Interactive visualisations, presentation series, and explorations in pure mathematics, cryptography, and coding theory.
Interactive slide decks covering modern cryptographic systems end-to-end — from the underlying mathematics through NIST standards to SystemVerilog RTL and Python implementations.
Finite fields, elliptic curves, AES, hash functions, public-key crypto, digital signatures, post-quantum, FHE, side-channel attacks, hardware accelerators, zero-knowledge proofs, MPC, and TLS 1.3.
Error detection and error correction — from parity bits and Hamming codes through Reed-Solomon, turbo codes, LDPC, and polar codes.
Foundations, parity checks, Hamming codes, CRC, linear block codes, convolutional codes, BCH, Reed-Solomon, turbo codes, LDPC, fountain codes, polar codes, and real-world applications.
Interactive companion to Paul Wilmott's Paul Wilmott Introduces Quantitative Finance (2nd edition, Wiley, 2007). Decks 01–05 introduce products, markets and the random walk; decks 06–10 develop the Black–Scholes world and its exotic extensions; decks 11–12 cover fixed income and interest-rate models; decks 13–14 close with risk management and the numerical methods that price what closed forms cannot. Every deck has at least one in-browser interactive widget.
Fourteen interactive decks — products & markets, derivatives, the binomial model, stochastic calculus, Black–Scholes, the Greeks, volatility, exotics, multi-asset, fixed income, interest-rate models, portfolio & risk, and the numerical methods underneath everything. Companion to Paul Wilmott's textbook of the same name.
Interactive companion to Deisenroth, Faisal & Ong's textbook of the same name (Cambridge University Press, 2020). Part I builds the foundations — linear algebra, geometry, matrix decompositions, calculus, probability, optimisation. Part II derives regression, PCA, GMMs and SVMs from them. Every deck has at least one in-browser interactive widget.
Twelve interactive decks — linear algebra, analytic geometry, matrix decompositions, vector calculus, probability, optimisation, then linear regression, PCA, GMMs, and SVMs. Companion to the freely available Cambridge University Press textbook.
A self-contained curriculum in the core mathematical methods used across the physical sciences — single-variable and multivariable calculus, infinite series, complex analysis, vector calculus, linear algebra & vector spaces, and differential equations. A companion to R. Shankar's Basic Training in Mathematics. Every chapter is an interactive single-page app.
Limits, derivative as a limit, rules of differentiation, L'Hôpital, extrema & concavity, linearisation
Riemann sums, fundamental theorem, substitution, parts, partial fractions, improper integrals, Gaussian & Gamma
Scalar fields, partial derivatives, gradient, directional derivatives, Lagrange multipliers, Jacobians, solid angle
Sequences, partial sums, convergence tests, power series & radius of convergence, asymptotic series
Argand arithmetic, De Moivre, Euler, Cauchy–Riemann, singularities, residue theorem, Riemann sphere
Vector fields, gradient, divergence, curl, line & surface integrals, Green's/Stokes'/divergence theorems, electromagnetism
Matrix operations, determinants, inverses, linear transformations, eigenvalues & eigenvectors (paired with the Eigenvalue Explorer)
Axioms, span & independence, inner products, Gram-Schmidt, linear operators, eigenvalue problem, function spaces — plus Advanced, History, DSP & Audio, Quantum, and ML companion repos
Direction fields, damped oscillator, linear systems, Frobenius/Bessel/Legendre, wave & heat equations, Green's functions
Interactive single-page visualisations built with Plotly.js and vanilla HTML/CSS/JS — no build step, no dependencies to install.
