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What a 24-year-old learns

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

At age 24, 141 topics open up across Science, Mathematics, Computing. Each one has prerequisites that come first, so the order matters more than the list: Characterisation Standards: What Counts as Proof of a New Compound is a typical starting point.

How do I know what a 24-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. Characterisation Standards: What Counts as Proof of a New CompoundChemistry · on the way
  2. Chain Growth and Step Growth: Two Routes to a PolymerChemistry · on the way
  3. Choosing Between Vibrational Methods: Infrared, Raman and Resonance RamanChemistry · on the way
  4. Single-Crystal Diffraction: From Reflections to a Refined StructureChemistry · on the way
  5. Cross-Coupling in Practice: Choosing Ligand, Base and ConditionsChemistry · on the way
  6. Controlled Radical Polymerisation and Block ArchitectureChemistry · on the way
  7. Electron Correlation and Methods Past Hartree-FockChemistry · on the way
  8. Excited States by Calculation and Simulated Electronic SpectraChemistry · on the way
  9. Functionalising a Carbon-Hydrogen Bond Without a HandleChemistry · on the way
  10. Glass Transition, Crystallinity and Entanglement in PolymersChemistry · on the way
  11. Molecular Recognition: Preorganisation, Complementarity and Binding ConstantsChemistry · on the way
  12. Olefin Metathesis and Ring-Closing StrategyChemistry · on the way
  13. Photoredox and Electrochemical Routes to Radical IntermediatesChemistry · on the way
  14. Putting the Solvent Into a CalculationChemistry · on the way
  15. Molecular Dynamics and Free Energy from SamplingChemistry · on the way
  16. Reaction Dynamics: Trajectories Across a Potential Energy SurfaceChemistry · on the way
  17. Risk Assessment for a Reaction Nobody Has Run HereChemistry · on the way
  18. Self-Assembly: Templates, Reversibility and Error CorrectionChemistry · on the way
  19. Taking a Route into Flow and Onto ScaleChemistry · on the way
  20. Reading a Total Synthesis as an ArgumentChemistry · on the way
  21. Writing a Research Proposal: Question, Feasibility and MilestonesChemistry · on the way
  22. Reporting Chemical Data: Statistics, Figures and Data AvailabilityChemistry · on the way
  23. Ultrafast Spectroscopy and Watching a Reaction HappenChemistry · on the way
  24. Noether's Theorem: Symmetry and Conserved QuantitiesForces & Motion · on the way
  25. From Coordinates to Fields: the Lagrangian DensityForces & Motion · on the way
  26. Unitary Time Evolution and the Heisenberg PictureQuantum & Modern Physics · on the way
  27. Angular Momentum from Its Commutation RelationsQuantum & Modern Physics · on the way
  28. Adding Angular Momenta and the Coupled BasisQuantum & Modern Physics · on the way
  29. Identical Particles and the Symmetry of a Many-Body StateQuantum & Modern Physics · on the way
  30. Degenerate Perturbation Theory and the Variational MethodQuantum & Modern Physics · on the way
  31. The Path Integral and the Sum Over HistoriesQuantum & Modern Physics · on the way
  32. Time-Dependent Perturbation Theory and Fermi's Golden RuleQuantum & Modern Physics · on the way
  33. Scattering: Cross-Sections and the Born ApproximationQuantum & Modern Physics · on the way
  34. Density Matrices, Entanglement and the Bell TestQuantum & Modern Physics · on the way
  35. Field Quantisation: Creation Operators and Particle NumberQuantum & Modern Physics · on the way
  36. The Klein-Gordon and Dirac EquationsQuantum & Modern Physics · on the way
  37. Covariant Electrodynamics and the Field TensorElectricity & Magnetism · on the way
  38. Gauge Freedom and the Potentials as the Working VariablesElectricity & Magnetism · on the way
  39. Radiation from an Accelerating ChargeElectricity & Magnetism · on the way
  40. Fluctuations, Linear Response and the Fluctuation-Dissipation RelationThermal & Statistical Physics · on the way
  41. Phase Transitions, Order Parameters and Broken SymmetryThermal & Statistical Physics · on the way
  42. The Ising Model and the Mean-Field ApproximationThermal & Statistical Physics · on the way
