26 learning modules, from foundations to doctoral research practice. Read, explain, solve, test, and document what remains unknown.
Broad self-study pathway, not universal standards alignment, an accredited program, all textbooks, or model training. Specialized professional practice and doctoral assessment require qualified supervision.
Hosted content consists of original study notes, prerequisites and reading references. Textbooks remain at their publishers. Some sources restrict commercial reuse; no full books were copied or uploaded. Adding references does not train the model or demonstrate mastery.
Foundation
Literacy and communication
Recognize sounds and letters; read short sentences and explain their meaning.
Study note: Read a short passage, distinguish what it says from what you infer, then retell it in your own words.
Practice: Explain a passage and identify the sentence supporting your explanation.
Prerequisites: Start here; adapt to the learner.
Read the external textbook or course collectionNetwork0-authored study scaffold; not textbook extraction · Mastery: not assessed.
Number sense and arithmetic
Count, compare quantities, and connect addition and subtraction to objects.
Study note: An equation states equality. For 3 + x = 8, subtract 3 from both sides to obtain x = 5. Check by substitution.
Practice: Solve five new arithmetic problems and explain one using objects or a diagram.
Prerequisites: Start here; adapt to the learner.
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Observation and questions
Separate direct observations from guesses and ask testable questions.
Study note: Record what you see, when, and under what conditions. A drawing or explanation is not the event itself.
Practice: Describe an everyday observation and offer two possible explanations.
Prerequisites: Start here; adapt to the learner.
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Art, music and expression
Explore rhythm, visual composition, listening and respectful interpretation.
Study note: Describe color, shape, rhythm and repetition before assigning an interpretation. Artistic preference is not a measurement of truth.
Practice: Create a short visual or rhythmic piece and explain two choices.
Prerequisites: Start here; adapt to the learner.
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Primary
Fractions, ratios and measurement
Work with fractions, proportional reasoning, lengths, areas and units.
Study note: A ratio compares quantities. Units must be compatible before addition; 1 m + 20 cm equals 1.2 m after conversion.
Practice: Solve a recipe-scaling problem and a mixed-unit measurement problem.
Prerequisites: Number sense and arithmetic
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Reading, writing and source use
Summarize, construct paragraphs and distinguish primary accounts from retellings.
Study note: A summary should preserve the original meaning. Quote briefly, name the source, and distinguish your interpretation from the author’s claim.
Practice: Write a sourced paragraph and explain what its source cannot establish.
Prerequisites: Literacy and communication
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History, geography and civic understanding
Use maps and timelines; compare perspectives and evaluate historical sources.
Study note: Historical accounts have authors, dates, purposes and limitations. Agreement between dependent retellings is not independent corroboration.
Practice: Compare two accounts of one event and explain their origin and differences.
Prerequisites: Literacy and communication
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Living systems, matter and Earth
Study organisms, materials, weather, and change through observations.
Study note: Choose a quantity to observe and record consistent units. Changing several conditions at once makes causal interpretation harder.
Practice: Keep an observation log and identify a confounding variable.
Prerequisites: Observation and questions, Fractions, ratios and measurement
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Secondary
Algebra, functions and geometry
Model relationships with equations, graphs, geometry and functions.
Study note: A function assigns one output to each input in its domain. Model assumptions determine where an equation applies; matching one point is not validation.
Practice: Fit a line to two supplied points and state why two points cannot validate the model.
Prerequisites: Fractions, ratios and measurement
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Chemistry and material change
Study atoms, stoichiometry, bonding and energy changes.
Study note: Balance atom counts in a chemical equation. Conservation of mass in a closed chemical system constrains the coefficients; it does not determine the reaction rate.
Practice: Balance a supplied equation and calculate a limiting reagent using given molar masses.
Prerequisites: Algebra, functions and geometry, Living systems, matter and Earth
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Biology and evolution
Study cells, inheritance, evolution and ecological systems.
Study note: A biological explanation should connect a mechanism to observations. Correlation among traits does not alone identify genetic or environmental causes.
Practice: Explain a controlled comparison that distinguishes two biological explanations.
Prerequisites: Living systems, matter and Earth
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Classical physics and energy
Use force, motion, work, power, waves and conservation laws within declared limits.
Study note: For constant net force and constant mass in Newtonian mechanics, F = ma. If m = 2 kg and a = 3 m/s², F = 6 N. This worked example is calculated, not measured.
Practice: Solve a new mechanics problem, check dimensions and name a boundary of the model.
Prerequisites: Algebra, functions and geometry
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Economics, civics and critical reasoning
Compare incentives, institutions, arguments, evidence and ethical tradeoffs.
Study note: Separate descriptive claims from value judgments. An economic model needs its assumptions and should not be treated as a guaranteed prediction.
Practice: Compare two policy options using explicit goals, evidence and uncertainty.
Prerequisites: Reading, writing and source use, History, geography and civic understanding, Algebra, functions and geometry
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Undergraduate
Calculus and differential equations
Use derivatives, integrals, rates of change and initial conditions.
