Matrix Group [Dh]—written by Kristopher Tapp.
Currently the most advanced protege, Sarthak Dattatray Dhobale, is learning Da, Db and De.