?

Branches

Branches	Applied philosophy Logic Metaphilosophy Philosophical methodology Philosophy of education Philosophy of information Philosophy of language Philosophy of mathematics Philosophy of religion Philosophy of science Political philosophy Practical philosophy Social philosophy Theoretical philosophy
Aesthetics	Aesthetic response Formalism Institutionalism
Epistemology	Empiricism Fideism Naturalism Particularism Rationalism Skepticism Solipsism
Ethics	Consequentialism Deontology Virtue
Free will	Compatibilism Determinism Hard Incompatibilism Hard Libertarianism
Metaphysics	Atomism Dualism Idealism Monism Naturalism Realism
Mind	Behaviorism Eliminativism Emergentism Epiphenomenalism Functionalism Objectivism Subjectivism
Normativity	Absolutism Particularism Relativism Nihilism Skepticism Universalism
Ontology	Action Event Process
Reality	Anti-realism Conceptualism Idealism Materialism Naturalism Nominalism Physicalism Realism

By era

Ancient

Chinese	Agriculturalism Confucianism Legalism Logicians Mohism Chinese naturalism Taoism Yangism
Greco-Roman	Presocratic Ionians Pythagoreans Eleatics Atomists Sophists Cyrenaics Cynicism Eretrian school Megarian school Academy Peripatetic school Hellenistic philosophy Pyrrhonism Stoicism Epicureanism Academic Skepticism Middle Platonism School of the Sextii Neopythagoreanism Second Sophistic Neoplatonism Church Fathers Dispositio
Indian	Hindu Samkhya Nyaya Vaisheshika Yoga Mīmāṃsā Ājīvika Ajñana Cārvāka Jain Anekantavada Syādvāda Buddhist Abhidharma Sarvāstivadā Pudgalavada Sautrāntika Madhyamaka Svatantrika and Prasangika Śūnyatā Yogacara Tibetan
Persian	Mazdakism Mithraism Zoroastrianism Zurvanism

Medieval

East Asian	Neotaoism Tiantai Huayan Chan Zen Neo-Confucianism Korean Confucianism
European	Christian Byzantine Augustinianism Scholasticism Thomism Scotism Occamism Renaissance humanism
Indian	Vedanta Acintya bheda abheda Advaita Bhedabheda Dvaita Nimbarka Sampradaya Shuddhadvaita Vishishtadvaita Navya-Nyāya
Islamic	Aristotelianism Averroism Avicennism Illuminationism ʿIlm al-Kalām Sufi
Jewish	Judeo-Islamic

Modern

People

Contemporary

Analytic	Applied ethics Analytic feminism Analytical Marxism Communitarianism Consequentialism Critical rationalism Experimental philosophy Falsificationism Foundationalism / Coherentism Internalism and externalism Logical positivism Legal positivism Meta-ethics Moral realism Quinean naturalism Normative ethics Ordinary language philosophy Postanalytic philosophy Quietism Rawlsian Reformed epistemology Systemics Scientism Scientific realism Scientific skepticism Transactionalism Contemporary utilitarianism Vienna Circle Wittgensteinian
Continental	Critical theory Deconstruction Existentialism Feminist Frankfurt School Hermeneutics Neo-Marxism New Historicism Phenomenology Posthumanism Postmodernism Post-structuralism Social constructionism Structuralism Western Marxism
Miscellaneous	Kyoto School Objectivism Postcritique Russian cosmism

By region

By region

African	Bantu Egyptian Ethiopian Africana
Eastern	Buddhist Chinese Indian Indonesian Japanese Korean Taiwanese Vietnamese
Middle Eastern	Iranian Islamic Jewish Pakistani Turkish
Western	(Analytic / Continental) American Australian British Scottish Canada Czech Danish Dutch Finland French German Greek Italian Maltese Polish Slovene Spanish
Miscellaneous	Amerindian Aztec Romanian Russian Yugoslav

Philosophy portal
Category

v t e Important publications in science
Mathematics	Mathematics Statistics
Natural science	Astronomy Biology Chemistry Physics
Social science	Anthropology Economics Sociology
Related	Antiquarian science books Philosophy

$f(x)={\frac {y^{1}}{1}}$

[edit]

Software engineering

Fields

Concepts

Orientations

Models

Developmental	Agile EUP Executable UML Incremental model Iterative model Prototype model RAD Scrum Spiral model UP V-model Waterfall model XP Model-driven engineering Round-trip engineering
Other	CMMI Data model ER model Function model Information model Metamodeling Object model SPICE Systems model View model
Languages	IDEF SysML UML USL

Related fields

Data transformation
Concepts
Metadata Data element Data mapping Data migration Data transformation Model transformation Macro Preprocessor
Transformation languages
ATL AWK MOFM2T QVT XML languages
Techniques and transforms
Identity transform Data refinement
Applications
Data conversion Data migration Data integration Extract, transform, load (ETL) Web template system
Related
Data wrangling Transformation languages
v t e

