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What a 21-year-old learns

111 topics open up at age 21, 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 20age 22
What should a 21-year-old be learning?

At age 21, 111 topics open up across Science, Computing, Mathematics. Each one has prerequisites that come first, so the order matters more than the list: Generalised Coordinates and the Lagrangian is a typical starting point.

How do I know what a 21-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. Generalised Coordinates and the LagrangianForces & Motion · on the way
  2. The Euler-Lagrange Equation and Conserved MomentaForces & Motion · on the way
  3. The Microcanonical and Canonical EnsemblesThermal & Statistical Physics · on the way
  4. Catalytic Cycles: Hydroformylation and Cross-CouplingChemistry · on the way
  5. Close Packing, Unit Cells and Ionic Lattice TypesChemistry · on the way
  6. Band Theory, Defects and Why Some Solids ConductChemistry · on the way
  7. Retrosynthesis: Disconnections and SynthonsChemistry · on the way
  8. Planning a Multi-Step Synthesis: Order, Protection and YieldChemistry · on the way
  9. Carbohydrates: Anomers, Mutarotation and the Glycosidic BondChemistry · on the way
  10. Amino Acids and Peptides: Zwitterions and the Peptide BondChemistry · on the way
  11. Designing a Safer Process: Hazard, Scale and WasteChemistry · on the way
  12. The Nernst Equation and Cells Away from Standard ConditionsChemistry · on the way
  13. Electrode Kinetics: Exchange Current and OverpotentialChemistry · on the way
  14. Two-Dimensional NMR and Assigning a Whole StructureChemistry · on the way
  15. Potentiometry, Ion-Selective Electrodes and VoltammetryChemistry · on the way
  16. Method Validation: Accuracy, Precision, Recovery and RobustnessChemistry · on the way
  17. Fourier Analysis and the Wave PacketWaves, Light & Sound · on the way
  18. Stimulated Emission and How a Laser WorksWaves, Light & Sound · on the way
  19. Orbital Angular Momentum and the Quantum NumbersQuantum & Modern Physics · on the way
  20. Electron Spin and the Stern-Gerlach ExperimentQuantum & Modern Physics · on the way
  21. The Exclusion Principle and Multi-Electron AtomsQuantum & Modern Physics · on the way
  22. First-Order Perturbation TheoryQuantum & Modern Physics · on the way
  23. The Nuclear Shell Model and the Magic NumbersQuantum & Modern Physics · on the way
  24. Plane Electromagnetic Waves from Maxwell's EquationsElectricity & Magnetism · on the way
  25. The Poynting Vector and Radiation PressureElectricity & Magnetism · on the way
  26. Fermi-Dirac and Bose-Einstein StatisticsThermal & Statistical Physics · on the way
  27. The Free Electron Gas and the Fermi EnergyThermal & Statistical Physics · on the way
  28. The Hertzsprung-Russell Diagram and Stellar EvolutionAstronomy & Astrophysics · on the way
  29. General Relativity: Curved Spacetime and Its TestsAstronomy & Astrophysics · on the way
  30. Stellar Death: White Dwarfs, Neutron Stars and Black HolesAstronomy & Astrophysics · on the way
  31. Galaxies, Redshift and the Expanding UniverseAstronomy & Astrophysics · on the way
  32. Galaxy Types, the Milky Way's Structure and Active NucleiAstronomy & Astrophysics · on the way
  33. The Cosmic Microwave Background and the Light ElementsAstronomy & Astrophysics · on the way
  34. Dark Matter, Dark Energy and What the Universe Is Made OfAstronomy & Astrophysics · on the way
  35. The Interstellar Medium and How Stars FormAstronomy & Astrophysics · on the way
  36. The Scale Factor, the Friedmann Equation and the Age of the UniverseAstronomy & Astrophysics · on the way
  37. The Sun as a Star: Photosphere, Corona and the Activity CycleAstronomy & Astrophysics · on the way
  38. Motor Control: From Intention to MuscleThe Human Body · on the way
  39. Memory Systems: What Amnesia SeparatesThe Human Body · on the way
  40. Annotation, Orthologues and Comparative GenomicsGenetics & Evolution · on the way
  41. Association Studies and What They Can and Cannot ShowGenetics & Evolution · on the way
  42. Measuring Genetic Variation: Heterozygosity and Population StructureGenetics & Evolution · on the way
  43. Fluorescent Tagging and Reading a Live-Cell ImageBiochemistry & Molecular Biology · on the way
  44. Fractionation, Blotting and Pulling Down a Binding PartnerBiochemistry & Molecular Biology · on the way
  45. The Pentose Phosphate Pathway and Reducing Power for BiosynthesisBiochemistry & Molecular Biology · on the way
  46. Transamination, Ammonia and the Urea CycleBiochemistry & Molecular Biology · on the way
  47. Flux Control and Following Atoms with Labelled SubstratesBiochemistry & Molecular Biology · on the way
  48. Antimicrobial Targets, Resistance Mechanisms and Selective ToxicityMicrobiology · on the way
  49. Epidemiology: Incidence, the Reproduction Number and Tracking an OutbreakMicrobiology · on the way
  50. Applied Microbiology: Fermentation, Bioremediation and Host MicrobiomesMicrobiology · on the way
  51. Predation, Herbivory and Trophic CascadesEcology & Conservation · on the way
  52. Measuring Diversity: Richness, Evenness and Turnover Between SitesEcology & Conservation · on the way
  53. Productivity, Nutrient Limitation and Ecosystem StoichiometryEcology & Conservation · on the way
  54. Conservation: Small Populations, Fragmentation and Reserve DesignEcology & Conservation · on the way
  55. Global Change Ecology: Ranges, Phenology and Regime ShiftsEcology & Conservation · on the way
  56. Adaptive Immunity: Antigen Presentation and T-Cell SelectionThe Human Body · on the way
  57. Antibody Diversity, Memory and What Tolerance Failure CostsThe Human Body · on the way
  58. Fuel Homeostasis and the Fed to Fasted SwitchThe Human Body · on the way
  59. Innate Immunity: Pattern Recognition, Complement and InflammationThe Human Body · on the way
  60. Sleep, Circadian Rhythms and the Clock in the BrainThe Human Body · on the way
  61. The Stress Response: Fast Nerves, Slow Hormones and the Cost of Staying OnThe Human Body · on the way

