MathLex

MathLex

Ptolemy's mathematical lexicon — 64 interactive lessons. Each lesson covers definition, geometric intuition, relational analysis (density / pull / attraction), three-level exposition (Novice / Journeyman / Master), derivation, Hello World, and Jupyter build.

Live interactive concept graph: docs/MathLex/index.html

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Foundation Layer

Lesson	File
Balmer Series	balmer_series.html
Bernoulli Numbers	bernoulli_number.html
Berry-Keating Conjecture	berry_keating_conjecture.html
Catalan Numbers	catalan_number.html
Cayley-Dickson Algebra	cayley_dickson_algebra.html
Clifford Algebra	clifford_algebra.html
Dixon Algebra	dixon_algebra.html
Fourier Decomposition	fourier_decomposition.html
Galois Group	galois_group.html
Hamilton Product	hamilton_product.html
Hurwitz Theorem	hurwitz_theorem.html
Lie Algebra	lie_algebra.html
Lindemann-Weierstrass	lindemann_weierstrass.html
Moufang Identity	moufang_identity.html
Pauli Algebra	pauli_algebra.html
Riemannian Manifold	riemannian_manifold.html

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Applied Layer

Lesson	File
Bekenstein Entropy	bekenstein_entropy.html
Bekenstein-Hawking Entropy	bekenstein_hawking_entropy.html
Bianchi Identity	bianchi_identity.html
Cauchy-Riemann Equation	cauchy_riemann_equation.html
Chebyshev Polynomials	chebyshev_polynomial.html
Chern Numbers	chern_number.html
Covariant Derivative	covariant_derivative.html
Dirac Equation	dirac_equation.html
Dirac Field	dirac_field.html
Dirac Operator	dirac_operator.html
Dirac Representation	dirac_representation.html
Dixon Product	dixon_product.html
Frobenius Norm	frobenius_norm.html
Gauge Field	gauge_field.html
Hodge Decomposition	hodge_decomposition.html
Jacobian Form	jacobian_form.html
Klein-Gordon Equation	klein_gordon_equation.html
Langlands Kernel	langlands_kernel.html
Legendre Transform	legendre_transform.html
Lie Group	lie_group.html
Liouville Equation	liouville_equation.html
Lorentz Group	lorentz_group.html
Lorentz Transform	lorentz_transform.html
Lucas Polynomials	lucas_polynomial.html
Maclaurin Series	maclaurin_series.html
Majorana Representation	majorana_representation.html
Mellin Transform	mellin_transform.html
Minkowski Metric	minkowski_metric.html
Minkowski Space	minkowski_space.html
Möbius Transform	mobius_transform.html
Perturbation Series	perturbation_series.html
Renormalization Group	renormalization_group.html
Rydberg Formula	rydberg_formula.html
Schwarzschild Metric	schwarzschild_metric.html
Shannon Entropy	shannon_entropy.html
Spectral Representation	spectral_representation.html
Symplectic Manifold	symplectic_manifold.html
Von Neumann Entropy	von_neumann_entropy.html
Ward Identity	ward_identity.html
Ward-Takahashi Identity	ward_takahashi.html
Wilson-Hilferty Approximation	wilson_hilferty.html
Wirtinger Derivative	wirtinger_derivative.html
Yang-Mills Equation	yang_mills_equation.html

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Ptolemy Layer

Lesson	File
Berry-Keating Operator	berry_keating_operator.html
Bigram Entropy	bigram_entropy.html
Cayley Graph	cayley_graph.html
Leech Lattice	leech_lattice.html
Wyler Formula	wyler_formula.html

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Index Integrity

64 lesson files. 5 nodes in the concept graph (dixon_theorem, hilbert_space, modular_form, yang_mills_field, ward_takahashi_identity) reference lessons not yet built — stubs pending. ward_takahashi_identity resolves to ward_takahashi.html.