Data compression methods

Lossless
type

Entropy	Adaptive coding Arithmetic Asymmetric numeral systems Golomb Huffman Adaptive Canonical Modified Range Shannon Shannon–Fano Shannon–Fano–Elias Tunstall Unary Universal Exp-Golomb Fibonacci Gamma Levenshtein
Dictionary	Byte-pair encoding Lempel–Ziv 842 LZ4 LZJB LZO LZRW LZSS LZW LZWL Snappy
Other	BWT CTW CM Delta Incremental DMC DPCM Grammar Re-Pair Sequitur LDCT MTF PAQ PPM RLE
Hybrid	LZ77 + Huffman Deflate LZX LZS LZ77 + ANS LZFSE LZ77 + Huffman + ANS Zstandard LZ77 + Huffman + context Brotli LZSS + Huffman LHA/LZH LZ77 + Range LZMA LZHAM RLE + BWT + MTF + Huffman bzip2

Lossy
type

Transform	Discrete cosine transform DCT MDCT DST FFT Wavelet Daubechies DWT SPIHT
Predictive	DPCM ADPCM LPC ACELP CELP LAR LSP WLPC Motion Compensation Estimation Vector Psychoacoustic

Audio

Concepts	Bit rate ABR CBR VBR Companding Convolution Dynamic range Latency Nyquist–Shannon theorem Sampling Silence compression Sound quality Speech coding Sub-band coding
Codec parts	A-law μ-law DPCM ADPCM DM FT FFT LPC ACELP CELP LAR LSP WLPC MDCT Psychoacoustic model

Image

Concepts	Chroma subsampling Coding tree unit Color space Compression artifact Image resolution Macroblock Pixel PSNR Quantization Standard test image Texture compression
Methods	Chain code DCT Deflate Fractal KLT LP RLE Wavelet Daubechies DWT EZW SPIHT

Video

Concepts	Bit rate ABR CBR VBR Display resolution Frame Frame rate Frame types Interlace Video characteristics Video quality
Codec parts	DCT DPCM Deblocking filter Lapped transform Motion Compensation Estimation Vector Wavelet Daubechies DWT

Theory

Community

Hutter Prize

People

v t e Sorting algorithms
Theory	Computational complexity theory Big O notation Total order Lists Inplacement Stability Comparison sort Adaptive sort Sorting network Integer sorting X + Y sorting Transdichotomous model Quantum sort
Exchange sorts	Bubble sort Cocktail shaker sort Odd–even sort Comb sort Gnome sort Proportion extend sort Quicksort
Selection sorts	Selection sort Heapsort Smoothsort Cartesian tree sort Tournament sort Cycle sort Weak-heap sort
Insertion sorts	Insertion sort Shellsort Splaysort Tree sort Library sort Patience sorting
Merge sorts	Merge sort Cascade merge sort Oscillating merge sort Polyphase merge sort
Distribution sorts	American flag sort Bead sort Bucket sort Burstsort Counting sort Interpolation sort Pigeonhole sort Proxmap sort Radix sort Flashsort
Concurrent sorts	Bitonic sorter Batcher odd–even mergesort Pairwise sorting network Samplesort
Hybrid sorts	Block merge sort Introsort Kirkpatrick–Reisch sort Merge-insertion sort Powersort Timsort Spreadsort
Other	Topological sorting Pre-topological order Pancake sorting Spaghetti sort
Impractical sorts	Stooge sort Slowsort Bogosort

Polymorphism
Ad hoc polymorphism
Function overloading Operator overloading
Parametric polymorphism
Generic function Generic programming
Subtyping
Virtual function Single and dynamic dispatch Double dispatch Multiple dispatch Predicate dispatch
v t e

Evaluation strategies
Eager evaluation Lazy evaluation Partial evaluation Remote evaluation Short-circuit evaluation
v t e

Type systems
General concepts
Type safety Strong vs. weak typing
Major categories
Static vs. dynamic Manifest vs. inferred Nominal vs. structural Duck typing
Minor categories
Abstract Dependent Flow-sensitive Gradual Intersection Latent Refinement Substructural Unique Session
v t e

v t e Data structures
Types	Collection Container
Abstract	Associative array Multimap Retrieval Data Structure List Stack Queue Double-ended queue Priority queue Double-ended priority queue Set Multiset Disjoint-set
Arrays	Bit array Circular buffer Dynamic array Hash table Hashed array tree Sparse matrix
Linked	Association list Linked list Skip list Unrolled linked list XOR linked list
Trees	B-tree Binary search tree AA tree AVL tree Red–black tree Self-balancing tree Splay tree Heap Binary heap Binomial heap Fibonacci heap R-tree R* tree R+ tree Hilbert R-tree Rope Trie Hash tree
Graphs	Binary decision diagram Directed acyclic graph Directed acyclic word graph
List of data structures

v t e Data types
Uninterpreted	Bit Byte Trit Tryte Word Bit array
Numeric	Arbitrary-precision or bignum Complex Decimal Fixed point Block floating point Floating point Reduced precision Minifloat Half precision bfloat16 Single precision Double precision Quadruple precision Octuple precision Extended precision Long double Integer signedness Interval Rational
Pointer	Address physical virtual Reference
Text	Character String null-terminated
Composite	Algebraic data type generalized Array Associative array Class Dependent Equality Inductive Intersection List Object metaobject Option type Product Record or Struct Refinement Set Union tagged
Other	Any type Boolean Bottom type Collection Enumerated type Exception Function type Opaque data type Recursive data type Semaphore Stream Strongly typed identifier Type class Empty type Unit type Void
Related topics	Value Abstract data type Boxing Data structure Generic Kind metaclass Parametric polymorphism Primitive data type Interface Subtyping Type constructor Type conversion Type system Type theory Variable

v t e Computer laws
Amdahl's law Bell's law Brooks's law Edholm's law Grosch's law Gustafson's law Haitz's law Koomey's law Linus's law Metcalfe's law Moore's law Moore's second law Pollack's rule Wirth's law
Semantically, a computer law is not a hard and fast law, but a rule of thumb, or axiom (postulation)

