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

Mathematics

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

Computing

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