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What a 23-year-old learns

91 topics open up at age 23, 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 22age 24
What should a 23-year-old be learning?

At age 23, 91 topics open up across Science, Mathematics, Computing. Each one has prerequisites that come first, so the order matters more than the list: Controlled Radical Polymerisation and Block Architecture is a typical starting point.

How do I know what a 23-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. Controlled Radical Polymerisation and Block ArchitectureChemistry · on the way
  2. Electron Correlation and Methods Past Hartree-FockChemistry · on the way
  3. Excited States by Calculation and Simulated Electronic SpectraChemistry · on the way
  4. Functionalising a Carbon-Hydrogen Bond Without a HandleChemistry · on the way
  5. Glass Transition, Crystallinity and Entanglement in PolymersChemistry · on the way
  6. Molecular Recognition: Preorganisation, Complementarity and Binding ConstantsChemistry · on the way
  7. Olefin Metathesis and Ring-Closing StrategyChemistry · on the way
  8. Photoredox and Electrochemical Routes to Radical IntermediatesChemistry · on the way
  9. Putting the Solvent Into a CalculationChemistry · on the way
  10. Molecular Dynamics and Free Energy from SamplingChemistry · on the way
  11. Reaction Dynamics: Trajectories Across a Potential Energy SurfaceChemistry · on the way
  12. Risk Assessment for a Reaction Nobody Has Run HereChemistry · on the way
  13. Self-Assembly: Templates, Reversibility and Error CorrectionChemistry · on the way
  14. Taking a Route into Flow and Onto ScaleChemistry · on the way
  15. Reading a Total Synthesis as an ArgumentChemistry · on the way
  16. Writing a Research Proposal: Question, Feasibility and MilestonesChemistry · on the way
  17. Reporting Chemical Data: Statistics, Figures and Data AvailabilityChemistry · on the way
  18. Ultrafast Spectroscopy and Watching a Reaction HappenChemistry · on the way
  19. Adding Angular Momenta and the Coupled BasisQuantum & Modern Physics · on the way
  20. Identical Particles and the Symmetry of a Many-Body StateQuantum & Modern Physics · on the way
  21. Degenerate Perturbation Theory and the Variational MethodQuantum & Modern Physics · on the way
  22. The Path Integral and the Sum Over HistoriesQuantum & Modern Physics · on the way
  23. Time-Dependent Perturbation Theory and Fermi's Golden RuleQuantum & Modern Physics · on the way
  24. Scattering: Cross-Sections and the Born ApproximationQuantum & Modern Physics · on the way
  25. Density Matrices, Entanglement and the Bell TestQuantum & Modern Physics · on the way
  26. Field Quantisation: Creation Operators and Particle NumberQuantum & Modern Physics · on the way
  27. The Klein-Gordon and Dirac EquationsQuantum & Modern Physics · on the way
  28. Radiation from an Accelerating ChargeElectricity & Magnetism · on the way
  29. The Ising Model and the Mean-Field ApproximationThermal & Statistical Physics · on the way
  30. Critical Exponents, Scaling and UniversalityThermal & Statistical Physics · on the way
  31. Crystal Lattices, the Reciprocal Lattice and Bloch's TheoremMatter & Materials · on the way
  32. Phonons and the Heat Capacity of SolidsMatter & Materials · on the way
  33. Band Structure: Metals, Insulators and the GapMatter & Materials · on the way
  34. Semiconductors, Doping and the p-n JunctionMatter & Materials · on the way
  35. Superconductivity: the Meissner Effect and Cooper PairsMatter & Materials · on the way
  36. Tensors and the Metric on a Curved ManifoldAstronomy & Astrophysics · on the way
  37. Parallel Transport, Christoffel Symbols and the Geodesic EquationAstronomy & Astrophysics · on the way
  38. Curvature and the Einstein Field EquationAstronomy & Astrophysics · on the way
  39. The Schwarzschild Solution: Orbits, Redshift and the HorizonAstronomy & Astrophysics · on the way
  40. Linearised Gravity and Gravitational WavesAstronomy & Astrophysics · on the way
  41. Reading a Paper: the Claim, the Evidence and the AssumptionScientific Inquiry · on the way
  42. Writing Physics: the Figure, the Error Bar and the Defensible ClaimScientific Inquiry · on the way
  43. From Hit to Lead: Structure-Activity RelationshipsChemistry · on the way
  44. Drug-Like Properties: Solubility, Permeability and Metabolic FateChemistry · on the way
  45. Chemical Biology: Bioconjugation and Reporting on a Molecule in a CellChemistry · on the way
  46. Testing Thousands of Genes at Once: False Discovery Rate and What q MeansGenetics & Evolution · on the way
  47. From a Gene List to Biology: Enrichment Tests and Their BackgroundsGenetics & Evolution · on the way
  48. Reproducibility in Practice: Data, Code and What Another Lab Can RerunScientific Inquiry · on the way
  49. Single-Cell Analysis: Normalisation, Embedding and Naming Cell StatesGenetics & Evolution · on the way
  50. Modelling a Biological System: Rate Equations, Parameters and FitGenetics & Evolution · on the way
  51. Ethics of Emerging Biotechnology: Editing, Enhancement and BiosecurityScientific Inquiry · on the way
  52. Pooled Genetic Screens: Library Design, Selection and Reading a Hit ListGenetics & Evolution · on the way
  53. Synthetic Circuits: Switches, Oscillators and Why They Misbehave in CellsMicrobiology · on the way
  54. Metabolic Engineering: Redirecting Flux Through a Production HostMicrobiology · on the way
  55. Proteomics: Mass Spectra, Quantification and Interaction MapsBiochemistry & Molecular Biology · on the way
  56. Clinical Trials: Phases, Endpoints and Why Most Candidates FailThe Human Body · on the way
  57. Engineered Cell Therapy: Receptor Design, Manufacture and ToxicityThe Human Body · on the way
  58. Target Validation and Lead Discovery: From a Biological Claim to a MoleculeBiochemistry & Molecular Biology · on the way
  59. The Host Microbiome: Composition, Causation and InterventionMicrobiology · on the way