Artificial intelligence (AI)
Part of a series on

Major goals Artificial general intelligence Intelligent agent Recursive self-improvement Planning Computer vision General game playing Knowledge representation Natural language processing Robotics AI safety
Approaches Machine learning Symbolic Deep learning Bayesian networks Evolutionary algorithms Hybrid intelligent systems Systems integration Open-source
Applications Bioinformatics Deepfake Earth sciences Finance Generative AI Art Audio Music Government Healthcare Mental health Industry Software development Translation Military Physics Projects
Philosophy AI alignment Artificial consciousness The bitter lesson Chinese room Friendly AI Ethics Existential risk Turing test Uncanny valley
History Timeline Progress AI winter AI boom AI bubble
Controversies Deepfake pornography Taylor Swift deepfake pornography controversy Google Gemini image generation controversy Pause Giant AI Experiments Removal of Sam Altman from OpenAI Statement on AI Risk Tay (chatbot) Théâtre D'opéra Spatial Voiceverse NFT plagiarism scandal
Glossary Glossary
v t e

Machine learning and data mining
Part of a series on
Paradigms Supervised learning Unsupervised learning Semi-supervised learning Self-supervised learning Reinforcement learning Meta-learning Online learning Batch learning Curriculum learning Rule-based learning Neuro-symbolic AI Neuromorphic engineering Quantum machine learning
Problems Classification Generative modeling Regression Clustering Dimensionality reduction Density estimation Anomaly detection Data cleaning AutoML Association rules Semantic analysis Structured prediction Feature engineering Feature learning Learning to rank Grammar induction Ontology learning Multimodal learning
Supervised learning (classification • regression) Apprenticeship learning Decision trees Ensembles Bagging Boosting Random forest k-NN Linear regression Naive Bayes Artificial neural networks Logistic regression Perceptron Relevance vector machine (RVM) Support vector machine (SVM)
Clustering BIRCH CURE Hierarchical k-means Fuzzy Expectation–maximization (EM) DBSCAN OPTICS Mean shift
Dimensionality reduction Factor analysis CCA ICA LDA NMF PCA PGD t-SNE SDL
Structured prediction Graphical models Bayes net Conditional random field Hidden Markov
Anomaly detection RANSAC k-NN Local outlier factor Isolation forest
Neural networks Autoencoder Deep learning Feedforward neural network Recurrent neural network LSTM GRU ESN reservoir computing Boltzmann machine Restricted GAN Diffusion model SOM Convolutional neural network U-Net LeNet AlexNet DeepDream Neural field Neural radiance field Physics-informed neural networks Transformer Vision Mamba Spiking neural network Memtransistor Electrochemical RAM (ECRAM)
Reinforcement learning Q-learning Policy gradient SARSA Temporal difference (TD) Multi-agent Self-play
Learning with humans Active learning Crowdsourcing Human-in-the-loop Mechanistic interpretability RLHF
Model diagnostics Coefficient of determination Confusion matrix Learning curve ROC curve
Mathematical foundations Kernel machines Bias–variance tradeoff Computational learning theory Empirical risk minimization Occam learning PAC learning Statistical learning VC theory Topological deep learning
Journals and conferences AAAI ECML PKDD NeurIPS ICML ICLR IJCAI ML JMLR
Related articles Glossary of artificial intelligence List of datasets for machine-learning research List of datasets in computer vision and image processing Outline of machine learning
v t e

v t e Evolutionary computation
Main Topics	Evolutionary algorithm Evolutionary data mining Evolutionary multimodal optimization Human-based evolutionary computation Interactive evolutionary computation
Algorithms	Cellular evolutionary algorithm Covariance Matrix Adaptation Evolution Strategy (CMA-ES) Cultural algorithm Differential evolution Evolutionary programming Genetic algorithm Genetic programming Gene expression programming Evolution strategy Natural evolution strategy Neuroevolution Learning classifier system
Related techniques	Swarm intelligence Ant colony optimization Bees algorithm Cuckoo search Particle swarm optimization Bacterial Colony Optimization
Metaheuristic methods	Firefly algorithm Harmony search Gaussian adaptation Memetic algorithm
Related topics	Artificial development Artificial intelligence Artificial life Digital organism Evolutionary robotics Fitness function Fitness landscape Fitness approximation Genetic operators Interactive evolutionary computation No free lunch in search and optimization Machine learning Mating pool Premature convergence Program synthesis
Organizationa	ACM IEEE ACM SIGEVO IEEE CIS
Conferences	CEC GECCO PPSN EvoStar EA FOGA
Journals	Evolutionary Computation (journal) IEEE Trans Evol Comput ACM Trans Evol Learning Optim

