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What a 19-year-old learns

170 topics open up at age 19, 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 18age 20
What should a 19-year-old be learning?

At age 19, 170 topics open up across Science, Mathematics, Computing. Each one has prerequisites that come first, so the order matters more than the list: Continuity and Bernoulli's Equation for Ideal Flow is a typical starting point.

How do I know what a 19-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. Continuity and Bernoulli's Equation for Ideal FlowForces & Motion · on the way
  2. Damped Oscillations and the Three Damping RegimesForces & Motion · on the way
  3. Driven Oscillations, Resonance and the Quality FactorForces & Motion · on the way
  4. Coupled Oscillators and Normal ModesForces & Motion · on the way
  5. The Centre of Mass and the Motion of a SystemForces & Motion · on the way
  6. Variable Mass and the Rocket EquationForces & Motion · on the way
  7. Least-Squares Calibration and the Uncertainty of a Result Read From ItChemistry · on the way
  8. Main-Group Chemistry: What Changes Down a p-Block GroupChemistry · on the way
  9. Work in Isothermal, Isobaric and Adiabatic ProcessesThermal & Statistical Physics · on the way
  10. Heat Engines and the Second LawThermal & Statistical Physics · on the way
  11. The Carnot Cycle and the Ceiling on EfficiencyThermal & Statistical Physics · on the way
  12. Entropy as a State FunctionThermal & Statistical Physics · on the way
  13. Total Internal Reflection, Optical Fibres and DispersionWaves, Light & Sound · on the way
  14. Thin Lenses and the Lens Maker's EquationWaves, Light & Sound · on the way
  15. Curved Mirrors, the Mirror Equation and Real ImagesWaves, Light & Sound · on the way
  16. Magnifiers, Microscopes and TelescopesWaves, Light & Sound · on the way
  17. Phasor Addition and the Mathematics of InterferenceWaves, Light & Sound · on the way
  18. Thin-Film Interference and Anti-Reflection CoatingsWaves, Light & Sound · on the way
  19. Atomic Absorption and Emission for Trace MetalsChemistry · on the way
  20. Diastereomers, Meso Compounds and Fischer ProjectionsChemistry · on the way
  21. How a Chromatographic Separation WorksChemistry · on the way
  22. Molecular Mechanics: Force Fields and Conformational SearchingChemistry · on the way
  23. Molecular Motion Quantised: The Oscillator and the RotorChemistry · on the way
  24. Resolution, Efficiency and the van Deemter CurveChemistry · on the way
  25. Gas Chromatography: Columns, Temperature Programming and DetectorsChemistry · on the way
  26. HPLC: Reversed Phase, Gradients and Method DevelopmentChemistry · on the way
  27. Selection Rules and Why Some Transitions Never AppearChemistry · on the way
  28. Character Tables and What Symmetry PredictsChemistry · on the way
  29. Reading Bond Lengths and Force Constants from SpectraChemistry · on the way
  30. Electronic Spectra, Franck-Condon and the Origin of ColourChemistry · on the way
  31. Stereochemistry as Mechanistic EvidenceChemistry · on the way
  32. SN1 and SN2: Kinetics, Stereochemistry and What Decides the RouteChemistry · on the way
  33. Carbocations: Stability, Rearrangement and Neighbouring GroupsChemistry · on the way
  34. E1, E2 and E1cb: Three Ways to Lose Two GroupsChemistry · on the way
  35. Substitution Against Elimination: Predicting the Major ProductChemistry · on the way
  36. Electrophilic Addition Revisited: Bridged Ions and StereospecificityChemistry · on the way
  37. Hydroboration, Oxidation and Cleavage of Alkenes and AlkynesChemistry · on the way
  38. Radical Selectivity, Stability and Allylic PositionsChemistry · on the way
  39. Symmetry-Adapted Orbitals for Polyatomic MoleculesChemistry · on the way
  40. Acid-Base Models Beyond Bronsted: Lewis, Solvents and Hard and SoftChemistry · on the way
  41. Coordination Compounds: Naming, Geometry and IsomerismChemistry · on the way
  42. Crystal Field Theory and the Splitting of d OrbitalsChemistry · on the way
  43. The Spectrochemical Series, Spin State and MagnetismChemistry · on the way
  44. What an Excited Molecule Does Next: Fluorescence and PhosphorescenceChemistry · on the way
  45. The Boltzmann Distribution over Molecular LevelsChemistry · on the way
  46. Normalisation and Expectation ValuesQuantum & Modern Physics · on the way
  47. The Lorentz Transformation and Velocity AdditionQuantum & Modern Physics · on the way
