Labs
Interactive experiments — visual, audible, and exploratory
Linear Algebra
View Course →Mathematical Intuition
View Course →Number Line Transformer
See how operations move, scale, and warp points
Function Composer
Chain functions and watch compositions build
Equation Decoder
Break equations into subject, verb, object
Number Systems Explorer
Integers, rationals, irrationals — zoom in
Operation Drill
Timed quiz — identify the main operation
Theory of Music
View Course →Statistics
View Course →Game Theory
View Course →Nash Equilibrium Finder
Edit payoff matrices, see equilibria shift
Repeated Games
Cooperation emergence with tit-for-tat, grim trigger
Evolutionary Dynamics
Replicator dynamics and ESS stability
Auction Theory
Bid functions and revenue equivalence
Learning in Games
Fictitious play and regret matching convergence
Economics
View Course →Utility & Indifference
Budget line tangencies across Cobb-Douglas, Leontief, and perfect substitutes
Market Equilibrium
Tâtonnement animation and price-ceiling deadweight loss
Second-Price Auction
Truthful bidding as a dominant strategy, 1000-trial histograms
Lemons Market
Adverse selection unraveling under quality asymmetry
Cournot vs. Bertrand
Best-response intersections for quantity and price duopoly
Systems Thinking
View Course →Feedback Loop Simulator
Cobweb diagrams, gain, and delay-driven oscillations
Phase Portrait Explorer
Vector fields, fixed points, and bifurcations
Network Dynamics
Topology, centrality, and robustness under attack
Emergence Simulator
Cellular automata -- local rules, global order
Coupled Oscillators
Kuramoto model and synchronization transitions
Variational Quantum Algorithms
View Course →Parameterized Circuit Lab
Build a 1-qubit ansatz on the Bloch sphere
Cost Landscape Explorer
Visualize the VQA cost surface and gradient field
Barren Plateau Detector
Gradient variance vs circuit depth and width
Optimization Dynamics
Race GD, Adam, and SPSA on the same landscape
Shot Noise Explorer
Finite measurement statistics and state-dependent noise
Biological Systems
View Course →Genetic Drift in Small Populations
Wright-Fisher across N and p0, fixation probability converges
Enzyme Kinetics
Michaelis-Menten saturation and competitive inhibition
Predator-Prey Dynamics
Lotka-Volterra cycles and the carrying-capacity spiral
Selection vs. Drift
Sweep Ns through 1 -- beneficial mutations fix or vanish
Regulatory Network Toggle Switch
Two-gene mutual repression: bistable, monostable, oscillatory
Internet Systems
View Course →TCP Congestion Control
Slow-start and sawtooth: Reno vs. CUBIC vs. BBR
Consistent Hashing Ring
Nodes on a ring, keys remap minimally
CAP Theorem Sandbox
Partition three replicas, pick C or A
BGP Route Propagation
Path-vector propagation and hijack spread
Rate Limiter Comparison
Token, leaky, sliding log, sliding counter on one burst
Quantum Foundations
View Course →Bloch Sphere & Gates
Visualize qubit states and apply quantum gates
Measurement & Born Rule
Collapse statistics and Born-rule convergence
Bell Test & CHSH
Entanglement correlations and nonlocality
Decoherence Visualizer
Quantum channels and loss of coherence
Stern-Gerlach Sequences
Sequential measurements and basis incompatibility
All labs are linked to their respective course chapters and lessons.