Feature detection
Edge detection
Canny Deriche Differential Sobel Prewitt Robinson Roberts cross
Corner detection
Harris operator Shi and Tomasi Level curve curvature Hessian feature strength measures SUSAN FAST
Blob detection
Laplacian of Gaussian (LoG) Difference of Gaussians (DoG) Determinant of Hessian (DoH) Maximally stable extremal regions PCBR
Ridge detection
Hough transform
Hough transform Generalized Hough transform
Structure tensor
Structure tensor Generalized structure tensor
Affine invariant feature detection
Affine shape adaptation Harris affine Hessian affine
Feature description
SIFT SURF GLOH HOG
Scale space
Scale-space axioms Implementation details Pyramids
v t e

Computer vision

Categories

Technologies

Applications

3D reconstruction	3D reconstruction from multiple images 2D to 3D conversion Gaussian splatting Neural radiance field Shape from focus Simultaneous localization and mapping Structure from motion View synthesis Visual hull 4D reconstruction Free viewpoint television Volumetric capture

Main category

Classes of automata

(Clicking on each layer gets an article on that subject)

Automata theory: formal languages and formal grammars

Chomsky hierarchy	Grammars	Languages	Abstract machines
Type-0 — Type-1 — — — — — Type-2 — — Type-3 — —	Unrestricted (no common name) Context-sensitive Positive range concatenation Indexed — Linear context-free rewriting systems Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular — Non-recursive	Recursively enumerable Decidable Context-sensitive Positive range concatenation^* Indexed^* — Linear context-free rewriting language Tree-adjoining Context-free Deterministic context-free Visibly pushdown Regular Star-free Finite	Turing machine Decider Linear-bounded PTIME Turing Machine Nested stack Thread automaton restricted Tree stack automaton Embedded pushdown Nondeterministic pushdown Deterministic pushdown Visibly pushdown Finite Counter-free (with aperiodic finite monoid) Acyclic finite

Each category of languages, except those marked by a ^*, is a proper subset of the category directly above it. Any language in each category is generated by a grammar and by an automaton in the category in the same line.

Subfields
Computational Lexical Lexis Lexicology Statistical Structural
Topics
Analysis Compositionality Context Prototype theory Force dynamics Semantic feature Semantic gap Theory of descriptions
Analysis
Latent Computational Machine learning
Applications
Desktop File system Matching Parsing Querying web wiki Similarity

Linguistics
Part of a series on
Outline History Index
General linguistics Diachronic Lexicography Morphology Phonology Pragmatics Semantics Syntax Syntax–semantics interface Typology
Applied linguistics Acquisition Anthropological Applied Mathematical Computational Conversation analysis Corpus linguistics Discourse analysis Determinism Distance Documentation Ethnography of communication Ethnomethodology Forensic History of linguistics Interlinguistics Neurolinguistics Philology Philosophy of language Phonetics Psycholinguistics Sociolinguistics Text Translating and interpreting Writing systems
Theoretical frameworks Formalist Constituency Dependency Distributionalism Generative Glossematics Functional Cognitive Construction grammar Functional discourse grammar Grammaticalization Interactional linguistics Prague circle Systemic functional Usage-based Structuralism
Topics Autonomy of syntax Compositionality Conservative and innovative language Descriptivism Etymology Iconicity Internet linguistics LGBTQ linguistics Origin of language Orismology Orthography Philosophy of linguistics Prescriptivism Second-language acquisition Theory of language Terminology
Portal
v t e

v t e Parsing algorithms
Top-down	Earley LL Recursive descent Tail recursive
Bottom-up	Precedence Simple Operator Shunting-yard LR Simple Look-ahead Canonical Generalized CYK Recursive ascent Shift-reduce
Mixed, other	Combinator Chart Left corner Statistical
Related topics	PEG Definite clause grammar Deterministic parsing Dynamic programming Memoization Parser generator LALR Parse tree AST Scannerless parsing History of compiler construction Comparison of parser generators Operator-precedence grammar

v t e Types of computer language
Types	Architecture description Data exchange Hardware description Knowledge representation Markup Modeling Programming language Query Shading Specification Stylesheet Transformation
See also	Category:Lists of computer languages Category:Lists of programming languages List of programming languages by type

Programming paradigms (Comparison by language)

Imperative

Structured	Jackson structures Block-structured Modular Non-structured Procedural Programming in the large and in the small Design by contract Invariant-based Nested function
Object-oriented (comparison, list)	Class-based, Prototype-based, Object-based Agent Immutable object Persistent Uniform function call syntax

Declarative

Functional (comparison)	Recursive Anonymous function (Partial application) Higher-order Purely functional Total Strict GADTs Dependent types Functional logic Point-free style Expression-oriented Applicative, Concatenative Function-level, Value-level Monad
Dataflow	Flow-based Reactive (Functional reactive) Signals Streams Synchronous
Logic	Abductive logic Answer set Constraint (Constraint logic) Inductive logic Nondeterministic Ontology Probabilistic logic Query
Domain- specific language (DSL)	Algebraic modeling Array Automata-based (Action) Command (Spacecraft) Differentiable End-user Grammar-oriented Interface description Language-oriented List comprehension Low-code Modeling Natural language Non-English-based Page description Pipes and filters Probabilistic Quantum Scientific Scripting Set-theoretic Simulation Stack-based System Tactile Templating Transformation (Graph rewriting, Production, Pattern) Visual

