“With mathematics we stand precisely at that intersection of freedom and bondage that is the essence of the human itself ” – Hermann Weyl (Mathematician)

*At AMMOC, we practice exactly one ritual that “Mathematics is our fashion, faith, and fantasy. In particular, mathematics is our intellectual necessity and this same belief is perpetually permeated in protégés of AMMOC – A math circle devoted to rigorous academic development & mathematization of its pupils. “In this world, identifying and fostering pupils interested in the pursuit of fundamental sciences is the noblest of endeavour” – Yaashaa Golovanov (Director & Founder)*

Vision and Mission

**AMMOC** is an “advanced pre-college math and science circle” for the cultivation, nourishment, and continual advancement of early scientific and mathematical talents. It is a systematic & rigorous academic development program. The vision of AMMOC is to create mathematicians, physicists, and computer scientists in the same way as math circles (working physically) did in USSR, Hungary, Romania, Bulgaria, and other Eastern European nations. To achieve this, AMMOC is on a mission “to teach elementary mathematics from the advanced standpoint and advanced mathematics from the elementary standpoint” to middle and high school students. With our vision and mission in mind, the contents of seminars at AMMOC are as “ancient and rigorous” as Axiomatic Euclidean Geometry, Inversion and Projective Geometry, Pigeonhole principles, Inequalities, Algebraic properties of Integers, axiomatic construction of an ordered field and “introductory and modern” as Group, Rings, Integer Polynomials, Fields, Vector Spaces, Theory of Graphs, Games and Generating Functions, Algebraic Number Theory, rigorous Calculus/Analysis, Functional Equation, Galois Theory, Riemann Surfaces, Knot Theory, Metric Topology, and Theory of Classification of Surfaces.

More specifically,

**A**ttract pre-college pupils in their grades VI-XI and prepare them with fundamental knowledge in proof-theoretic mathematics, problem-solving skills, improve their proof writing abilities, and attain scientific maturity while deriving joy in whatever they do with us.*When one meditates upon the scientific contributions of mathematicians and scientists educated in Eastern European circles during twentieth century, one witnesses everlasting role of mathematical maturity which they had achieved before entering universities.*At AMMOC, we want to impart such education that would further participants’ grasp of diverse branches of Mathematics with their applications in problem solving. We share the conviction of our heroes Vladimir Arnold and Jerrold E. Marsden that such teaching to high school pupils will initiate them to a lifelong love for the joy of discovery and critical thinking. “AMMOC is an instance of such schema of how to start such a noble pursuit of cultivation of future scientists and academicians.”

**M**athematics is treated as a sport at AMMOC. Therefore, preparing, mentoring, and persuading mentees to win medals in top math contests like Caltech Math Meet, Stanford Math Tournament, IMO, EGMO, AMC/AIME/USAMO, COMC, and CEMC serves as a strong barometer of growing understanding of our circlers (participants are known so !). Additionally, winning math contests also validates and multiplicate the faith of circlers in themselves. Moreover, we impart education as an intellectual art and cognitive necessity.**Therefore, even for such a noble, rigorous, and artistic pursuit, math contests serve as a stage for pupils to showcase their talent and earn an identity. Permeating these early scholastic qualities and academic ambitions, helped us to convince, prepare, and eventually succeed in creating young protégés and aspiring mathematicians**Tisya Chandrashekhar Rawat, Konstantinos Charalampous, Adelina Patlatii, and Sarthak Dattatray Dhobale. These four fellows of the inaugural class 2020-23 and the instructor, Yaashaa P. Golovanov, of our program continually inspire the incumbent participants to emulate the same early scholarly trajectory.

**M**entor our protégés for “**guided early career research**” and inspire them to choose mathematics/fundamental sciences as their career path. In this way, “we bridge the gap between professional studies in mathematics, where abstraction is the theme, and pre-college mathematics, where merely application is the theme.**This aspect of “guided early career research” was strongly validated by professional mathematicians at the CALTECH when admission committee sent a**“letter of exceptional appreciation” to Tisya for her research project with the title – “Proof of some classical theorems of number theory using Group Theory“. This was one of the most ambitious scientific task which tisya carried out under the supervision of her mentor Yaashaa P. Golovanov. Moreover, the**Office of Admissions at the**University of Chicago**wrote a**letter of appreciation**for the founder of AMMOC, Yaashaa P. Golovanov**, appreciating “his tireless work as an educator and that his students are lucky to have a teacher who works hard and cares for the academic advances of his pupil”. This appreciation is reinforced by the very fact that protégés of the inaugural class 2020-23,*who participated in seminars/lectures daily for several hours*, have received admission offers with “**full scholarships**” to study**undergraduate degrees in Mathematics, Physics, and Computer Sciences**from prestigious institutions CALTECH, UChicago, UCornell, UWisconsin (Madison), UToronto , UWaterloo, Reed College, ICL(UK), UAmsterdam, Columbia University, SUNY Stonybrook, CUNY, & Rensselaer Polytechnic Institute

**O**nline functioning of AMMOC gives it the unique standing as a leading program of its kind because the very conception of it is an outgrowth of the meditation on mathematical maturity of matriculating high school students applying for higher studies in mathematics at top universities. University mathematicians are often critical of the abilities of the current generation of incoming students for UG in Mathematics. Generally, people interpret comments of professional mathematicians as “that there should be more material in the syllabus”. However, in reality, “their concern is more subtle than this plain misinterpretation”. AMMOC is committed to mathematizing its protégés to a standard, professional mathematicians of top universities look for in incoming students.**The protégés of the inaugural class of AMMOC have academically impressed even those several top mathematicians who have delivered invited lectures at the**International Congress of Mathematicians and quoting Wikipedia itself, being invited to talk at the ICM has been called “the equivalent … of an induction to a hall of fame” and is the highest honor for any professional mathematician. At AMMOC,

- The standard of rigor in writing proofs, academic impetus, vision, and feel that instructor Yaashaa P. Golovanov provides, to our small select number of pupils from around the world, through his completely online seminars, is at par with those happening in best offline math circles, run by professional mathematicians, in North Americas, Mainland China, and Eastern European nations.
- Our senior high school mentees learn theoretical mathematics (covering until the first two years of undergraduate mathematics) and concrete applications in problems solving of various international math contests at the school and university levels. Lectures of AMMOC have theoretical contents and problems of uncommon difficulty level and will challenge the ingenuity of any research mathematician.

**C**reation of mathematical abilities of students and its continual advances – Every theorem, problem, and definition begins with an attempt at the end of participants. In encouraging them through guided discovery of their proofs of classical theorems, we permeate and culminate

- mathematization in their thought process,
- ingenuity and creativity, and
- cognitive endurance.

Culmination of these traits in pupils, while learning at AMMOC, give them a sense of happiness and an idea of a culture of scientific life ahead of them. **Therefore, we don’t measure the mathematical abilities of students. Instead, we create and continually advance these traits. Three protégés of AMMOC, Tisya, Adelina, and Konstantinos received invaluable mentorship on college selection and research projects in fields like Group Theory, Algebraic Number Theory, and Combinatorics.** Moreover, Tisya and Konstantinos continue to prepare for PUTNAM Competition with their mentor Yaashaa Golovanov.