Mathematics & Physics Notes
Begin with intuition.
Arrive at something checkable.
A notebook on structure, space, and change — and on the physical world those ideas describe. Mathematics, physics and computational modeling are developed side by side: exposition and derivation written in Typst, proofs checked with Lean 4, and small models you can rerun yourself.
Mathematics
Structure, space and change, developed from definition to proof.
Latest IMO 1992 P2
3 notes · 3 subjectsPhysics
Mechanics, fields and quanta, with the mathematics each of them demands.
Latest Velocity in Horizontal Projection with Resistance
1 note · 1 subjectModeling & computation
Optimisation, simulation and numerical models, with every assumption stated up front.
Latest Optimal Departure Time and Walking Speed for the Cafeteria
Real analysis
Limits, continuity and the structure of the real line, with the counterexamples that shape them.
Latest Infinite Product of Sums of Squares
1 noteTopology
Open sets, continuity and the invariants that survive deformation.
Latest Continuity
2 notesGeometry
Differential forms, curvature and the calculus of smooth spaces.
Latest Taylor Form
1 noteLie theory
Groups, their linearizations, and the symmetry behind functional equations.
Latest Cover Linear
1 noteInequalities
Comparisons and bounds between quantities, and the estimates that make each one rigorous.
Latest Exchanging Exponentials
3 notesProblems
Olympiad problems and functional equations, with complete solutions and Lean formalisations.
Latest IMO 1992 P2
Dynamics
Forces, momentum and energy, and how an equation of motion is set up and solved.
Latest The Frequency of the Sling
1 noteStatics
Equilibrium of forces and moments, and the conditions under which nothing moves.
Latest Derivation of the Catenary Equation
1 noteKinematics
Position, velocity and acceleration described first, before asking what causes the motion.
Latest Velocity in Horizontal Projection with Resistance
Recently added
Newest firstOne intuition, one derivation, one verification at a time.
Gathering what I learn, leaving a trail for the next idea.
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