Concurrent,
distributed,
parallel

Metaprogramming

Attribute-oriented
Automatic (Inductive)
Dynamic
Extensible
Generic
Homoiconicity
Interactive
Macro (Hygienic)
Metalinguistic abstraction
Multi-stage
Program synthesis (Bayesian, Inferential, by demonstration, by example)
Reflective
Self-modifying code
Symbolic
Template

Separation
of concerns

v t e Programming languages
Comparison Timeline History
Ada ALGOL Simula APL Assembly BASIC Visual Basic classic .NET C C++ C# COBOL Erlang Elixir Forth Fortran Go Haskell Java JavaScript Julia Kotlin Lisp Lua MATLAB ML Caml OCaml Pascal Object Pascal Perl Raku PHP Prolog Python R Ruby Rust SAS SQL Scratch Shell Smalltalk Swift more...
Lists: Alphabetical Categorical Generational Non-English-based Category

Program execution
General concepts
Code Translation Compiler Compile time Optimizing compiler Linking Execution Runtime system Executable Interpreter Virtual machine Intermediate representation (IR)
Types of code
Source code Object code Bytecode Machine code Microcode
Compilation strategies
Ahead-of-time (AOT) Just-in-time (JIT) Tracing just-in-time Compile and go system Precompilation Transcompilation Recompilation Meta-tracing
Notable runtimes
Android Runtime (ART) BEAM (Erlang) Common Language Runtime (CLR) and Mono CPython and PyPy crt0 (C target-specific initializer) Java virtual machine (JVM) LuaJIT Objective-C and Swift's V8 and Node.js Zend Engine (PHP)
Notable compilers & toolchains
GNU Compiler Collection (GCC) LLVM and Clang MSVC Glasgow Haskell Compiler (GHC)
v t e

v t e Processor scheduling
Algorithms	Deadline-monotonic Earliest deadline Earliest eligible virtual deadline first Fair-share Fixed-priority pre-emptive Foreground-background Gang Generalized foreground-background Highest response ratio next Lottery Multilevel feedback queue Process Contention Scope Proportional share Rate-monotonic Round-robin Shortest job next Shortest remaining time Statistical time-division multiplexing Stride Two-level Windows NT YDS algorithm
Linux	Brain Fuck Completely Fair O(1) O(n) SCHED DEADLINE SCHED FIFO SCHED NORMAL
Other	Processor affinity Starvation

Turing machines
Machine
Turing machine equivalents Turing machine examples
Variants
Alternating Turing machine Neural Turing machine Nondeterministic Turing machine Quantum Turing machine Post–Turing machine Probabilistic Turing machine Multitape Turing machine Multi-track Turing machine Symmetric Turing machine Total Turing machine Unambiguous Turing machine Universal Turing machine Zeno machine
Science
Alan Turing Category:Turing machine
v t e

Machine code
General concepts
Instruction set Opcode Illegal opcode Opcode table Opcode prefix Operand Addressing mode
Instructions
NOP Branch Indirect branch Repeat instruction Execute instruction Bit manipulation instructions
v t e

Prefixes for decimal and binary multiples
v
t
e
Decimal			Binary
Value	SI		Value	IEC		JEDEC
1000	k	kilo	1024	Ki	kibi	K	kilo
1000²	M	mega	1024²	Mi	mebi	M	mega
1000³	G	giga	1024³	Gi	gibi	G	giga
1000⁴	T	tera	1024⁴	Ti	tebi	T	tera
1000⁵	P	peta	1024⁵	Pi	pebi	—
1000⁶	E	exa	1024⁶	Ei	exbi	—
1000⁷	Z	zetta	1024⁷	Zi	zebi	—
1000⁸	Y	yotta	1024⁸	Yi	yobi	—
1000⁹	R	ronna	1024⁹	Ri	robi	—
1000¹⁰	Q	quetta	1024¹⁰	Qi	quebi	—

Computer architecture bit widths
Bit
1 4 8 12 16 18 24 26 30 31 32 36 45 48 60 64 128 256 512 bit slicing
Application
8 16 32 64
Binary floating-point precision
16 (×½) 24 32 (×1) 40 64 (×2) 80 128 (×4) 256 (×8)
Decimal floating-point precision
32 64 128
v t e

Processor technologies

Models

Architecture

Instruction set
architectures

Types	Orthogonal instruction set CISC RISC Application-specific EDGE TRIPS VLIW EPIC MISC OISC NISC ZISC VISC architecture Quantum computing Comparison Addressing modes
Instruction sets	Motorola 68000 series VAX PDP-11 x86 ARM Stanford MIPS MIPS MIPS-X Power POWER PowerPC Power ISA Clipper architecture SPARC SuperH DEC Alpha ETRAX CRIS M32R Unicore Itanium OpenRISC RISC-V MicroBlaze LMC System/3x0 S/360 S/370 S/390 z/Architecture Tilera ISA VISC architecture Epiphany architecture Others

Execution

Instruction pipelining	Pipeline stall Operand forwarding Classic RISC pipeline
Hazards	Data dependency Structural Control False sharing
Out-of-order	Scoreboarding Tomasulo's algorithm Reservation station Re-order buffer Register renaming Wide-issue
Speculative	Branch prediction Memory dependence prediction

