Early Career Scientific Research Activities & Opportunities at AMMOC
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 brief list of very specialized research projects for middle school mentees of AMMOC is here.
Research Apprenticeship through Directed Reading Program (DRP)
It 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 honor 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 (a current student at Caltech on a full ride), joined AMMOC in January 2021, and she has committed to a 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.” Two weeks after her acceptance at Caltech, she received a FedEx package containing an admission letter and praise from Caltech: “We were really impressed by your research on classical theorems, and a copy of the same is shown alongside on the left and can be accessed here.
- Sarthak Dattatray Dhobale (a current student at Princeton on a full ride) joined AMMOC in October 2020. As a part of his senior thesis, he produced a highly scholarly piece of work: Study of Topological and Abstract Algebraic Structures.
- Prasanna Mahesh Pawar (received a full ride at KAIST (South Korea)) joined AMMOC in June 2021; as a part of his thesis, he wrote an expository research work at the heart of graduate algebra spanning groups, rings & modules, fields & Galois theory.
- Five other pupils, Shaurya Patil, Vibhu Konduru, Raeyaan Muppaneni, Parth Sakharam Andhare, and Sergei Makarevich, are undergoing research apprenticeships in various fields of pure mathematics.
- In addition to the core curriculum covering the IMO syllabus, groups, rings, fields, and vector spaces, here is a list of available research projects as “Advanced Directed Reading”—part of a high school thesis in the form of expository work:
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- Algebra—Chapter 0, Paolo Aluffi.
- Analysis in Metric Spaces using the textbooks written by Terence Tao & D.J.H. Garling.
- Multidimensional Real Analysis, using the textbook written by J.J. Dieustermaat. This is an abstract treatment of differentiation, the inverse & implicit function theorem, manifolds, and tangent space.
- Stokes’ Theorem and Whitney Manifolds, using the textbook written by Anthony W. Knapp. A soft copy is freely available at his website.
- Manifolds and Differential Forms, using the notes of Reyer Sajamar (Cornell). A soft copy is freely available at the website of Prof. Sjamaar.
- Differential Geometries of Plane Curves using the book with the same title written by Hilario Alencar.
- Basic Study of Different Kinds of Geometries: Euclidean, Projective, Spherical, and Hyperbolic [Dd]—written by A.B. Sossinsky.
- Fields and Galois Theory using the textbook ‘Basic Algebra,’ written by Anthony W. Knapp. A soft copy is freely available at his website.
- Introduction to Topology using the textbook with the same title written by V.A. Vassiliev.
- Study of Surfaces Almost everything you need to know’ by using the textbook written by Anatole Katok.
- Study of Matrix Group [Dh]—using the textbook with the same title by Kristopher Tapp.