Open Problem Solving Library
Free mathematics, physics, competitive programming, and astronomy resources for learners, educators, and Olympiad students.
Featured Resources
Quantum Theory
Quantum physics from wave-particle duality to the Schrödinger equation.
Category Theory
Functors, natural transformations, and universal properties.
General Relativity
Einstein field equations, spacetime curvature, and applications.
Vieta Jumping Extension
Non-linear Root Flipping and Surface Orbits — original research.
Graph Theory Handbook
BFS, DFS, shortest paths, MST for competitive programming.
The Gliding Principle
Moving Points on Conics and Beyond — original geometry research.
Dynamic Programming
DP techniques from classic problems to advanced optimizations.
Entropy-Minimal Noise Schedules
Thermodynamics approach to diffusion probabilistic models.
📐Mathematics
Algebra, geometry, number theory, combinatorics, and analysis — from fundamentals to research.
Problems
Resources
Comprehensive applied mathematics reference.
An introduction to category theory.
Analytic Continuation and the Limits of Generalization.
Coordinate Geometry and Circles.
Circle Problem Solving.
Basic Combinatorics.
Advanced combinatorics techniques.
Basic EigenVectors.
Introduction to general relativity.
Introduction to graph theory.
Generating functions and Legendre polynomials.
Basic note on modular arithmetic.
Power of point and radical axis.
Introduction to projective geometry.
Introduction to tensors.
Intro to jacobians.
Moving Points and Beyond.
Introduction to functional equations.
Mathematical models of warp drives.
Mathematical models of wormholes.
⚛️Physics
Classical mechanics, electromagnetism, thermodynamics, quantum physics, relativity, and astrophysics.
Handouts
Basic Physics Concepts and formulae.
Basic Physics Concepts and formulae.
Basic Astrophysics Concepts and formulae.
Mechanics and Oscillatory Systems.
Basic Physics Concepts and formulae.
Astrophysics Concepts and formulae.
Quantum Physics Concepts.
Special and general relativity.
Collaboration notes on celestial energy.
Collaboration class notes.
Collaboration class notes.
Collaboration class notes.
💻Competitive Programming
Algorithms, data structures, and problem-solving techniques for programming contests.
Handouts
Comprehensive handbook on algorithms.
Number theory concepts for CP.
Graph theory concepts and algorithms.
Techniques and applications of greedy algorithms.
DP techniques from basics to advanced.
String matching and pattern recognition.
🔭Astronomy
Astrophysics, cosmology, observational astronomy, and space exploration.
Built because a student in Bangladesh should have the same access to quality STEM education as a student anywhere else. All materials free, open-access, and yours to use.