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

Mathematics

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

Computing

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