Study note: A derivative describes local rate of change. For x(t) = 3t² metres with t in seconds, v(t) = 6t m/s. Initial conditions distinguish solutions of many differential equations.
Practice: Derive and check a simple differential-equation solution with stated initial conditions.
Prerequisites: Algebra, functions and geometry
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Linear algebra
Study vector spaces, linear systems, eigenvalues and least squares.
Study note: A matrix can represent a linear transformation after bases are chosen. Graph adjacency, quantum operators and data tables are different uses; their shared format does not prove physical equivalence.
Practice: Solve Ax = b and check the residual; explain singularity and conditioning.
Prerequisites: Algebra, functions and geometry
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Probability, statistics and inference
Work with distributions, sampling, confidence intervals and causal limitations.
Study note: A sample estimate has uncertainty. Predeclare a comparison and report effect size alongside assumptions; failure to reject a null is not proof that it is true.
Practice: Analyze a supplied dataset with a baseline, uncertainty estimate and limitation.
Prerequisites: Algebra, functions and geometry
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Programming, algorithms and systems
Learn executable specifications, data structures, complexity and software testing.
Study note: Specify inputs, outputs and invariants. A passing example is weaker than tests across boundary cases; source code is not proof of correct execution.
Practice: Implement a small algorithm and test empty, typical and boundary inputs.
Prerequisites: Algebra, functions and geometry
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Philosophy, psychology and social inquiry
Study arguments, cognition, social methods and ethical reasoning.
Study note: Ask whether evidence supports the exact claim. Clarify definitions and separate an argument’s validity from whether its premises are true.
Practice: Analyze an argument, challenge a premise, and propose evidence that would change your view.
Prerequisites: Reading, writing and source use, Economics, civics and critical reasoning
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Engineering design and control
Translate requirements into models, prototypes, tests and feedback systems.
Study note: A design needs a measurable requirement, operating envelope and failure conditions. A feedback controller must be checked for stability and response under disturbances.
Practice: Write a bounded design specification and a reproducible acceptance test.
Prerequisites: Classical physics and energy, Calculus and differential equations, Programming, algorithms and systems
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Graduate
Quantum theory
Study state spaces, operators, measurement and time evolution.
Study note: Quantum amplitudes are not ordinary probabilities; probabilities follow from the measurement rule. A simulated state vector is not evidence that quantum hardware ran.
Practice: Calculate a normalized state’s measurement probabilities and state the assumptions.
Prerequisites: Linear algebra, Calculus and differential equations, Classical physics and energy
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Machine learning and deep learning
Study optimization, generalization, representation learning and evaluation.
Study note: Separate training, validation and held-out test data. Compare a model to a simple baseline and check leakage before attributing improvement to learning.
Practice: Design a leakage-resistant benchmark with an ablation and an untouched test set.
Prerequisites: Linear algebra, Calculus and differential equations, Probability, statistics and inference, Programming, algorithms and systems
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Advanced physical and mathematical models
Specialize in statistical mechanics, fields, numerical methods or applied mathematics.
Study note: Choose a specific model family and derive its predictions within an operating regime. Similar-looking equations may describe different quantities and mechanisms.
Practice: Reproduce one derivation and compare a limiting case with a known result.
Prerequisites: Quantum theory, Probability, statistics and inference, Engineering design and control
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Measurement uncertainty and study design
Plan measurements, characterize uncertainty and distinguish exploratory from confirmatory work.
Study note: List uncertainty contributions and dependencies before combining them. Instrument resolution alone is not the total measurement uncertainty.
Practice: Prepare an uncertainty budget with units, assumptions and justified inputs.
Prerequisites: Probability, statistics and inference, Engineering design and control
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Doctoral research
Systematic literature and problem formulation
Identify an unresolved question, search reproducibly and trace each claim to evidence.
Study note: Record search terms, inclusion rules, exclusions and provenance. A literature gap is not automatically an important or feasible research question.
Practice: Produce a reproducible evidence map and a narrowly scoped research question.
Prerequisites: Measurement uncertainty and study design, Reading, writing and source use
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Replication and reproducible computation
Reproduce a published result and document deviations before proposing extensions.
Study note: Preserve versions, data lineage, parameters and outputs. A rerun with identical code and data tests reproducibility, not independent replication of the underlying observation.
Practice: Reproduce a baseline, report discrepancies and release a permitted reproducibility package.
Prerequisites: Programming, algorithms and systems, Probability, statistics and inference, Systematic literature and problem formulation
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Original contribution and independent defense
Develop a field-specific original contribution subject to qualified independent scrutiny.
Study note: A doctoral contribution must state what is new, what evidence supports it, competing explanations and limitations. A generated essay or completed reading list is not a doctorate.
Practice: Defend a bounded contribution against independent critique and specify remaining uncertainty.
Prerequisites: Replication and reproducible computation, Advanced physical and mathematical models
Read the external textbook or course collectionNetwork0-authored study scaffold; not textbook extraction · Mastery: not assessed.
After reading: solve an unfamiliar problem, explain assumptions, check a counterexample and obtain independent feedback. At advanced levels, select a discipline and a supervisor; this library is a starting framework.