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Ideas, derivations and stories from the classroom

Blog posts on education, learning and teaching, written for parents and teachers. In-depth articles on pure mathematics.
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On how children learn and how teachers teach: pedagogy, classroom ideas and practical tips for school and home.
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PDF articles

In-depth PDF articles

Pure mathematics, written in depth. Each article takes one problem or idea and works it through to the proof. They open as PDFs in Google Drive.
PDFCombinatorics

Stirling Numbers and Bell Numbers: Counting Partitions, Cycles and Equivalence Relations

How many equivalence relations does a set have? Count its partitions: Stirling numbers, Bell numbers and Dobinski’s formula.
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PDFCo-ordinate Geometry

One Definition, Three Curves: Common Properties of Conic Sections

One focus–directrix law, SP = e·PM, proves the shared properties of the parabola, ellipse and hyperbola at once.
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PDFCo-ordinate Geometry

Frégier’s Theorem in Coordinate Geometry: Proofs, Formulas, and Problem Solving

Chords making a right angle at a conic concur at a fixed point on its normal.
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PDFCalculus

Checking Differentiability by using Continuity of Derivative

A quick, reliable test for differentiability at a point, with its limits.
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PDFTrigonometry

Unifying Trigonometric Finite Products and Sums

From roots of unity to logarithmic derivatives: one method for many classic results.
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PDFCombinatorics

Uncoupling the Circle: Lucas’s Problème des Ménages

Solving the ménage problem with inclusion–exclusion.
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PDFNumber theory

Why Functional Symmetry and Term-by-Term Comparison Fail to Prove the Riemann Hypothesis

Where a tempting line of argument breaks down.
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