LightMySky
Explore

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

Computing

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

Mathematics

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