There are three tracks of studies available at AMMOC – Rigorous pre-college mathematics – divided into Middle School & High School, introduction to UG mathematics, and research projects.
AMMOC is an extremely demanding curriculum for mathematics instruction. Both new and returning students must maintain a significant level of hardwork and perseverance. Students who have had at least a year to study high school mathematics in proof style are the only ones admitted to AMMOC. We don’t consider any students with some immediate goals.
Program overview
Textbooks for foundational studies – Year I & II (HS)
Textbooks for Year III
Textbooks for Directed Reading Courses
Directed Reading is only available to very advanced and select mentee(s) who have already finished core courses of regular 3 years program
- Mathematics and Culture in Russia
- Golden Years of Moscow Mathematics
- Read the steps in writing a rigorous mathematical proofs.
Education in the foundational pre-college Mathematics
- Religion of Rigor & Proofs – Transition to Pure Mathematics. In this course we cover [in a quarter]
- Sets & Logics
- Techniques of proofs – Induction, Direct Proofs, Proof by Contrapositive, Proofs by Contradiction
- Equivalence relations, Partitions, functions, infinite sets & cardinalities
- Euclidean Geometry of Triangles & Circles.
- Elementary Number Theory
- Introductory Combinatorics
- Topics in Algebra & Analysis on R
- A suitable list of such books that AMMOC have been using since its creation in 2020, can be accessed here. Note that many of these books are “problem oriented” and therefore, rigorous and detailed theoretical supplements needed to solve these problems is what constitutes the core of Golovanov’s lecture for mentees at AMMOC.
- Details of syllabus that we cover for grade VI – X is documented here.
Apprenticeship in pure Mathematics courses for pre-college students under the regular 3 years intense program
- 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” – Dummit & Foote and
- “Contemporary Abstract Algebra” – Joseph Gallian.
Currently the most advanced protege – Sarthak Dattatray Dhobale [mentee of AMMOC since 2020] has already finished these courses.
Directed Reding Course ( not for everyone !)
- 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 kind 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.