Computing

  1. Software Architecture: Layers, Services and Their Trade-offsSoftware Engineering · on the way
  2. Technical Debt and the Cost of the Next ChangeSoftware Engineering · on the way
  3. Working in a Team: Issues, Estimates and IterationsSoftware Engineering · on the way
  4. Network Flow and the Max-Flow Min-Cut TheoremAlgorithms & Data Structures · on the way
  5. From Perceptron to Multilayer NetworkMachine Learning · on the way
  6. Backpropagation: Assigning Blame for an ErrorMachine Learning · on the way
  7. Reductions: Solving One Problem by Turning It into AnotherAlgorithms & Data Structures · on the way
  8. P, NP and What NP-Complete MeansAlgorithms & Data Structures · on the way
  9. Living with NP-Hardness: Approximation and HeuristicsAlgorithms & Data Structures · on the way
  10. Message Passing and Asynchronous WorkComputer Systems · on the way
  11. Lexing and Parsing: From Text to a Syntax TreeComputer Systems · on the way
  12. Semantic Analysis and the Intermediate RepresentationComputer Systems · on the way
  13. Code Generation and What an Optimiser May ChangeComputer Systems · on the way
  14. Deep Learning: Convolution, Sequence and ScaleMachine Learning · on the way
  15. Hashes, Signatures and CertificatesNetworks & Security · on the way
  16. TLS: Putting the Pieces TogetherNetworks & Security · on the way
  17. Threat Modelling: Assets, Adversaries and Trust BoundariesNetworks & Security · on the way
  18. Authentication, Authorisation and Secure DefaultsNetworks & Security · on the way
  19. Partitioning and Replication for ScaleData & Databases · on the way
  20. Data Pipelines: Batch, Streaming and Doing It TwiceData & Databases · on the way
  21. The Data Science WorkflowData & Databases · on the way
  22. Cleaning Real Data: Missing, Duplicated and WrongData & Databases · on the way
  23. Exploratory Analysis and an Honest ChartData & Databases · on the way
  24. Dependencies, Licences and the Supply ChainSoftware Engineering · on the way
  25. Fairness, Accountability and the Limits of a ModelMachine Learning · on the way

Mathematics

  1. Solving Initial Value Problems with Laplace TransformsDifferential Equations · on the way
  2. Sturm-Liouville Problems and Eigenfunction ExpansionsDifferential Equations · on the way
  3. Green's Functions for Boundary Value ProblemsDifferential Equations · on the way
  4. Systems of Differential Equations and Eigenvalue SolutionsDifferential Equations · on the way
  5. Phase Portraits, Equilibria and StabilityDifferential Equations · on the way
  6. Laurent Series and Classifying Isolated SingularitiesComplex Analysis · on the way
  7. The Residue TheoremComplex Analysis · on the way
  8. Evaluating Real Integrals by ResiduesComplex Analysis · on the way
  9. The Argument Principle and Rouche's TheoremComplex Analysis · on the way
  10. Conformal Maps and Mobius TransformationsComplex Analysis · on the way
  11. Comparing Two PopulationsData & Statistics · on the way
  12. Chi-Square Tests for Categorical DataData & Statistics · on the way
  13. One-Way Analysis of VarianceData & Statistics · on the way
  14. Simple Linear Regression and Inference on the SlopeData & Statistics · on the way
  15. Multiple Regression and Model DiagnosticsData & Statistics · on the way
  16. Groups, Subgroups and SymmetryAbstract Algebra · on the way
  17. Homomorphisms, Cosets and Lagrange's TheoremAbstract Algebra · on the way
  18. Rings, Fields and Their First PropertiesAbstract Algebra · on the way
  19. Quadratic Residues and the Law of ReciprocityNumber Theory · on the way
  20. The Distribution of Primes and What Is Still OpenNumber Theory · on the way
  21. Completeness and the Contraction Mapping TheoremTopology · on the way
  22. Compactness in Metric SpacesTopology · on the way
  23. Euler Trails and Hamilton CyclesDiscrete Mathematics · on the way
  24. Graph Colouring and PlanarityDiscrete Mathematics · on the way
  25. Matchings and Hall's TheoremDiscrete Mathematics · on the way
What a 21-year-old learns · LightMySky