  43. Critical Exponents, Scaling and UniversalityThermal & Statistical Physics · on the way
  44. Crystal Lattices, the Reciprocal Lattice and Bloch's TheoremMatter & Materials · on the way
  45. Phonons and the Heat Capacity of SolidsMatter & Materials · on the way
  46. Band Structure: Metals, Insulators and the GapMatter & Materials · on the way
  47. Semiconductors, Doping and the p-n JunctionMatter & Materials · on the way
  48. Superconductivity: the Meissner Effect and Cooper PairsMatter & Materials · on the way
  49. Tensors and the Metric on a Curved ManifoldAstronomy & Astrophysics · on the way
  50. Parallel Transport, Christoffel Symbols and the Geodesic EquationAstronomy & Astrophysics · on the way
  51. Curvature and the Einstein Field EquationAstronomy & Astrophysics · on the way
  52. The Schwarzschild Solution: Orbits, Redshift and the HorizonAstronomy & Astrophysics · on the way
  53. Linearised Gravity and Gravitational WavesAstronomy & Astrophysics · on the way
  54. Systematic Error, Controls and the Design of a MeasurementScientific Inquiry · on the way
  55. Reading a Paper: the Claim, the Evidence and the AssumptionScientific Inquiry · on the way
  56. Writing Physics: the Figure, the Error Bar and the Defensible ClaimScientific Inquiry · on the way
  57. From Hit to Lead: Structure-Activity RelationshipsChemistry · on the way
  58. Drug-Like Properties: Solubility, Permeability and Metabolic FateChemistry · on the way
  59. Chemical Biology: Bioconjugation and Reporting on a Molecule in a CellChemistry · on the way
  60. Bayesian Phylogenetics: Priors, Sampling and Judging ConvergenceGenetics & Evolution · on the way
  61. Phylogenomics: Gene Trees, Species Trees and Why They DisagreeGenetics & Evolution · on the way
  62. Differential Expression from Counts: Dispersion, Fit and ShrinkageGenetics & Evolution · on the way
  63. Testing Thousands of Genes at Once: False Discovery Rate and What q MeansGenetics & Evolution · on the way
  64. From a Gene List to Biology: Enrichment Tests and Their BackgroundsGenetics & Evolution · on the way
  65. Power and Effect Size, Decided Before the DataScientific Inquiry · on the way
  66. Researcher Degrees of Freedom and the Pre-registered Analysis PlanScientific Inquiry · on the way
  67. Reading a Primary Paper: The Claim, the Figure and the Missing ControlScientific Inquiry · on the way
  68. Reproducibility in Practice: Data, Code and What Another Lab Can RerunScientific Inquiry · on the way
  69. Mapping Regulatory Elements: Accessibility, Occupancy and ContactGenetics & Evolution · on the way
  70. Single-Cell Analysis: Normalisation, Embedding and Naming Cell StatesGenetics & Evolution · on the way
  71. Modelling a Biological System: Rate Equations, Parameters and FitGenetics & Evolution · on the way
  72. Genome Engineering: Cut Site, Repair Choice and Editing OutcomeGenetics & Evolution · on the way
  73. Ethics of Emerging Biotechnology: Editing, Enhancement and BiosecurityScientific Inquiry · on the way
  74. Base and Prime Editing: Changing a Letter Without Breaking Both StrandsGenetics & Evolution · on the way
  75. Pooled Genetic Screens: Library Design, Selection and Reading a Hit ListGenetics & Evolution · on the way
  76. Synthetic Circuits: Switches, Oscillators and Why They Misbehave in CellsMicrobiology · on the way
  77. Metabolic Engineering: Redirecting Flux Through a Production HostMicrobiology · on the way
  78. Proteomics: Mass Spectra, Quantification and Interaction MapsBiochemistry & Molecular Biology · on the way
  79. The Tumour Microenvironment: Stroma, Hypoxia and Immune ExclusionOrganisms & Life Processes · on the way
  80. Targeted Therapy and the Resistance That Follows ItOrganisms & Life Processes · on the way
  81. Checkpoint Blockade: Taking a Brake Off a T CellThe Human Body · on the way
  82. Clinical Trials: Phases, Endpoints and Why Most Candidates FailThe Human Body · on the way
  83. Engineered Cell Therapy: Receptor Design, Manufacture and ToxicityThe Human Body · on the way
  84. Target Validation and Lead Discovery: From a Biological Claim to a MoleculeBiochemistry & Molecular Biology · on the way
  85. The Host Microbiome: Composition, Causation and InterventionMicrobiology · on the way

