Mathematics. Teaching. And Epsilon.

Journal of a solo mathematician
The graduateschool days are zooming away quickly from my life. It seems that the space of human memory is hyperbolic in nature. Things get thin and small at an exponential rate. I defended my thesis in July 2020 and reached India in August of the same year. The pandemic was in full swing. It was […]

Geometry problems in math olympiads
This is an ongoing survey of olympiad problems. Source material is INMO, USAMO and IMO. The goal is to indicate key ideas involved in the proof. USAMO 2010 Problem 1 Let $A X Y Z B$ be a convex pentagon inscribed in a semicircle of diameter $A B$. Denote by $P, Q, R, S$ the […]

How to teach mathematics : an experiment with triangular numbers and splitting of plane
Mathematics is all about the beauty of patterns and their reasonable connections. How about connecting patterns from seemingly different domains of the subject? This is a note borne out of a Geometry workshop at Cheenta where we tried exactly that. The audience comprised of 9 to 11 years old students. The purpose of this note […]

Game of Mario in Heisenberg group
Yesterday we were discussing the Heisenberg group in our weekly Geometric group theory workshop. The game of Mario came up! If you have not played Mario, then here is a the only thing you need to know. Mario can jump and hit floating bricks. These bricks may pop open to produce gold coins. The method […]

Not far not near groups
We use \(NFNN\) as an abbreviation for ‘not far not near’. Annulus \(A(w, r, R)\) in a metric space \((X, d)\), for \(w \in X, 0 < r < R < \infty \) is defined as the set \[A =\{ x \in X  r \leq d(w, x) \leq R \} \]. Definition Suppose \(P\) […]

About the ‘Creative Math’ Project
Creative Math project is an attempt to create books and resources useful for children who have an inclination for mathematics. It introduces nonroutine math, olympiad styled problems in an interdisciplinary style.

Geogebra model for hyperbolic isometries
The goals of this GeoGebra model are the following: 1) Input a hyperbolic isometry of the hyperbolic plane using the matrix representation. In other words input a real matrix with determinant 1 and trace more than 2. 2) Programmatically draw the axis. 3) Mark any point P on the hyperbolic plane (upper half plane) 4) […]

Protected: Tameness 1
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Dunwoody’s accessibility theorem – Talk Day 4
This is a personal musing. Possible errors, uncredited excerpts lie ahead. We constructed sequence of equivariant maps \(f_k\) from the universal cover \( \tilde {X} \) to the sequence of refinements \(T_k\). The construction was complete up to the 1skeleton. We want to extend the maps to 2skeleton in a certain way. To motivate the […]

Cut points in Bowditch Boundary of Relatively hyperbolic groups 2
Understanding Swenson (large excerpt.. some diagrams .. some remarks). Please be cautious. Potentially wrong remarks lie ahead. Continuum A continuum is a compact connected Hausdorff space. Cut Point In a continuum Z, \( c \in Z \) is a cut point if \( Z = A \cup B \) where A and B are nonsingleton continua and \( A \cap B = \{c\} \). If in addition \( D \subset […]
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