Mathematics

  1. Bounded Linear Operators and the Operator NormCalculus & Analysis · on the way
  2. Baire Category and the Uniform Boundedness PrincipleCalculus & Analysis · on the way
  3. The Hahn-Banach Theorem and the Dual SpaceCalculus & Analysis · on the way
  4. Hilbert Spaces and Orthogonal Projection in Infinite DimensionsCalculus & Analysis · on the way
  5. Compact Self-Adjoint Operators and the Spectral TheoremCalculus & Analysis · on the way
  6. Convolution, Plancherel and Transforming a DerivativeCalculus & Analysis · on the way
  7. Martingales and Optional StoppingProbability · on the way
  8. Brownian Motion and Its Defining PropertiesProbability · on the way
  9. Conditioning, Stability and Floating-Point ErrorCalculus & Analysis · on the way
  10. Iterative Methods for Large Linear SystemsLinear Algebra · on the way
  11. Numerical Schemes for Evolution EquationsDifferential Equations · on the way
  12. Characters and the Orthogonality RelationsAbstract Algebra · on the way
  13. Decomposing a Representation from Its CharacterAbstract Algebra · on the way
  14. Topological Spaces: Continuity Without DistanceTopology · on the way
  15. Open Problems as a GenreMathematical Thinking · on the way
  16. Compactness and ConnectednessTopology · on the way
  17. The Fundamental Group and Loops on a CircleTopology · on the way

Computing

  1. Temporal-Difference Learning and Q-LearningMachine Learning · on the way
  2. Policy Gradients and the Actor-Critic SplitMachine Learning · on the way
  3. Learning from Human Preferences: Reward Models and Policy OptimisationMachine Learning · on the way
  4. Training Across Many Devices: Data, Model and Pipeline ParallelismMachine Learning · on the way
  5. Serving a Model: Batching, the Key-Value Cache and QuantisationMachine Learning · on the way
  6. Stream Processing: Windows, Watermarks and Late EventsData & Databases · on the way
  7. Cloud-Native Architecture: Containers, Schedulers and the Control LoopComputer Systems · on the way
  8. Observability and Tail Latency Across ServicesComputer Systems · on the way
  9. Model Checking and the State-Space ExplosionSoftware Engineering · on the way
  10. Hoare Logic and Proving a Program Meets Its SpecificationSoftware Engineering · on the way
  11. Type Soundness: Progress and PreservationComputer Systems · on the way
  12. Cryptographic Security Definitions and Proof by ReductionNetworks & Security · on the way
  13. Reproducibility: Seeds, Environments and the AblationSoftware Engineering · on the way
  14. Scoping and Writing a Thesis-Scale ProjectSoftware Engineering · on the way
  15. Interpretability: Probes, Features and CircuitsMachine Learning · on the way
What a 23-year-old learns · LightMySky