  48. Relativistic Momentum and EnergyQuantum & Modern Physics · on the way
  49. Spacetime Intervals and Four-VectorsQuantum & Modern Physics · on the way
  50. Properties of Nuclei and the Nuclear ForceQuantum & Modern Physics · on the way
  51. The Uncertainty Principle from Wave PacketsQuantum & Modern Physics · on the way
  52. The Time-Independent Schrödinger EquationQuantum & Modern Physics · on the way
  53. The Infinite Square Well and Energy QuantisationQuantum & Modern Physics · on the way
  54. Recovering the Field from the Potential GradientElectricity & Magnetism · on the way
  55. Dielectrics and the Polarisation of MatterElectricity & Magnetism · on the way
  56. Current Density, Drift Velocity and the Microscopic Ohm's LawElectricity & Magnetism · on the way
  57. Kirchhoff's Rules for Multi-Loop CircuitsElectricity & Magnetism · on the way
  58. The Biot-Savart Law and the Field of a Current ElementElectricity & Magnetism · on the way
  59. Ampere's Law: Wires, Solenoids and ToroidsElectricity & Magnetism · on the way
  60. Induced Electric Fields and Motional EMFElectricity & Magnetism · on the way
  61. Regional Anatomy of the Central Nervous SystemThe Human Body · on the way
  62. Fertilisation and the First CleavagesOrganisms & Life Processes · on the way
  63. The Neutral Theory and Reading a Molecular ClockGenetics & Evolution · on the way
  64. Selection on Quantitative Traits and Predicting the ResponseGenetics & Evolution · on the way
  65. Speciation: Isolation, Hybrid Zones and Where the Boundary BlursGenetics & Evolution · on the way
  66. Building a Phylogeny: Homology, Shared Derived Characters and ParsimonyGenetics & Evolution · on the way
  67. Membrane Lipid Composition, Asymmetry and FluidityOrganisms & Life Processes · on the way
  68. Ion Channels: Selectivity, Gating and the Evidence from Single ChannelsOrganisms & Life Processes · on the way
  69. Ligand Binding: Dissociation Constants and Receptor OccupancyOrganisms & Life Processes · on the way
  70. G-Protein-Coupled Receptors and Second MessengersOrganisms & Life Processes · on the way
  71. Plant Hormone Signalling and How a Plant DecidesOrganisms & Life Processes · on the way
  72. Receptor Tyrosine Kinases and Phosphorylation CascadesOrganisms & Life Processes · on the way
  73. Bone, Cartilage and the Mechanics of a JointThe Human Body · on the way
  74. From Photons to Spikes: the RetinaThe Human Body · on the way
  75. Transmitter Systems and Two Kinds of ReceptorThe Human Body · on the way
  76. Synaptic Plasticity and the Molecular Rules of ChangeThe Human Body · on the way
  77. Pacemaker Potentials, Conduction and Reading an ECGThe Human Body · on the way
  78. Preload, Afterload and the Frank-Starling RelationshipThe Human Body · on the way
  79. Allosteric Enzymes, Cooperativity and the Sigmoid CurveBiochemistry & Molecular Biology · on the way
  80. Coenzymes, Cofactors and the Chemistry They SupplyBiochemistry & Molecular Biology · on the way
  81. Coupled Reactions and Why ATP Is the Cell's CurrencyBiochemistry & Molecular Biology · on the way
  82. Control Points in Glycolysis and the Committed StepBiochemistry & Molecular Biology · on the way
  83. Replication Machinery: Origins, Forks and TelomeresBiochemistry & Molecular Biology · on the way
  84. DNA Damage and the Repair Pathways That Fix ItBiochemistry & Molecular Biology · on the way
  85. Homologous Recombination and Double-Strand Break RepairGenetics & Evolution · on the way
  86. Transcription Initiation: Promoters, General Factors and Polymerase RecruitmentBiochemistry & Molecular Biology · on the way
  87. Enhancers, Accessibility and Combinatorial ControlGenetics & Evolution · on the way
  88. Metabolic Diversity: Choosing an Electron Donor and AcceptorMicrobiology · on the way
  89. Virus Structure and Classification by Genome TypeMicrobiology · on the way
  90. Viral Life Cycles: Lysis, Lysogeny and LatencyMicrobiology · on the way
  91. Bacteriophages as Predators and as Laboratory ToolsMicrobiology · on the way
  92. Operon Logic: Induction, Repression and Feedback on TranscriptionMicrobiology · on the way
  93. Land Plants: Vascular Tissue and a Life Cycle That AlternatesOrganisms & Life Processes · on the way
  94. Animal Body Plans: Symmetry, Cavities and the Deep SplitsOrganisms & Life Processes · on the way
  95. Gastrulation and Laying Down the Body AxesOrganisms & Life Processes · on the way
  96. Biomes and What Draws Their BoundariesEcology & Conservation · on the way

