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

Mathematics

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

Computing

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