Parallelism

Level	Bit Bit-serial Word Instruction Pipelining Scalar Superscalar Task Thread Process Data Vector Memory Distributed
Multithreading	Temporal Simultaneous Hyperthreading Simultaneous and heterogenous Speculative Preemptive Cooperative
Flynn's taxonomy	SISD SIMD Array processing (SIMT) Pipelined processing Associative processing SWAR MISD MIMD SPMD

Processor
performance

Transistor count
Instructions per cycle (IPC)
- Cycles per instruction (CPI)
Instructions per second (IPS)
Floating-point operations per second (FLOPS)
Transactions per second (TPS)
Synaptic updates per second (SUPS)
Performance per watt (PPW)
Cache performance metrics
Computer performance by orders of magnitude

Types

By application	Embedded system Microprocessor Microcontroller Mobile Ultra-low-voltage ASIP Soft microprocessor
Systems on chip	System on a chip (SoC) Multiprocessor (MPSoC) Cypress PSoC Network on a chip (NoC)
Hardware accelerators	Coprocessor AI accelerator Graphics processing unit (GPU) Image processor Vision processing unit (VPU) Physics processing unit (PPU) Digital signal processor (DSP) Tensor Processing Unit (TPU) Secure cryptoprocessor Network processor Baseband processor

Word size

Core count

Components

Functional units	Arithmetic logic unit (ALU) Address generation unit (AGU) Floating-point unit (FPU) Memory management unit (MMU) Load–store unit Translation lookaside buffer (TLB) Branch predictor Branch target predictor Integrated memory controller (IMC) Memory management unit Instruction decoder
Logic	Combinational Sequential Glue Logic gate Quantum Array
Registers	Processor register Status register Stack register Register file Memory buffer Memory address register Program counter
Control unit	Hardwired control unit Instruction unit Data buffer Write buffer Microcode ROM Counter
Datapath	Multiplexer Demultiplexer Adder Multiplier CPU Binary decoder Address decoder Sum-addressed decoder Barrel shifter
Circuitry	Integrated circuit 3D Mixed-signal Power management Boolean Digital Analog Quantum Switch

Power
management

Quantum information science

General

Theorems

Quantum
communication

Quantum cryptography	Post-quantum cryptography Quantum coin flipping Quantum money Quantum key distribution BB84 SARG04 other protocols Quantum secret sharing

Quantum algorithms

Quantum
complexity theory

Quantum
processor benchmarks

Quantum
computing models

Quantum
error correction

Codes
- 5 qubit
- CSS
- GKP
- quantum convolutional
- stabilizer
- Shor
- Bacon–Shor
- Steane
- Toric
- gnu
Entanglement-assisted

Physical
implementations

Quantum optics	Cavity QED Circuit QED Linear optical QC KLM protocol
Ultracold atoms	Neutral atom QC Trapped-ion QC
Spin-based	Kane QC Spin qubit QC NV center NMR QC
Superconducting	Charge qubit Flux qubit Phase qubit Transmon

Quantum
programming

v t e Computer science
Note: This template roughly follows the 2012 ACM Computing Classification System.
Hardware	Printed circuit board Peripheral Integrated circuit Very-large-scale integration System on a chip (SoC) Energy consumption (green computing) Electronic design automation Hardware acceleration Processor Size / Form
Computer systems organization	Computer architecture Computational complexity Dependability Embedded system Real-time computing Cyber-physical system Fault tolerance Wireless sensor network
Networks	Network architecture Network protocol Network components Network scheduler Network performance evaluation Network service
Software organization	Interpreter Middleware Virtual machine Operating system Software quality
Software notations and tools	Programming paradigm Programming language Compiler Domain-specific language Modeling language Software framework Integrated development environment Software configuration management Software library Software repository
Software development	Control flow Software development process Requirements analysis Software design Software construction Software deployment Software engineering Software maintenance Programming team Open-source model
Theory of computation	Model of computation Stochastic Formal language Automata theory Computability theory Computational complexity theory Logic Semantics
Algorithms	Algorithm design Analysis of algorithms Algorithmic efficiency Randomized algorithm Computational geometry
Mathematics of computing	Discrete mathematics Probability Statistics Mathematical software Information theory Mathematical analysis Numerical analysis Theoretical computer science Computational problem
Information systems	Database management system Information storage systems Enterprise information system Social information systems Geographic information system Decision support system Process control system Multimedia information system Data mining Digital library Computing platform Digital marketing World Wide Web Information retrieval
Security	Cryptography Formal methods Security hacker Security services Intrusion detection system Hardware security Network security Information security Application security
Human-centered computing	Interaction design Augmented reality Virtual reality Social computing Ubiquitous computing Visualization Accessibility Human–computer interaction Mobile computing
Concurrency	Concurrent computing Parallel computing Distributed computing Multithreading Multiprocessing
Artificial intelligence	Natural language processing Knowledge representation and reasoning Computer vision Automated planning and scheduling Search methodology Control method Philosophy of artificial intelligence Distributed artificial intelligence
Machine learning	Supervised learning Unsupervised learning Reinforcement learning Multi-task learning Cross-validation
Graphics	Animation Rendering Photograph manipulation Graphics processing unit Image compression Solid modeling
Applied computing	Quantum computing E-commerce Enterprise software Computational mathematics Computational physics Computational chemistry Computational biology Computational social science Computational engineering Differentiable computing Computational healthcare Digital art Electronic publishing Cyberwarfare Electronic voting Video games Word processing Operations research Educational technology Document management
Specialized Platform Development	Thermodynamic computing
Category Outline Glossaries

