International Math & Physics Summer Camp
Thank you for your interest in the International Math & Physics Summer Camp (IMPSC). I am Dr. Shubhrangshu Dasgupta, a Professor of Physics at the Indian Institutes of Technology (IIT) and the Head Director of both IMC and IMPSC. It is our pleasure to offer this opportunity for high school students in collaboration with the esteemed professors at IIT.
We are organizing a summer camp for students who show exceptional promise in mathematics and physics. Over three weeks of intensive physics and mathematics classes, we aim to provide substantial support to those planning to pursue degrees in science and engineering.
Thank you.
Head Director
Dr. Shubhrangshu Dasgupta
IMPSC was established by Professor S. Dasgupta, a Physics professor at the Indian Institute of Technology (IIT) Ropar campus. It is an online summer camp designed to provide high school students with intensive education in college-level Physics and Math, which are typically not accessible in school, over a three-week period.
Classes are conducted by professors and PhDs from the Indian Institute of Technology (IIT), and daily assignments are checked, with students required to make presentations.
Eligibility: Students in grades 9–12 worldwide who are capable of communicating in English and were born before August 2011.
Camp Participation Fee: $2,900 (Payment instructions will be sent to personal email upon acceptance).
We define Topological spaces and importants invariants (homotopy and homology) and see how these invariants help us understand the real world via data analysis.
| Timeline | Topology Topics | Physics I (Classical Mechanics) |
|---|---|---|
| Day 1 | Continuous functions, argument | Projectile motion |
| Day 2 | Open and closed sets (in metric spaces) | Potential energy and stability |
| Day 3 | Topological spaces (basis, product/subspace topology) | Simple harmonic oscillators |
| Day 4 | Quotient spaces and quotient topology | Damped harmonic oscillators |
| Day 5 | Classification of Surfaces; cutting and pasting | Forced damped harmonic oscillators |
| Day 6 | Basics of Group theory, Topological troup | Resonance |
| Day 7 | Homotopy of paths, Fundamental group | Central force |
| Day 8 | Covering spaces and Fundamental group of circle | Equation of orbits |
| Day 9 | Fundamental proof of algebra, Homotopy overview | Three dimensional rotation |
| Part II. Applications and Dynamics | ||
| Day 10 | Operations on spaces and Homotopy Equivalence | Inertia tensor |
| Day 11 | Complexes, Simplicial and Singular homology | Inertia tensor in different coordinate system |
| Day 12 | Introduction to Homological Algebra | Equation of motions, symmetric top |
| Day 13 | Computation of Homology, Mayer-vietoris Sequences | Calculus of variations |
| Day 14 | Introduction to clustering methods | Euler's equation and Lagrangian dynamics |
| Day 15 | Persistence homology and landscape | Examples of Lagrangian dynamics |
| Day 16 | Statistics with Persistence landscapes | Hamiltonian equations |
| Day 17 | TDA I: Financial Crisis prediction | Coupled oscillators |
| Day 18 | TDA II: Brain network application | General coupled oscillators |