Mathematics

  1. Monotone Convergence, Fatou and Dominated ConvergenceCalculus & Analysis · on the way
  2. Product Measure and Fubini's TheoremCalculus & Analysis · on the way
  3. Lp Spaces and the Inequalities They Rest OnCalculus & Analysis · on the way
  4. Normed Spaces, Completeness and Banach SpacesCalculus & Analysis · on the way
  5. Bounded Linear Operators and the Operator NormCalculus & Analysis · on the way
  6. Baire Category and the Uniform Boundedness PrincipleCalculus & Analysis · on the way
  7. The Hahn-Banach Theorem and the Dual SpaceCalculus & Analysis · on the way
  8. Hilbert Spaces and Orthogonal Projection in Infinite DimensionsCalculus & Analysis · on the way
  9. Compact Self-Adjoint Operators and the Spectral TheoremCalculus & Analysis · on the way
  10. Convolution, Plancherel and Transforming a DerivativeCalculus & Analysis · on the way
  11. Weak Solutions and Test FunctionsDifferential Equations · on the way
  12. Markov Chains and the Memoryless AssumptionProbability · on the way
  13. Stationary Distributions and Long-Run BehaviourProbability · on the way
  14. Martingales and Optional StoppingProbability · on the way
  15. Brownian Motion and Its Defining PropertiesProbability · on the way
  16. Conditioning, Stability and Floating-Point ErrorCalculus & Analysis · on the way
  17. Iterative Methods for Large Linear SystemsLinear Algebra · on the way
  18. Numerical Schemes for Evolution EquationsDifferential Equations · on the way
  19. Polynomial Rings, Irreducibility and Unique FactorisationAbstract Algebra · on the way
  20. Modules: Linear Algebra Over a RingAbstract Algebra · on the way
  21. Field Extensions and Their DegreesAbstract Algebra · on the way
  22. The Galois CorrespondenceAbstract Algebra · on the way
  23. Characters and the Orthogonality RelationsAbstract Algebra · on the way
  24. Decomposing a Representation from Its CharacterAbstract Algebra · on the way
  25. Topological Spaces: Continuity Without DistanceTopology · on the way
  26. Definitions as Design DecisionsMathematical Thinking · on the way
  27. Counterexamples and Testing a ConjectureMathematical Thinking · on the way
  28. Open Problems as a GenreMathematical Thinking · on the way
  29. Compactness and ConnectednessTopology · on the way
  30. The Fundamental Group and Loops on a CircleTopology · on the way

Computing

  1. Complexity Beyond NP: Space, Randomness and the HierarchyAlgorithms & Data Structures · on the way
  2. SAT Solvers and What Makes Search PracticalAlgorithms & Data Structures · on the way
  3. Adapting a Pretrained Model: Fine-Tuning and Low-Rank UpdatesMachine Learning · on the way
  4. Generative Models: Learning a Distribution You Can SampleMachine Learning · on the way
  5. Diffusion Models: Learning to Undo NoiseMachine Learning · on the way
  6. Markov Decision Processes: States, Actions and ReturnMachine Learning · on the way
  7. Temporal-Difference Learning and Q-LearningMachine Learning · on the way
  8. Policy Gradients and the Actor-Critic SplitMachine Learning · on the way
  9. Learning from Human Preferences: Reward Models and Policy OptimisationMachine Learning · on the way
  10. Training Across Many Devices: Data, Model and Pipeline ParallelismMachine Learning · on the way
  11. Serving a Model: Batching, the Key-Value Cache and QuantisationMachine Learning · on the way
  12. Distributed Transactions and the Blocking Case of Two-Phase CommitData & Databases · on the way
  13. Conflict-Free Replicated Data TypesData & Databases · on the way
  14. Log-Structured Storage and CompactionData & Databases · on the way
  15. Stream Processing: Windows, Watermarks and Late EventsData & Databases · on the way
  16. Cloud-Native Architecture: Containers, Schedulers and the Control LoopComputer Systems · on the way
  17. Observability and Tail Latency Across ServicesComputer Systems · on the way
  18. Benchmarks and the Traps in ThemMachine Learning · on the way
  19. Specifying Correctness: Safety, Liveness and InvariantsSoftware Engineering · on the way
  20. Model Checking and the State-Space ExplosionSoftware Engineering · on the way
  21. Hoare Logic and Proving a Program Meets Its SpecificationSoftware Engineering · on the way
  22. Type Soundness: Progress and PreservationComputer Systems · on the way
  23. Cryptographic Security Definitions and Proof by ReductionNetworks & Security · on the way
  24. Reproducibility: Seeds, Environments and the AblationSoftware Engineering · on the way
  25. Scoping and Writing a Thesis-Scale ProjectSoftware Engineering · on the way
  26. Interpretability: Probes, Features and CircuitsMachine Learning · on the way
What a 24-year-old learns · LightMySky