Topics
- Astrophysics 1
- Calculus 2
- Classical Mechanics 17
- Complex Dynamics 1
- Differential Geometry 2
- Fluid Dynamics 1
- Fourier Analysis 2
- Geometry 1
- Linear Algebra 2
- Number Theory 5
- Numerical Methods 4
- Olympiad Problems 2
- Python 2
- Quantum Mechanics 2
- Research 12
- Statistical Mechanics 1
- Statistics 1
- Thermodynamics 1
- Three-Body Problem 12
By level
Every article carries a level badge describing the background it assumes.
Introductory
Accessible to mathematically minded secondary-school students.
- Plotting and Visualising the Three-Body ProblemJun 2024
- Linear Regression with OLS and SGD in PythonJun 2024
- Solving Systems of Congruences: The Chinese Remainder TheoremJun 2024
- Wilson's TheoremJun 2024
- Vieta Jumping and Infinite Descent: IMO 1988 Problem 6Jun 2024
- A Brief Introduction to Bose and Fermi GasesJun 2024
- Euler's Totient Function, the Carmichael Function and Carmichael NumbersJun 2024
- Overview of the Two-Body ProblemFeb 2024
- Kepler's Third Law and the Virial TheoremDec 2022
Undergraduate
Assumes the first two years of a mathematics or physics degree.
- Problem of Two Fixed Centres (Part III)Jul 2024
- Classifying and Finding New Possible Orbits (Part I)Jul 2024
- Problem of Two Fixed Centres (Part II)Jul 2024
- Ellipses and the Two-Body ProblemJun 2024
- Symplectic IntegratorsJun 2024
- The Discrete Fourier Transform and the FFT: A Worked ExampleJun 2024
- Image Processing with Python and the Convolution TheoremJun 2024
- Thermodynamic Potentials and Maxwell RelationsJun 2024
- IMO 1990 Problem 3: Lifting the Exponent and Fermat's Little TheoremJun 2024
- Evaluating Integrals with the Laplace TransformJun 2024
- Theorema Egregium: Why Every Flat Map Is WrongJun 2024
- Why Is Momentum Conserved?Apr 2024
- Julia Sets and the Mandelbrot SetMar 2024
- Pendulum Models for Liquid SloshMar 2024
- Tensors and Their TransformationsFeb 2024
- More on Multivariable CalculusOct 2023
- Two Particles Falling Together Under GravityAug 2023
- The Shell Theorem: A Gravitational Analogue of Gauss's LawJul 2023
- Plane Crash Problem: How Long Does It Take to Fall?Jul 2023
- Perturbations in Quantum MechanicsJan 2023
- Perturbations in Classical MechanicsJan 2023
- Conservation Laws in Physics: Noether's TheoremDec 2022
Advanced
For students specialising in mathematical or theoretical physics.
- Proving the Figure-Eight Orbit Exists: Action Minimisation on the Shape SphereJul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part II)Jul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part I)Jul 2024
- Understanding and Visualising the Shape SphereJul 2024
- Problem of Two Fixed Centres (Part I)Jun 2024
- The Third Fundamental Form and How to Find ItJun 2024
By topic
Astrophysics
Calculus
Classical Mechanics
- Problem of Two Fixed Centres (Part III)Jul 2024
- Proving the Figure-Eight Orbit Exists: Action Minimisation on the Shape SphereJul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part II)Jul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part I)Jul 2024
- Problem of Two Fixed Centres (Part II)Jul 2024
- Understanding and Visualising the Shape SphereJul 2024
- Problem of Two Fixed Centres (Part I)Jun 2024
- Ellipses and the Two-Body ProblemJun 2024
- Why Is Momentum Conserved?Apr 2024
- Overview of the Two-Body ProblemFeb 2024
- Tensors and Their TransformationsFeb 2024
- Two Particles Falling Together Under GravityAug 2023
- The Shell Theorem: A Gravitational Analogue of Gauss's LawJul 2023
- Plane Crash Problem: How Long Does It Take to Fall?Jul 2023
- Perturbations in Classical MechanicsJan 2023
- Conservation Laws in Physics: Noether's TheoremDec 2022
- Kepler's Third Law and the Virial TheoremDec 2022
Complex Dynamics
Differential Geometry
Fluid Dynamics
- Pendulum Models for Liquid SloshMar 2024
Fourier Analysis
Geometry
- More on Multivariable CalculusOct 2023
Linear Algebra
Number Theory
- Solving Systems of Congruences: The Chinese Remainder TheoremJun 2024
- Wilson's TheoremJun 2024
- Vieta Jumping and Infinite Descent: IMO 1988 Problem 6Jun 2024
- IMO 1990 Problem 3: Lifting the Exponent and Fermat's Little TheoremJun 2024
- Euler's Totient Function, the Carmichael Function and Carmichael NumbersJun 2024
Numerical Methods
Olympiad Problems
Python
Quantum Mechanics
Research
- Problem of Two Fixed Centres (Part III)Jul 2024
- Classifying and Finding New Possible Orbits (Part I)Jul 2024
- Proving the Figure-Eight Orbit Exists: Action Minimisation on the Shape SphereJul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part II)Jul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part I)Jul 2024
- Problem of Two Fixed Centres (Part II)Jul 2024
- Understanding and Visualising the Shape SphereJul 2024
- Problem of Two Fixed Centres (Part I)Jun 2024
- Ellipses and the Two-Body ProblemJun 2024
- Symplectic IntegratorsJun 2024
- Plotting and Visualising the Three-Body ProblemJun 2024
- Pendulum Models for Liquid SloshMar 2024
Statistical Mechanics
Statistics
Thermodynamics
Three-Body Problem
- Problem of Two Fixed Centres (Part III)Jul 2024
- Classifying and Finding New Possible Orbits (Part I)Jul 2024
- Proving the Figure-Eight Orbit Exists: Action Minimisation on the Shape SphereJul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part II)Jul 2024
- Sundman's Power Series Solution to the Three-Body Problem (Part I)Jul 2024
- Problem of Two Fixed Centres (Part II)Jul 2024
- Understanding and Visualising the Shape SphereJul 2024
- Problem of Two Fixed Centres (Part I)Jun 2024
- Ellipses and the Two-Body ProblemJun 2024
- Symplectic IntegratorsJun 2024
- Plotting and Visualising the Three-Body ProblemJun 2024
- Overview of the Two-Body ProblemFeb 2024