Mathematics

  1. Vectors in Three DimensionsGeometry · on the way
  2. The Dot Product: Angles and ProjectionsGeometry · on the way
  3. The Cross Product and Oriented AreaGeometry · on the way
  4. Lines and Planes in SpaceGeometry · on the way
  5. What a Differential Equation Says and What a Solution IsDifferential Equations · on the way
  6. Linear Maps and Their MatricesLinear Algebra · on the way
  7. Change of BasisLinear Algebra · on the way
  8. Eigenvalues and EigenvectorsLinear Algebra · on the way
  9. Diagonalisation and Powers of a MatrixLinear Algebra · on the way
  10. Inner Products, Length and OrthogonalityLinear Algebra · on the way
  11. Riemann Sums and the Definite Integral as a LimitCalculus & Analysis · on the way
  12. The Fundamental Theorem of CalculusCalculus & Analysis · on the way
  13. Integration by SubstitutionCalculus & Analysis · on the way
  14. Integration by PartsCalculus & Analysis · on the way
  15. Trigonometric Integrals and Trigonometric SubstitutionCalculus & Analysis · on the way
  16. Partial Fractions for Rational IntegrandsCalculus & Analysis · on the way
  17. Improper Integrals and Their ConvergenceCalculus & Analysis · on the way
  18. Vector-Valued Functions and Motion Along a CurveCalculus & Analysis · on the way
  19. Functions of Several Variables and Level CurvesCalculus & Analysis · on the way
  20. Partial DerivativesCalculus & Analysis · on the way
  21. Tangent Planes and Linear ApproximationCalculus & Analysis · on the way
  22. The Multivariable Chain RuleCalculus & Analysis · on the way
  23. Directional Derivatives and the GradientCalculus & Analysis · on the way
  24. Critical Points and Optimisation in Two VariablesCalculus & Analysis · on the way
  25. Lagrange MultipliersCalculus & Analysis · on the way
  26. Double Integrals over General RegionsCalculus & Analysis · on the way
  27. Volumes of Revolution: Disks, Washers and ShellsCalculus & Analysis · on the way
  28. Arc Length and the Area of a Surface of RevolutionCalculus & Analysis · on the way
  29. Sequences and Their LimitsCalculus & Analysis · on the way
  30. Infinite Series and the Geometric SeriesCalculus & Analysis · on the way
  31. Convergence Tests for Series of Positive TermsCalculus & Analysis · on the way
  32. Alternating Series and Absolute ConvergenceCalculus & Analysis · on the way
  33. Power Series and the Radius of ConvergenceCalculus & Analysis · on the way
  34. Taylor and Maclaurin SeriesCalculus & Analysis · on the way
  35. Complex Functions and the Complex Plane as a DomainComplex Analysis · on the way
  36. Complex Differentiability and the Cauchy-Riemann EquationsComplex Analysis · on the way
  37. Direction Fields and Euler's MethodDifferential Equations · on the way
  38. Separable EquationsDifferential Equations · on the way
  39. First-Order Linear Equations and the Integrating FactorDifferential Equations · on the way
  40. The Logistic Equation and Saturating GrowthDifferential Equations · on the way
  41. Continuous Random Variables and Density FunctionsProbability · on the way
  42. Expectation and Variance by IntegrationProbability · on the way
  43. Joint Distributions, Covariance and IndependenceProbability · on the way
  44. The Law of Large Numbers and the Central Limit TheoremData & Statistics · on the way
  45. The Pigeonhole PrincipleDiscrete Mathematics · on the way
  46. Inclusion-ExclusionDiscrete Mathematics · on the way
  47. Recurrence Relations and Characteristic RootsDiscrete Mathematics · on the way
  48. Modular Arithmetic and Congruence ClassesNumber Theory · on the way
  49. Linear Congruences and the Chinese Remainder TheoremNumber Theory · on the way

Computing

  1. Requirements: Turning a Wish into a Testable StatementSoftware Engineering · on the way
  2. Interfaces, Coupling and What a Module PromisesSoftware Engineering · on the way
  3. Design Patterns: Naming a Solution That Keeps RecurringSoftware Engineering · on the way
  4. Refactoring: Changing Structure Without Changing BehaviourSoftware Engineering · on the way
  5. Randomised Quicksort and Expected Running TimeAlgorithms & Data Structures · on the way
  6. The Comparison-Sorting Lower BoundAlgorithms & Data Structures · on the way
  7. Heaps and Priority QueuesAlgorithms & Data Structures · on the way
  8. Amortised AnalysisAlgorithms & Data Structures · on the way
  9. Greedy Choice and the Exchange ArgumentAlgorithms & Data Structures · on the way
  10. Linear Regression by Least SquaresMachine Learning · on the way
  11. Gradient Descent: Following the Slope DownhillMachine Learning · on the way
  12. Logistic Regression and the Decision BoundaryMachine Learning · on the way
  13. Overfitting and the Bias-Variance Trade-offMachine Learning · on the way
  14. Many Cores and the Limit on SpeedupComputer Systems · on the way
  15. What an Operating System Is: Privilege and System CallsComputer Systems · on the way
  16. Processes, Context Switches and What They CostComputer Systems · on the way
  17. Scheduling: Deciding Which Process Runs NextComputer Systems · on the way
  18. Virtual Memory and Address TranslationComputer Systems · on the way
  19. Naming: DNS and the Resolution PathNetworks & Security · on the way
  20. Routing: How a Path Is LearnedNetworks & Security · on the way
  21. The Web as a Protocol: Requests, State and CachingNetworks & Security · on the way
  22. Window Functions and Running CalculationsData & Databases · on the way
  23. Indexes: B-Trees and the Cost of a LookupData & Databases · on the way
  24. Reading a Query PlanData & Databases · on the way
  25. Transactions and the ACID PromiseData & Databases · on the way
What a 19-year-old learns · LightMySky