Laboratory equipment

General

Heaters Dryers	Alcohol burner Bunsen burner Desiccator Heating mantle Hot plate Lab oven Kiln Meker–Fisher burner Striker Teclu burner Water bath Vacuum dry box
Mixers Shakers	Chemostat Homogenizer Liquid whistle Magnetic stirrer Mortar and pestle Shaker Sonicator Static mixer Stirring rod Vortex mixer Wash bottle
Stands Clamps Holders	Beaker clamp Clamp holder Tripod Burette clamp Extension clamp Flask clamp Funnel support Iron ring Pinch clamp Retort stand Screw clamp Test tube holder Test tube rack Wire gauze Lab drying rack
Containers Storage	Agar plate Cryogenic storage dewar Incubator Laminar flow cabinet Microtiter plate Petri dish Picotiter plate Refrigerator Weighing boat Weighing dish
Other items	Aspirator Autoclave Balance brush Cork borer Crucible Filter paper File Forceps Centrifuge Microscope Pipeclay triangle Spectrophotometer Splint Stopper Scoopula Spatula Test tube brush Wire brush Inoculation needle Inoculation loop

Glassware

Apparatus	Dean–Stark Soxhlet extractor Kipp's
Bottles	Boston round
Condensers	Cold finger Liebig
Dishes	Evaporating Petri Syracuse Watch glass
Flasks	Büchner Vacuum (Dewar) Erlenmeyer Fernbach Fleaker Florence Retort Round-bottom Schlenk Volumetric
Funnels	Büchner Hirsch Dropping Separatory
Measuring devices	Burette Conical measure Cuvette Eye dropper Eudiometer Graduated cylinder Ostwald viscometer Pipette
Tubes	Drying Cragie Nuclear magnetic resonance (NMR) Test Thiele Thistle
Other items	Beaker Bell jar Gas syringe Vial

Analytical chemistry

Compositional	AutoAnalyzer CHN analyzer Colorimeter Inductively coupled plasma (ICP) device Gas chromatograph (GC) Liquid chromatograph (LC) Mass spectrometer (MS) pH indicator pH meter
Microscopy	Scanning electron microscope (SEM) Transmission electron microscope (TEM)
Thermochemistry	Calorimeter differential scanning Melting-point apparatus Thermometer Thermogravimetric analyzer (TGA)
Other items	Analytical balance Colony counter Spiral plater Nuclear magnetic resonance (NMR) instrument Plate reader

Electronics

Control devices	Bench power supply Current source Voltage source Function generator Galvanostat Pulse generator Potentiostat
Measurement	Ammeter Logic analyzer Multimeter Network analyzer Oscilloscope Spectrum analyzer Time-domain reflectometer Transistor tester Voltmeter
Tools	Heat gun Soldering iron Tweezers Wire stripper
General	Alligator clip Test probe

Safety

Personal protective
equipment (PPE)

Lab coat Face shield Respirator Rubber apron Safety shower
Eye and hand	Acid-resistant gloves Eyewash station Glove box Medical gloves Nitrile gloves Safety glasses Safety goggles

Other items

Instruments used in medical laboratories

Electronic components

Semiconductor
devices

MOS transistors	Transistor NMOS PMOS BiCMOS BioFET Chemical field-effect transistor (ChemFET) Complementary MOS (CMOS) Depletion-load NMOS Fin field-effect transistor (FinFET) Floating-gate MOSFET (FGMOS) Insulated-gate bipolar transistor (IGBT) ISFET LDMOS MOS field-effect transistor (MOSFET) Multi-gate field-effect transistor (MuGFET) Power MOSFET Thin-film transistor (TFT) VMOS UMOS
Other transistors	Bipolar junction transistor (BJT) Darlington transistor Diffused junction transistor Field-effect transistor (FET) Junction Gate FET (JFET) Organic FET (OFET) Light-emitting transistor (LET) Organic LET (OLET) Pentode transistor Point-contact transistor Programmable unijunction transistor (PUT) Static induction transistor (SIT) Tetrode transistor Unijunction transistor (UJT)
Diodes	Avalanche diode Constant-current diode (CLD, CRD) Gunn diode Laser diode (LD) Light-emitting diode (LED) Organic light-emitting diode (OLED) Photodiode PIN diode Schottky diode Step recovery diode Zener diode
Other devices	Printed electronics Printed circuit board DIAC Heterostructure barrier varactor Integrated circuit (IC) Hybrid integrated circuit Light emitting capacitor (LEC) Memistor Memristor Memtransistor Memory cell Metal-oxide varistor (MOV) Mixed-signal integrated circuit MOS integrated circuit (MOS IC) Organic semiconductor Photodetector Quantum circuit RF CMOS Silicon controlled rectifier (SCR) Solaristor Static induction thyristor (SITh) Three-dimensional integrated circuit (3D IC) Thyristor Trancitor TRIAC Varicap

