SchoolSpeak MathsMathematics AcademyAboutMy recordUnder construction. This area is a framework being built: most courses have no teaching material yet, and things may change or break. Private self-study. Not an official programme and not recognised by any ministry or school. No qualification, mark or document is issued, and “years 1 to 3” and “advanced” are names of study paths only.
Open mathematics at university level, free to study: a years 1 to 3 path and an advanced path, built on the Kamangir school lessons.
Checking your plan on this device…
Nothing is available to study yet. All 121 courses are planned: each has a syllabus, prerequisites and an assessment design, but no teaching material has been written.
The total includes 26 proposed E-series courses that are in no programme until the owner approves them. Planned workload across the catalogue: about 16,950 hours (an estimate, not a promise).
No diagnostic has questions yet, so none can be taken. These are the ones planned, and the foundation course each would suggest.
Four study pathways, each built from the course catalogue. They are named pathways, not qualifications.
Repairs school-level algebra, trigonometry and computing gaps. Placement-dependent: a prepared learner takes only what a diagnostic shows is needed; nothing here is a compulsory repeat.
3 courses named, 0 available to study, 3 planned
Broad, proof-based and computational mathematics: 24 common courses, six distinct electives with breadth, a writing seminar, a capstone and a cumulative assessment. A years 1 to 3 pathway, not an official programme.
45 courses named, 0 available to study, 45 planned
Deeper analysis, algebra, topology/geometry and advanced reasoning, with a reading seminar and a dissertation. An advanced pathway, not an official programme.
20 courses named, 0 available to study, 20 planned
Advanced analysis, modelling, numerical methods, probability and optimization, with modelling and scientific-computing case studies, a reading seminar and a dissertation. An advanced pathway, not an official programme.
34 courses named, 0 available to study, 34 planned
Interactive tools to explore ideas. Each states what it cannot show. Status is stated honestly. Laboratories from section 9 of the brief. The four labs of the earlier personal prototype were not supplied in the workspace, so they could not be preserved here; the framework offers capture and honesty notices for all labs, and one demonstration lab.
| Area | Laboratory | Status | What it cannot show |
|---|---|---|---|
| Logic/proof | Quantifier and finite-domain counterexample explorer (B01) | demonstration | Finite tests cannot prove an infinite-domain universal claim |
| Linear algebra | Linear maps, span, projections, eigenvectors, SVD (B04) | planned | Preserve the relation between the geometric object and coordinates |
| Calculus/optimization | Contours, directional derivatives, Hessians, gradient/Newton steps (B06) | planned | State norm/metric assumptions and finite-step limitations |
| Analysis | Epsilon definitions, sequence/function convergence (B09) | planned | Separate pictures from quantified arguments |
| Algebra | Finite groups, cosets, quotient maps, ring examples (B10) | planned | Bounded examples illustrate, not prove all group/ring theorems |
| Topology/geometry | Open sets, quotient constructions, charts, tangent projections (B15) | planned | Explain which properties depend on representation or metric |
| Probability/statistics | Sampling, conditioning, distributions, confidence procedures (B11) | planned | Distinguish stochastic variability from systematic error |
| Numerical methods | Conditioning, stability, interpolation, root finding, matrix solvers (B12) | planned | Show error, precision, cost, and convergence checks |
| Differential equations | Phase portraits, boundary conditions, discretization (B07) | planned | Report solver assumptions and numerical artifacts |
| Decision theory | Priors, losses, risk, and decision thresholds (U14) | planned | State the action/state/loss model explicitly |
| Computation theory | Automata, simulations, distinguishability, reduction builders (U04) | planned | Finite testing is not a proof of undecidability/nonregularity |
| Neural networks | Computational graphs and backpropagation (A18) | planned | Expose derivatives and numerical checks, not only animations |
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Unzip it, then open index.html. No internet needed.