The sessions introduced projective geometry, covering its axioms, duality, homogeneous coordinates, projective plane (affine plane + line at infinity), transformations, cross ratio, and applications in graphics, vision, architecture, and art.

Resources :

• Geometry Revisited
• Introduction to Geometry
• Euclidean and Non-Euclidean Geometry: Development and History
• Hartshorne: Algebraic Geometry — best read alongside:
  • Shafarevich’s Basic Algebraic Geometry
  • Mumford’s Complex Projective Varieties
  • Harris’s Algebraic Geometry: A First Course

Presented by Bhavi and Smitali

The session introduces number theory, covering the Well Ordering Principle, induction, divisibility, Euclidean algorithm, modular arithmetic (including CRT and Fermat’s Little Theorem), continued fractions, Pell’s equation, totient and Möbius functions, and cryptographic applications like RSA encryption.

Resource :

• Elementary Number Theory by David M. Burton

Presented By Arjun Arunachalam and Swaminath Shiju

This is based on combinatorics. Permutations, combinations, counting with repetitions, inclusion-exclusion principle, pigeon hole principle and a questions based on them.

Resource

• Enumerative Combinatorics: Volume 2 by Richard P. Stanley
• ▶️ Watch: Catalan Numbers – Visual Explanation

Presented By Ayaan Nawaz