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.

• Indian protégée, Tisya Chandrashekhar Rawat (a current student at Caltech on a full ride), joined AMMOC in January 2021 for exceptionally high-paced and rigorous training spanning 3-4 hours per day for a period of two years. She is a current student at Caltech, where she received a full ride. She did a research project with her mentor, Yaashaa Golovanov, with the title “Proof of some classical theorems of number theory using Group theory.” This work received an honorable mention from the Caltech admissions committee–“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:
  • Analysis on 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, tangent space, and manifolds.
  • 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 Groups by using the textbook with the same title by Kristopher Tapp
  • Elementary Real Analysis by using the textbook with the same title by Andrey Kolmogorov
  • Complex Analysis by using the textbook with the same title by Richard Silverman.
  • Ordinary Differential Equations by using the textbook with the same title and written by our mathematical hero, Vladimir Arnold.
  • Foundation of Mechanics using the textbook with the same title by Jerrold Eldon Marsden and Ralph Abraham
  • Topics in differential geometry and global analysis by using the textbook with the same title by Peter W. Michor.
  • Topology by using the textbooks primarily taught in Poland and written by preeminent Polish topologists. Currently, the most advanced protégé in the current cohort of pupils, Parth Sakahram Andhare, is learning this profound text. 

  Two of the most advanced protégés, Prasanna Mahesh Pawar (at KAIST on a full ride) and Sarthak Dattatray Dhobale (a freshman at Princeton), did read some of these directed reading courses. They both received full rides at their respective universities. Moreover, the senior pupils who graduated from AMMOC continue to receive academic support and mentorship if they are in need of the same.