All notes
COMPLETE INDEX
15 notes across 3 tracks and 10 subjects, newest first.
Mathematics
11 notes in 6 subjectsTrack pageStructure, space and change, developed from definition to proof.
Here we discuss how quickly the infinite product of sums of squares increases.
Provide a new way of defining e from the tangent-line inequality.
A new proof classifying continuous non-constant solutions of f(x+y)f(x−y)=f(x)²−f(y)² using finite-dimensional translation spaces and Lie group projections.
An equivalent characterization of continuity for functions on A ⊆ ℝ: the preimage of every open set is open in the subspace topology.
Properties of so-called Taylor Forms, which are close to jet bundles.
Deriving the exterior derivative of a 1-form as a 2-form in Euclidean space.
Solving the Cauchy-type functional equation f(xy)=f(x)+f(y) under monotonicity assumptions, with extensions to weaker regularity conditions such as continuity and measurability.
When exponentials get larger by exchanging the two parameters
A solution for IMO 1992 P2
Two solutions for IMO 2002 P5
A technique for solving a functional equation with finitely many ratios
Physics
3 notes in 3 subjectsTrack pageMechanics, fields and quanta, with the mathematics each of them demands.
Analyze the sling by projection on the y-axis.
Derive the form of the catenary using the infinitesimal method.
Relationship between horizontal velocity and vertical velocity in horizontal projection with resistance.
Modeling & computation
1 note in 1 subjectTrack pageOptimisation, simulation and numerical models, with every assumption stated up front.
Balancing departure time and walking speed for a cafeteria visit: jointly minimizing queueing time, food quality loss, and penalties for excessive speed.
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