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What a 18-year-old learns

122 topics open up at age 18, across 3 subjects. They are listed in the order they build on each other, not by importance: each one needs the ones above it.

age 17age 19
What should a 18-year-old be learning?

At age 18, 122 topics open up across Science, Mathematics, Computing. Each one has prerequisites that come first, so the order matters more than the list: Velocity and Acceleration as Derivatives is a typical starting point.

How do I know what a 18-year-old already knows?

LightMySky starts by assuming everything below the learner’s level is already known, then checks the assumption as they practise. What holds up stays lit; what does not comes back for review.

Science

  1. Velocity and Acceleration as DerivativesForces & Motion · on the way
  2. Recovering Motion by Integrating AccelerationForces & Motion · on the way
  3. Newton's Second Law as a Differential EquationForces & Motion · on the way
  4. Drag and Terminal Speed from the Equation of MotionForces & Motion · on the way
  5. Work as a Line Integral Along a PathEnergy · on the way
  6. Conservative Forces and the Potential Energy FunctionEnergy · on the way
  7. Potential Energy Curves, Turning Points and StabilityEnergy · on the way
  8. Simple Harmonic Motion as a Second-Order EquationForces & Motion · on the way
  9. Protists: The Eukaryotes That Are Not Plants, Animals or FungiOrganisms & Life Processes · on the way
  10. Calibration, the Blank and What Makes a Measurement TrustworthyChemistry · on the way
  11. Molecular Orbital Theory for Homonuclear DiatomicsChemistry · on the way
  12. Heteronuclear Diatomics and Polarity in Orbital TermsChemistry · on the way
  13. Molecular Symmetry: Elements, Operations and Point GroupsChemistry · on the way
  14. Signal, Noise and the Limit of DetectionChemistry · on the way
  15. The Beer-Lambert Law and Quantitative AbsorptionChemistry · on the way
  16. Uncertainty in a Measurement and Where It Comes FromChemistry · on the way
  17. Propagating Uncertainty Through a CalculationChemistry · on the way
  18. Significance Tests for Chemical DataChemistry · on the way
  19. The Maxwell-Boltzmann Distribution of Molecular SpeedsThermal & Statistical Physics · on the way
  20. Equipartition and the Heat Capacities of GasesThermal & Statistical Physics · on the way
  21. Thermodynamic State Variables and PV DiagramsThermal & Statistical Physics · on the way
  22. The First Law of Thermodynamics for Any ProcessThermal & Statistical Physics · on the way
  23. The Wave Equation and Its Travelling-Wave SolutionsWaves, Light & Sound · on the way
  24. Wave Speed on a String from Tension and Linear DensityWaves, Light & Sound · on the way
  25. Intensity: the Energy and Power Carried by a WaveWaves, Light & Sound · on the way
  26. Normal Modes of a Bounded SystemWaves, Light & Sound · on the way
  27. The Doppler Effect and Shock WavesWaves, Light & Sound · on the way
  28. Huygens's Principle and the Laws of Reflection and RefractionWaves, Light & Sound · on the way
  29. Hybridisation, Conjugation and Delocalisation in Organic MoleculesChemistry · on the way
  30. Curly Arrows as the Language of MechanismChemistry · on the way
  31. pKa as a Predictive Tool in Organic ChemistryChemistry · on the way
  32. Conformation: Newman Projections, Ring Strain and the ChairChemistry · on the way
  33. Chirality, R and S Assignment and Optical ActivityChemistry · on the way
  34. The Schrodinger Equation and What a Wavefunction SaysChemistry · on the way
  35. The Particle in a Box: Where Quantised Levels Come FromChemistry · on the way
  36. The Hydrogen Atom: Quantum Numbers and Orbital ShapesChemistry · on the way
  37. Many-Electron Atoms: Spin, Antisymmetry and Effective ChargeChemistry · on the way
  38. Blackbody Radiation and the Quantum of EnergyQuantum & Modern Physics · on the way
  39. The Compton Effect and Photon MomentumQuantum & Modern Physics · on the way
  40. The Postulates of Special Relativity and the Loss of SimultaneityQuantum & Modern Physics · on the way
  41. The Wavefunction and the Born Probability RuleQuantum & Modern Physics · on the way
  42. Time Dilation and Length ContractionQuantum & Modern Physics · on the way
  43. The Electric Field of a Continuous Charge DistributionElectricity & Magnetism · on the way
  44. Electric Flux and Gauss's LawElectricity & Magnetism · on the way
  45. Applying Gauss's Law to Symmetric Charge DistributionsElectricity & Magnetism · on the way
  46. Conductors, Shielding and Surface ChargeElectricity & Magnetism · on the way
  47. Calculating Electric Potential from a Charge DistributionElectricity & Magnetism · on the way
  48. Equilibrium Potentials and What Sets the Resting VoltageThe Human Body · on the way
  49. Channel Kinetics and the Ionic Basis of the SpikeThe Human Body · on the way
  50. Cable Properties and Dendritic IntegrationThe Human Body · on the way
  51. Linkage, Recombination Frequency and Genetic MapsGenetics & Evolution · on the way
  52. Epistasis and Reading Pathway Order from Double MutantsGenetics & Evolution · on the way
  53. Quantitative Traits, Variance Components and HeritabilityGenetics & Evolution · on the way
  54. Chromatin: Nucleosomes and Higher-Order PackingGenetics & Evolution · on the way
  55. Selection Coefficients and Predicting Allele Frequency ChangeGenetics & Evolution · on the way
  56. Genetic Drift and Effective Population SizeGenetics & Evolution · on the way
  57. Mutation, Gene Flow and the Balance That Holds VariationGenetics & Evolution · on the way
  58. Deriving the Michaelis-Menten Equation from the Steady StateBiochemistry & Molecular Biology · on the way
  59. Double-Reciprocal Plots and Telling Inhibitor Types ApartBiochemistry & Molecular Biology · on the way
  60. How Enzymes Lower the Activation BarrierBiochemistry & Molecular Biology · on the way
  61. Protein Folding, Chaperones and What Misfolding CostsBiochemistry & Molecular Biology · on the way
  62. Post-translational Modification and Protein TurnoverBiochemistry & Molecular Biology · on the way
  63. Protein Targeting and the Signal SequenceOrganisms & Life Processes · on the way
  64. Vesicle Traffic: Coats, Adaptors and FusionOrganisms & Life Processes · on the way
  65. Tissue Types and How a Body Is OrganisedThe Human Body · on the way
  66. Bacterial Cell Envelopes and What the Gram Stain RevealsMicrobiology · on the way
  67. Archaea: Different Membranes, Extreme Habitats, Separate DomainMicrobiology · on the way
  68. Microbial Growth: Generation Time, Growth Curves and Continuous CultureMicrobiology · on the way
  69. Controlling Growth: What Sterile Means and How It Is AchievedMicrobiology · on the way
  70. Fungi: Hyphae, Spores and Digestion Outside the BodyOrganisms & Life Processes · on the way

