Formal Sciences¶
← Back to Abstractions by Domain Group
The study of abstract structure. Proceed by definition, axiom, and proof. Their results are about patterns, not about things in the world. Claim to truth rests on internal consistency plus conformity to definition.
281 primes · 3,635 domain-specific abstractions across 4 domains in this group. Both layers draw on the same canonical roster; a domain's group is derived from it, never stored on an entity.
| Domain | Primes | Domain-specific |
|---|---|---|
| Experimental Design & Statistics | 75 | 431 |
| Information Theory | 21 | 92 |
| Mathematics | 161 | 3,038 |
| Operations Research | 24 | 74 |
Experimental Design & Statistics
The mathematical and methodological discipline of designing studies, quantifying uncertainty, and drawing inferences from data. Distinct from Data Science by its emphasis on inference under controlled designs rather than prediction at scale. Canonical traditions: Fisher, Neyman-Pearson, Bayesian inference, causal inference (Rubin, Pearl), survey methodology, psychometrics.
See also: Mathematics (probability theory), Data Science & Analytics, Operations Research
75 primes
- Aggregate-Marginal Divergence
- Aggregation
- Apparent Variety Masks Shared Driver
- Bayesian Updating
- Bias
- Blinding
- Blocking (In Experimental Design)
- Calibration
- Coincidence
- Confidence Annotation
- Confidence Intervals
- Confounding
- Construct Validity
- Continuum (measurement)
- Control Sample
- Correlated-Source Attribution Failure
- Counterfactual Subtraction
- Cromwell's Rule
- Cross-Dimensional Leakage
- Cross-Level Inference
- Crossover Interaction
- Data collection
- Dimensionality Reduction
- Distributional Assumption
- Effect Size
- Elicitation Channel Contribution
- Estimation
- Experimental Design
- Extrapolation Beyond Sampled Regime
- Extreme Capture Probability
- Factorial Design
- False Positive Paradox
- Heavy-Tailed Distributions
- Hypothesis Testing (Null vs. Alternative)
- Identifiability
- Inspection Paradox
- Instrument Interpretive Drift
- Intervention
- Markov Blanket
- Measurement
- Measurement Uncertainty and Observational Noise
- Missing Data Mechanisms (MCAR, MAR, MNAR)
- Monte Carlo Simulation
- Multiple Comparisons Correction
- Nonparametric Methods
- Outlier Leverage
- Overfitting
- Paradox of Unanimity
- Poisson Process
- Prediction Error
- … and 25 more — see all
431 domain-specific abstractions
- 68–95–99.7 rule
- Admissible Decision Rule
- Analytic and enumerative statistical studies
- Ancestral graph
- Anchor test
- Anderson–Darling test
- Antecedent variable
- Approximate Bayesian Computation
- Arbia's law of geography
- Area chart
- Asymptotic theory (statistics)
- Atomistic Fallacy
- Attenuation Bias
- Augmented Dickey–Fuller Test
- Autoregressive Integrated Moving Average
- Balanced repeated replication
- Bar chart
- Barnardisation
- Bayes classifier
- Bayesian Interpretation of Kernel Regularization
- Bayesian linear regression
- Bayesian model reduction
- Bayesian Optimal Mechanism
- Benford's Law
- Benjamini–Hochberg Procedure
- Best linear unbiased prediction
- Bhattacharyya distance
- Big O in probability notation
- Binary classification
- Binomial Proportion Confidence Interval
- Binomial Proportion Estimation
- Binomial regression
- Binomial test
- Biplot
- Biweight midcorrelation
- Bonferroni Correction
- Bootstrapping populations
- Box–Muller Transform
- Brown–Forsythe test
- Bubble Chart
- C-chart
- Canberra Distance
- Canonical correlation
- Carryover Effect
- Categorical Variable
- Causal Inference
- Chartjunk
- Chauvenet's criterion
- Chinese restaurant process
- Classical XY model
- … and 381 more — see all
Information Theory
The mathematical study of the quantification, storage, and transmission of information. Founded as a distinct discipline by Claude Shannon's A Mathematical Theory of Communication (1948); later extended into algorithmic information theory (Kolmogorov, Chaitin, Solomonoff), rate–distortion theory, and network information theory. Canonical concepts: entropy, channel capacity, mutual information, source coding, channel coding, noise, redundancy, and the fundamental limits they imply.
See also: Mathematics (probability), Computer Science & Software Engineering (coding and compression), Physics (especially statistical mechanics via entropy), Neuroscience (neural coding), Linguistics & Semiotics
21 primes
- Backpressure
- Branching and Merging
- Channel
- Channel Capacity
- Compression
- Conditional Entropy
- Coordination Problem and Equilibrium Selection
- Encoding And Decoding
- Garbage In, Garbage Out
- Holarchy
- Information
- Linearization-Meaning Mismatch
- Markov Process
- Regret
- Reversibility and Irreversibility
- Risk
- Rock-Paper-Scissors (Intransitive Cyclic Dominance)
- Social Dilemma
- Systems Thinking
- Validity-ending Event
- Winner's Curse
92 domain-specific abstractions
- Adaptive differential pulse-code modulation
- Adaptive feedback cancellation
- Algebraic geometry code
- Asymptotic equipartition property
- Bennett's Laws
- Bilinear Transform
- Binary entropy function
- Binary erasure channel
- Blahut–Arimoto algorithm
- Bruun's FFT algorithm
- Chirplet transform
- Circular convolution
- Colors of noise
- Constant-Q transform
- Convolutional code
- Cross-entropy
- Dependent component analysis
- Directed information
- Discrete Fourier transform
- Discrete wavelet transform
- Discrete-time Fourier transform
- Elias Bassalygo bound
- Entropy estimation
- Error exponents in hypothesis testing
- Error-Correcting Code
- Error-Correcting Codes with Feedback
- Even code
- EXIT Chart
- Expander code
- Filter (Signal Processing)
- Gabor wavelet
- Gambling and information theory
- Generator matrix
- Harmonic Wavelet Transform
- Hilbert spectral analysis
- Incompressibility method
- Infomax
- Information dimension
- Information Entropy
- Information projection
- Kelly criterion
- Kolmogorov complexity
- Krichevsky–Trofimov estimator
- Lag windowing
- Lanczos resampling
- Linear programming decoding
- Log Gabor filter
- Log-Sum Inequality
- Low-Density Parity-Check Code
- Lulu smoothing
- … and 42 more — see all
Mathematics
The study of abstract structure — number, quantity, space, change, and the formal relationships among them. Proceeds by definition, axiom, and proof; its canonical artefact is the theorem. Canonical traditions: Euclidean geometry, modern algebra, analysis, topology, category theory, mathematical logic.
