Open Frontier¶
Capability
How does it work? What can I build and verify?¶
Explain mechanisms, construct models, measure uncertainty and build systems that survive contact with physical reality.
Starting points¶
Choose an entry that fits your preparation. This is not a mandatory sequence.
- Mathematical reasoning and proof. Study and practice.
- Scientific computing. Study and practice.
- Metrology + experiments. Study and practice.
Seven specializations | Science Fiction to Science
Subjects¶
-
Mathematical reasoning and proofPractice available
Own definitions, quantifiers, implication, counterexample, induction and proof structure.
Preparation: No subject prerequisite recorded.
First attempt: Negate 'Every tested component is safe.' Give an example where many successful tests fail to establish safety. Explain the missing inference.
How to Prove It: A Structured Approach
Reading details -
Calculus + vector calculusPractice available
Own limits, derivatives as local linearization, integrals as accumulation, gradients/Jacobians, line/surface integrals and field theorems.
Preparation: Mathematical reasoning and proof
Calculus, Volumes I-II
Reading details -
Linear algebraPractice available
Own vector spaces, projections, least squares, matrix maps, rank/nullspace, conditioning, SVD and eigenstructure.
Preparation: Mathematical reasoning and proof; Calculus + vector calculus
Introduction to Linear Algebra
Reading details -
ODEs + dynamical systemsPractice available
Translate changing systems into state equations; solve and analyze equilibria, stability, oscillation, nonlinear behavior and feedback.
Preparation: Calculus + vector calculus; Linear algebra
Nonlinear Dynamics and Chaos
Reading details -
ProbabilityPractice available
Quantify uncertainty, conditioning, expectation, dependence, transformations, concentration and asymptotics.
Preparation: Mathematical reasoning and proof; Calculus + vector calculus; Linear algebra
Introduction to Probability
Open resource · Reading details -
Statistics + causal inferencePractice available
Define estimands; separate prediction from intervention; identify confounding, selection and measurement bias; estimate and stress-test effects.
Preparation: Probability
Causal Inference: What If
Open resource · Reading detailsApplication: AI scientist / artificial scientific intelligence
Application: Regenerative medicine
-
Scientific computingPractice available
Know conditioning, numerical stability, approximation, iterative solution, ODE/PDE discretization and computational verification.
Preparation: Calculus + vector calculus; Probability
Numerical Linear Algebra
Reading details -
OptimizationPractice available
Formulate objectives and constraints; understand convexity, duality, KKT conditions and numerical optimization; audit objectives.
Preparation: Calculus + vector calculus; Linear algebra; Probability; Scientific computing
Convex Optimization
Open resource · Reading detailsApplication: AI scientist / artificial scientific intelligence
-
Information + signalsPractice available
Own entropy, mutual information, channel capacity, transforms, sampling, filtering, spectral reasoning and estimation limits.
Preparation: Linear algebra; Probability; Scientific computing
Elements of Information Theory
Reading details -
Control + estimationPractice available
Design closed loops; analyze stability and robustness; infer hidden state; reason about controllability, observability and tradeoffs.
Preparation: Linear algebra; Probability; Scientific computing; Information + signals
Feedback Systems: An Introduction for Scientists and Engineers
Open resource · Reading detailsApplication: Eldercare/service robots
-
Metrology + experimentsPractice available
Calibrate, quantify uncertainty, design informative experiments, distinguish process variation from measurement variation and reproduce results.
Preparation: Probability
NIST/SEMATECH e-Handbook of Statistical Methods
Open resource · Reading detailsApplication: AI scientist / artificial scientific intelligence
-
Mechanics + electromagnetismPractice available
Convert forces, fields and conservation laws into predictive models; move between particle, rigid-body, orbital and field descriptions.
Preparation: Calculus + vector calculus; Linear algebra; ODEs + dynamical systems
Classical Mechanics
Reading detailsApplication: Fusion power
-
Thermodynamics + statistical mechanicsPractice available
Track energy, entropy and free energy; derive equilibrium tendencies; connect microscopic states to macroscopic limits and transport.
Preparation: Probability; Calculus + vector calculus; ODEs + dynamical systems
An Introduction to Thermal Physics
Reading detailsApplication: Fusion power
-
Quantum + condensed matterPractice available
Reason with wavefunctions/operators and connect quantum states to bands, semiconductors, phonons, magnetism and superconductivity.
Preparation: Linear algebra; ODEs + dynamical systems; Probability; Mathematical reasoning and proof
Introduction to Quantum Mechanics
Reading details -
Chemistry + materialsPractice available
Predict bonding, reaction direction/rate, electrochemistry, diffusion, phase behavior and processing-structure-property links.
Preparation: Mathematical reasoning and proof; Linear algebra
Materials Science and Engineering: An Introduction
Reading detailsApplication: Fusion power
-
Electronics + embedded systemsPractice available
Design and instrument circuits from passive networks through semiconductor interfaces, sensing, power conversion and real-time embedded control.
Preparation: Mathematical reasoning and proof
The Art of Electronics
Reading details -
Mechanical design + fluids + structuresPractice available
Turn loads and flows into safe geometry; reason about stress, fatigue, shells, fluids, pumps, pressure systems and mass-efficient structures.
Preparation: Mathematical reasoning and proof; ODEs + dynamical systems
Shigley's Mechanical Engineering Design
Reading details -
Molecular + cell biologyPractice available
Model cells as chemical, energetic, informational and mechanical systems; understand membranes, metabolism, signaling, division and gene expression.
Preparation: Calculus + vector calculus; ODEs + dynamical systems
Molecular Biology of the Cell
Reading detailsApplication: Regenerative medicine
-
Genetics + evolution + systems biologyPractice available
Reason about inheritance, variation, population change, gene circuits, network motifs, stochastic expression and evolutionary robustness.
Preparation: Scientific computing
Genetics: A Conceptual Approach
Reading detailsApplication: Regenerative medicine
-
Neuroscience + physiologyPractice available
Connect electrophysiology and neural coding to whole-body homeostasis and cardiovascular, respiratory, endocrine and renal control.
Preparation: Probability; Scientific computing
Neuroscience
Reading detailsApplication: Eldercare/service robots
-
Manufacturing + operationsPractice available
Translate prototypes into processes with rate, yield, variation, quality, cost, maintenance, supply chain and learning curves.
Preparation: ODEs + dynamical systems; Statistics + causal inference
Factory Physics
Reading details -
Safety + reliability + securityPractice available
Design systems that remain safe and dependable under component failure, software defects, organizational drift, misuse and adversaries.
Preparation: No subject prerequisite recorded.
An Introduction to System Safety Engineering
Reading detailsApplication: Eldercare/service robots
Bring it together¶
A shared-resource inquiry brings mechanisms, institutions, judgment and representation into one piece of work.