Mathematics

  1. Systems of Linear Equations and Their Solution SetsLinear Algebra · on the way
  2. Gaussian Elimination and Row Echelon FormLinear Algebra · on the way
  3. Matrix Multiplication and What It RepresentsLinear Algebra · on the way
  4. The Inverse of a Matrix and When It ExistsLinear Algebra · on the way
  5. Determinants and What They MeasureLinear Algebra · on the way
  6. One-Sided Limits and When a Limit Fails to ExistCalculus & Analysis · on the way
  7. The Limit Laws and Indeterminate FormsCalculus & Analysis · on the way
  8. Statements, Quantifiers and NegationMathematical Thinking · on the way
  9. Sets, Functions and Relations in the Language of ProofMathematical Thinking · on the way
  10. Proof by Induction and Strong InductionMathematical Thinking · on the way
  11. Equivalence Relations and PartitionsMathematical Thinking · on the way
  12. Countable and Uncountable SetsMathematical Thinking · on the way
  13. Vector Spaces and SubspacesLinear Algebra · on the way
  14. Linear Independence, Span and BasisLinear Algebra · on the way
  15. Dimension and the Rank-Nullity TheoremLinear Algebra · on the way
  16. Continuity and the Intermediate Value TheoremCalculus & Analysis · on the way
  17. The Epsilon-Delta Definition of a LimitCalculus & Analysis · on the way
  18. The Product and Quotient RulesCalculus & Analysis · on the way
  19. The Chain RuleCalculus & Analysis · on the way
  20. Derivatives of Exponential, Logarithmic and Trigonometric FunctionsCalculus & Analysis · on the way
  21. Implicit Differentiation and Derivatives of Inverse FunctionsCalculus & Analysis · on the way
  22. Related RatesCalculus & Analysis · on the way
  23. The Mean Value TheoremCalculus & Analysis · on the way
  24. L'Hopital's Rule and Comparing Growth RatesCalculus & Analysis · on the way
  25. Probability Spaces: Sample Spaces, Events and AxiomsProbability · on the way
  26. Conditional Probability, Independence and Bayes' TheoremProbability · on the way
  27. Discrete Models Beyond the BinomialProbability · on the way
  28. Counting with the Product and Sum RulesDiscrete Mathematics · on the way
  29. Permutations and CombinationsDiscrete Mathematics · on the way
  30. Binomial Coefficients and Combinatorial IdentitiesDiscrete Mathematics · on the way
  31. Divisibility and the Division AlgorithmNumber Theory · on the way
  32. Euclid's Algorithm and Bezout's IdentityNumber Theory · on the way

Computing

  1. Version Control as a Graph of CommitsSoftware Engineering · on the way
  2. Branching, Merging and Resolving a ConflictSoftware Engineering · on the way
  3. Code Review: Reading a Change You Did Not WriteSoftware Engineering · on the way
  4. Loop Invariants and Proving an Algorithm CorrectAlgorithms & Data Structures · on the way
  5. Asymptotic Notation Made PreciseAlgorithms & Data Structures · on the way
  6. Recurrence Relations and the Master TheoremAlgorithms & Data Structures · on the way
  7. Divide and Conquer as a Design MethodAlgorithms & Data Structures · on the way
  8. Joint, Marginal and Conditional ProbabilityMachine Learning · on the way
  9. Bayes' Rule and Updating a BeliefMachine Learning · on the way
  10. Likelihood and the Maximum Likelihood EstimateMachine Learning · on the way
  11. Data as a Matrix: Rows, Features and the TargetMachine Learning · on the way
  12. Instruction Set Architecture as a ContractComputer Systems · on the way
  13. The Memory Hierarchy and Why Caching WorksComputer Systems · on the way
  14. Pipelining and the Cost of a HazardComputer Systems · on the way
  15. Layering and Encapsulation in the Protocol StackNetworks & Security · on the way
  16. Reliable Delivery over an Unreliable NetworkNetworks & Security · on the way
  17. Congestion Control and Sharing a LinkNetworks & Security · on the way
  18. The Relational Model and Relational AlgebraData & Databases · on the way
  19. Functional Dependencies and Boyce-Codd Normal FormData & Databases · on the way
  20. SQL at Depth: Subqueries, Set Operations and ViewsData & Databases · on the way
What a 18-year-old learns · LightMySky