MATH-23 · Advanced · ENGLISH · PLANNED
Build the picture, explain the rule, work an example, then justify it.
Study time is an initial activity estimate, excluding extra reading, revision and extended laboratory or project work. Videos and question bodies have not been produced by adding this outline.
Complete these courses or demonstrate equivalent knowledge. These are recommended prerequisites, not enforced enrolment locks.
YouTube playlist: ARK Mathematics | Optimisation, Numerical Analysis and Stochastic Models
Playlist title reserved in the plan; no YouTube playlist or upload has been created yet.
Sign in to save this learning pathPractical outcome: Allocate a limited production budget and test sensitivity.
Explain convex sets using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain convex functions using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain gradient descent using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain newton optimisation using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Use the first concepts from this section. Allocate a limited production budget and test sensitivity. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain lagrange duality using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain kkt conditions using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain linear programming using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain integer programming using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Explain dynamic programming using a visual and one worked real-world example. Context: Allocate a limited production budget and test sensitivity. End with a prediction or check-for-understanding.
Allocate a limited production budget and test sensitivity. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Convex sets, Convex functions, Gradient descent and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Compare numerical answers against explicit error bounds.
Explain floating-point error using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain conditioning versus stability using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain root-finding bounds using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain polynomial interpolation using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Use the first concepts from this section. Compare numerical answers against explicit error bounds. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain splines using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain gaussian quadrature using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain finite differences using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain finite elements using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Explain monte carlo integration using a visual and one worked real-world example. Context: Compare numerical answers against explicit error bounds. End with a prediction or check-for-understanding.
Compare numerical answers against explicit error bounds. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Floating-point error, Conditioning versus stability, Root-finding bounds and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Practical outcome: Simulate service queues with reproducible uncertainty estimates.
Explain markov chains using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain stationary distributions using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain poisson processes using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain brownian motion using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Use the first concepts from this section. Simulate service queues with reproducible uncertainty estimates. Produce a labelled diagram, trace or calculation; explain each step and check one changed input.
3–6 questions on the preceding first-half concepts only: recall, visual interpretation, application and one plausible misconception. Explain each answer after submission.
Explain martingales using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain ito integral introduction using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain stochastic differential equations using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain queueing models using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Explain time-series stationarity using a visual and one worked real-world example. Context: Simulate service queues with reproducible uncertainty estimates. End with a prediction or check-for-understanding.
Simulate service queues with reproducible uncertainty estimates. Work without the example, compare two cases, record assumptions and limitations, then self-review correctness, reasoning and clarity.
6–12 questions covering Markov chains, Stationary distributions, Poisson processes and the remaining section concepts, with cumulative retrieval from earlier sections. Include a new transfer problem; 70% unlocks progression.
Combine all three sections: Simulate service queues with reproducible uncertainty estimates. Submit an original worked artifact, evidence or tests, assumptions and a reflection. Rubric: correctness, method, practical usefulness, reproducibility and communication. Self-reviewed, not certified.
6–12 balanced questions sampling every section of Optimisation, Numerical Analysis and Stochastic Models, including interpretation, calculation or reasoning, a misconception and a new application. Passing is 70%; review errors before retrying.
Visual constructions, worked problems and proofs. Guided work leads to an independent attempt, with a diagram, explanation, trace, calculation or tested artifact. Question bodies are generated when opened in your private learning path. Programming submissions are stored as text; the platform does not execute submitted code.
Use original or appropriately licensed datasets. Practical science activities use models or supplied data unless a qualified supervisor has reviewed a physical experiment.
Open the interactive practice sampler →