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Under 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.

Kamangir Mathematics Academy

Open mathematics at university level, free to study: a years 1 to 3 path and an advanced path, built on the Kamangir school lessons.

Your next concrete task

Checking your plan on this device…

More: how much is ready, placement check, the four layers, laboratories

What can be studied today

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).

Start here

The four layers

Four study pathways, each built from the course catalogue. They are named pathways, not qualifications.

Foundation and placement

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

Structure

  • Foundation courses, only where placement shows a gap (placement 3)

Years 1 to 3 path

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

Structure

  • The 24 common-core courses (B01–B24) (all of 24)
  • Six distinct electives from the U series or the approved AI-and-data electives (E31, E32, E33, E37, E43) (choose 6 from 21)
  • Mathematical writing seminar (portfolio of artifacts)
  • Capstone integrating at least two areas (portfolio of artifacts)
  • Cumulative undergraduate assessment (portfolio of artifacts)

Advanced path, pure

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

Structure

  • Required taught courses (all of 4)
  • Research methods, reading seminar and dissertation (all of 3)
  • Four graduate electives from P03–P14 and/or G03 (choose 4 from 13)
  • Dissertation and oral defence (portfolio of artifacts)

Advanced path, applied

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

Structure

  • Required taught courses (all of 6)
  • Research methods, reading seminar and dissertation (all of 3)
  • Two graduate electives from A05–A18, G03, P13 or the AI-and-data strand E34–E44 (choose 2 from 25)
  • A mathematical-modelling case study (case study)
  • A scientific-computing case study (case study)
  • Dissertation and oral defence (portfolio of artifacts)

The twelve laboratories

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.

AreaLaboratoryStatusWhat it cannot show
Logic/proofQuantifier and finite-domain counterexample explorer (B01)demonstrationFinite tests cannot prove an infinite-domain universal claim
Linear algebraLinear maps, span, projections, eigenvectors, SVD (B04)plannedPreserve the relation between the geometric object and coordinates
Calculus/optimizationContours, directional derivatives, Hessians, gradient/Newton steps (B06)plannedState norm/metric assumptions and finite-step limitations
AnalysisEpsilon definitions, sequence/function convergence (B09)plannedSeparate pictures from quantified arguments
AlgebraFinite groups, cosets, quotient maps, ring examples (B10)plannedBounded examples illustrate, not prove all group/ring theorems
Topology/geometryOpen sets, quotient constructions, charts, tangent projections (B15)plannedExplain which properties depend on representation or metric
Probability/statisticsSampling, conditioning, distributions, confidence procedures (B11)plannedDistinguish stochastic variability from systematic error
Numerical methodsConditioning, stability, interpolation, root finding, matrix solvers (B12)plannedShow error, precision, cost, and convergence checks
Differential equationsPhase portraits, boundary conditions, discretization (B07)plannedReport solver assumptions and numerical artifacts
Decision theoryPriors, losses, risk, and decision thresholds (U14)plannedState the action/state/loss model explicitly
Computation theoryAutomata, simulations, distinguishability, reduction builders (U04)plannedFinite testing is not a proof of undecidability/nonregularity
Neural networksComputational graphs and backpropagation (A18)plannedExpose derivatives and numerical checks, not only animations