Taylor polynomial approximations for 20 functions — convergence regions, adjustable order
Domain colouring and 3D magnitude surfaces for Taylor series of 12 complex functions
Build periodic waveforms term by term — Gibbs phenomenon, frequency spectra, adjustable harmonics
Osculating circles, curvature plots, and evolutes for parametric curves
Vector fields, gradient & contours, divergence & curl, line integrals, Green's/Stokes'/Divergence theorems, 3D fields
Limits with ε–δ strip, secant→tangent convergence, rules, L'Hôpital, critical & inflection detection, tangent linearisation
Riemann sums (five methods), FTC dual-plot, substitution, parts (LIATE), partial fractions, improper integrals, Gamma & Beta
3D surfaces, partial slices, gradient quiver on contours, directional derivatives, Lagrange multipliers, Jacobians, solid angle
Sequences with ε bands, partial sums, convergence tests, power series & radius of convergence, Stirling asymptotics
Complex mappings — z², eᶻ, 1/z, Möbius, Joukowski airfoil — grid warping, domain colouring
Domain colouring of ζ(s) on the critical strip — non-trivial zeros, functional equation
Argand arithmetic, roots of unity, Euler's formula, Cauchy–Riemann surfaces, singularity classification, residue theorem, Riemann sphere
2×2 matrices warp grids, circles, vectors — eigenvalue/eigenvector overlays, SVD
Drag matrix entries and watch eigenvalues move in the complex plane
Matrix Methods in Engineering — a three-deck series on the matrix structures engineers actually test for, what each guarantees about a real system, and what happens when the whole apparatus meets a real design problem. Interactive slide decks with live canvas widgets and a long-form PDF alongside each.
Reciprocity as symmetry, passivity as positive semidefiniteness, losslessness as unitarity; poles and zeros, Kramers–Kronig, the Smith chart as a Möbius map
State-matrix eigenvalues and the unit circle, Wiener–Hopf and Toeplitz structure, the eigenfilter as a Rayleigh quotient, paraunitary filter banks
One 28 GBd backplane channel from S-parameters to a link budget — CTLE, FFE, DFE, PAM4 and FEC, with seven remedies priced in dB
A six-repo series — history, basics, advanced theory, and applications in audio DSP, quantum mechanics, and machine learning. Every transform is viewed as a change of basis.
Timeline 1799–1932, portrait cards, force-directed concept map, idea threads, and period quotations
Axioms, span, independence, basis, subspaces, inner products, Gram–Schmidt, p-norms, linear maps, change of basis
Dual space, quotient, direct sum, tensor product, Hilbert & Banach, operator norm, spectral theorem, Riesz
Signal as vector, DFT, DCT/MDCT, STFT, wavelets, mel/MFCC, SVD denoising, PCA/KL, NMF, ICA, matching pursuit, CQT
State vector, Bloch sphere, observables, measurement, unitary evolution, entanglement via tensor product, density matrices
Features, word embeddings, kernel trick, PCA, attention, contrastive geometry, latent interpolation
Vector fields and trajectories — Van der Pol, Lotka-Volterra, Duffing, nullclines
Interactive s-plane — drag poles/zeros, live impulse response and Bode plots
Direction fields with RK4 trajectories, damped oscillator, 2×2 phase portraits, Bessel/Legendre/Airy, wave & heat equations, Green's functions
Cayley graphs, multiplication tables, subgroup lattices for cyclic, dihedral, symmetric groups
GF(2ⁿ) theory — finite field arithmetic, irreducible polynomials, CRC, LFSR, AES
Möbius strip, Klein bottle, torus, Euler characteristic, knot explorer
Gaussian curvature, geodesic tracer, parallel transport, Gauss-Bonnet theorem
Poincaré disk, upper half-plane, hyperbolic tilings, isometry explorer
Sample from any distribution, watch convergence — animated histogram, Q-Q plot
1D/2D random walks, Brownian motion, Lévy flights, diffusion envelopes
State diagram editor, animated simulation, stationary distribution, matrix analysis
37 interactive presentations (17 slides each) on the lives, experiments, and theories of history's greatest physicists — from Galileo through Penrose, including signal processing and electronics pioneers.
Galileo, Kepler, Huygens, Newton, Ampère, Faraday, Kelvin, Tait, Maxwell, Boltzmann, Gibbs, FitzGerald, Lodge, Hertz, Tesla, Thomson, Curie, Planck, Rutherford, Einstein, Bohr, Bromwich, Born, Schrödinger, Heisenberg, Pauli, Dirac, Oppenheimer, Fermi, Bardeen, Feynman, Gell-Mann, Bell, Penrose, Higgs, Deutsch, and Hawking.