ToolPrototype
Probability and Statistics Lab
Investigate binomial distributions and sampling behaviour.
Beauty in maths topic
Statistics, Probability and AI
Statistics, probability and AI ask how we reason from uncertainty, data and repeated experiments.
6
live pages
6
prototype tools
6
planned ideas
What this area includes
Sampling, distributions and hypothesis testing
Monte Carlo simulation and random walks
Regression, overfitting and model choice
Optimisation and neural-network ideas
Questions to explore
What does the data support, and what does it not support?
How can randomness produce reliable patterns?
When does a model start learning noise instead of structure?
Working pages and tools
These are the pages currently available to open from this topic.
ToolPrototype
Normal Distribution and Hypothesis Testing
See rejection regions, z statistics, p-values and conclusions.
ToolPrototype
Monte Carlo Simulator
Estimate pi and area under a curve using random sampling.
ToolPrototype
Linear Regression and Overfitting
Compare training error, test error and model complexity.
ToolPrototype
Gradient Descent Visualiser
Watch optimisation move across a loss landscape.
ToolPrototype
GCSE Probability Tree Lab
Build two-stage probability trees, compare replacement, and highlight combined events.
Planned directions
These ideas are not built yet, but they show where this topic could grow next.
ideaPlanned
Markov Chain Explorer
Planned lab linking probability, matrices and long-run behaviour in systems that move between states.
ideaPlanned
Neural Network Playground
Planned AI visualisation connecting functions, optimisation, data and model training.
ideaPlanned
Random Walks
Planned bridge from simple probability to diffusion, finance, physics and wandering paths.
ideaPlanned
A Level Hypothesis Testing Toolkit
Planned guide for binomial and normal tests, critical regions, p-values and careful conclusion writing.
ideaPlanned
A Level Modelling Assumptions Lab
Planned page asking students to choose, test and critique modelling assumptions in mechanics and statistics.
ideaPlanned
Hashing and Digital Fingerprints
Planned page about one-way functions, checksums, tamper detection and avalanche effects.
Connected topics
themeLive
Beauty in Maths
A portal for connected mathematical explorations: pattern, surprise, structure, nature and emergence.
themeLive
Cryptography and Secret Messages
Codes, ciphers, primes, modular arithmetic, public keys and secure communication.
themeLive
Game Theory and Decisions
Strategy, cooperation, competition, voting, incentives and mathematical decision making.
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Information Theory
Entropy, compression, communication, error correction and the mathematics of messages.
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Financial Maths and Risk
Growth, uncertainty, modelling, risk, portfolios and the mathematics behind financial decisions.
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Data Geometry
Clustering, dimensions, similarity, projection and the hidden shape of high-dimensional data.
How to use this section
This area is increasingly important because it connects school mathematics to evidence, modelling and AI literacy.