See also: Physics (shared formal language), Computer Science & Software Engineering (logic and computation), Operations Research (applied optimization), Experimental Design & Statistics
161 primes
- Abstract Structure
- Addition
- Approximation
- Associativity
- Asymmetry
- Asymptotic Behavior
- Attractor
- Axiom
- Axiomatic Incompatibility
- Basis
- Bijectivity
- Bimodality
- Birthday Problem
- Boundedness
- Canonical Form
- Cardinality
- Cartesian Product
- Category
- Central Limit Theorem
- Chaos
- Closure
- Coaxiality
- Commutativity
- Complement
- Completeness
- Conditional Probability
- Connectedness
- Consistency
- Constraint
- Continuity
- Contradiction
- Contraposition
- Convergence
- Convexity
- Convolution
- Coordinate-free
- Correlation
- Covariance
- Cut
- Cycle
- Decomposition
- Dense Set
- Diagonal Impossibility
- Dimension
- Directed Acyclic Graph
- Discreteness
- Discretization-Induced Artifact
- Disjoint union
- Disjointness
- Distance
- … and 111 more — see all
3,038 domain-specific abstractions
- (a, b)-decomposition
- (B, N) Pair
- 0/1-polytope
- 2-Category
- 2-group
- 2-Yoneda lemma
- 3-Category
- 3-transposition group
- 3D rotation group
- 3D4
- A-paracompact Space
- AB5 category
- ABACABA pattern
- Abel Transform
- Abel's Limit Theorem
- Abelian Lie group
- Absolute continuity
- Absolute convergence
- Absolute value
- Absolute value (algebra)
- Absolutely convex set
- Absorbing boundary condition
- Absorbing element
- Absorbing set
- Abstract additive Schwarz method
- Abstract index notation
- Abstract polytope
- Accelerated failure time model
- Acceptable ring
- Accessibility Relation
- Accessible category
- Accessible quasi-category
- Achilles Number
- Action algebra
- Action groupoid
- Acute and obtuse triangles
- AD+
- Adams Spectral Sequence
- Addition principle
- Additive function
- Additive group
- Additive inverse
- Additively indecomposable ordinal
- Adequate subcategory
- Adherent point
- Adjunction (field theory)
- Admissible set
- Affiliated operator
- Affine hull
- Affine logic
- … and 2,988 more — see all
Operations Research
The discipline of applying advanced analytical methods — optimization, simulation, stochastic modeling, decision analysis — to complex decision-making problems. Originated in WWII military logistics; now applied across industry, logistics, healthcare, and government. Canonical traditions: linear and integer programming, Markov decision processes, queueing theory, network flow, game theory extensions.
See also: Mathematics, Computer Science & Software Engineering, Engineering & Design (beyond software), Data Science & Analytics, Economics & Finance
24 primes
- Allocation
- Batch Processing
- Batch Size
- Branch and Bound
- Dynamic Programming
- Incident Response
- Integer Linear Programming (ILP)
- Linear Programming (LP)
- Markov Decision Processes (MDPs)
- Multiobjective Optimization
- Network Flow Models
- Parallel Independent Inspection
- Prioritization
- Pull Flow
- Queueing
- Resource Management
- Scheduling
- Sensitivity Analysis (in Operations Research)
- Sequencing
- Serial Local Optimization Failure
- Simulated Annealing
- Traceability
- Unevenness Waste
- Value of Information
74 domain-specific abstractions
- 1-Center Problem
- 3-dimensional matching
- Assemble-to-order system
- Balanced matrix
- Bayesian search theory
- BCMP network
- Biconvex optimization
- Bilinear program
- Chance-Constrained Programming
- Circulation problem
- Closure problem
- Complementarity theory
- Concurrent Estimation
- Covector mapping principle
- Cutting Stock Problem
- Decision Method
- Decision Quality
- Discrete rate simulation
- Discrete-Event Simulation
- Dual linear program
- Generalized Semi-Infinite Programming
- Gittins index
- Goal programming
- Gomory–Hu tree
- Greedy Randomized Adaptive Search Procedure
- Guillotine cutting
- Imperialist competitive algorithm
- Jackson's Theorem (Queueing Theory)
- Job-shop scheduling
- Kingman's Formula
- Lexicographic Optimization
- Lindley equation
- Linear programming relaxation
- Liner shipping network design and scheduling problem
- Local search (optimization)
- Makespan
- Markovian arrival process
- Matroid parity problem
- Maximum satisfiability problem
- Minimum Relevant Variables in a Linear System
- Minimum-cost flow problem
- Multi-attribute utility
- Multi-commodity flow problem
- Nesting (process)
- Network Simplex Algorithm
- Nonlinear programming
- Nurse scheduling problem
- Offered load
- Optimal Kidney Exchange
- Optimistic knowledge gradient
- … and 24 more — see all