Adjustable

Passive

Reactive

Other devices

Cam timer

Category:Mathematics templates

[edit]

v t e Major mathematics areas
History Timeline Future Lists Glossary
Foundations	Category theory Information theory Mathematical logic Philosophy of mathematics Set theory Type theory
Algebra	Abstract Commutative Elementary Group theory Homological Linear Multilinear Universal
Analysis	Calculus Real analysis Complex analysis Hypercomplex analysis Differential equations Functional analysis Harmonic analysis Measure theory
Discrete	Combinatorics Graph theory Order theory
Geometry	Algebraic Analytic Arithmetic Complex Computational Differential Discrete Euclidean Finite
Number theory	Algebraic Analytic Arithmetic Diophantine geometry
Topology	General Algebraic Differential Geometric Homotopy theory Knot theory
Applied	Engineering mathematics Mathematical biology Mathematical chemistry Mathematical economics Mathematical finance Mathematical physics Mathematical psychology Mathematical sociology Mathematical statistics Probability Statistics Systems science Control theory Game theory Operations research
Computational	Computer science Theory of computation Computational complexity theory Numerical analysis Optimization Computer algebra
Related topics	Mathematicians lists Informal mathematics Films about mathematicians Recreational mathematics Mathematics and art Mathematics education Number Large
Mathematics portal Category Commons WikiProject

v t e Metalogic and metamathematics
Cantor's theorem Entscheidungsproblem Church–Turing thesis Consistency Effective method Foundations of mathematics of geometry Gödel's completeness theorem Gödel's incompleteness theorems Soundness Completeness Decidability Interpretation Löwenheim–Skolem theorem Metatheorem Satisfiability Independence Type–token distinction Use–mention distinction

Mathematical logic

General

Theorems (list)
and paradoxes

Gödel's completeness and incompleteness theorems
Tarski's undefinability
Banach–Tarski paradox
Cantor's theorem, paradox and diagonal argument
Compactness
Halting problem
Lindström's
Löwenheim–Skolem
Russell's paradox

Logics

Traditional	Classical logic Logical truth Tautology Proposition Inference Logical equivalence Consistency Equiconsistency Argument Soundness Validity Syllogism Square of opposition Venn diagram
Propositional	Boolean algebra Boolean functions Logical connectives Propositional calculus Propositional formula Truth tables Many-valued logic 3 finite ∞
Predicate	First-order list Second-order Monadic Higher-order Fixed-point Free Quantifiers Predicate Monadic predicate calculus

Set theory

Set hereditary Class (Ur-)Element Ordinal number Extensionality Forcing Relation equivalence partition Set operations: intersection union complement Cartesian product power set identities
Types of sets	Countable Uncountable Empty Inhabited Singleton Finite Infinite Transitive Ultrafilter Recursive Fuzzy Universal Universe constructible Grothendieck Von Neumann
Maps and cardinality	Function/Map domain codomain image In/Sur/Bi-jection Schröder–Bernstein theorem Isomorphism Gödel numbering Enumeration Large cardinal inaccessible Aleph number Operation binary
Set theories	Zermelo–Fraenkel axiom of choice continuum hypothesis General Kripke–Platek Morse–Kelley Naive New Foundations Tarski–Grothendieck Von Neumann–Bernays–Gödel Ackermann Constructive

Formal systems (list),
language and syntax

Alphabet
Arity
Automata
Axiom schema
Expression
- ground
Extension
- by definition
- conservative
Relation
Formation rule
Grammar
Formula
- atomic
- closed
- ground
- open
Free/bound variable
Language
Metalanguage
Logical connective
- ¬
- ∨
- ∧
- →
- ↔
- =
Predicate
- functional
- variable
- propositional variable
Proof
Quantifier
- ∃
- !
- ∀
- rank
Sentence
- atomic
- spectrum
Signature
String
Substitution
Symbol
- function
- logical/constant
- non-logical
- variable
Term
Theory
- list

Example axiomatic
systems (list)

of true arithmetic:
of the real numbers
- Tarski's axiomatization
of Boolean algebras
- canonical
- minimal axioms
of geometry:
- Euclidean:
- non-Euclidean

Principia Mathematica

Proof theory

Model theory

Computability theory

Mathematics portal

Logic

History

Major fields

Logics	Classical Informal Critical thinking Reason Mathematical Non-classical Philosophical
Theories	Argumentation Metalogic Metamathematics Set

Foundations

Lists

Topics	Mathematical logic Boolean algebra Set theory
Other	Logicians Rules of inference Paradoxes Fallacies Logic symbols

Transformation rules
Propositional calculus
Rules of inference (List)
Implication introduction / elimination (modus ponens) Biconditional introduction / elimination Conjunction introduction / elimination Disjunction introduction / elimination Disjunctive / hypothetical syllogism Constructive / destructive dilemma Absorption / modus tollens / modus ponendo tollens Modus non excipiens Negation introduction
Rules of replacement
Associativity Commutativity Distributivity Double negation De Morgan's laws Transposition Material implication Exportation Tautology
Predicate logic
Rules of inference
Universal generalization / instantiation Existential generalization / instantiation
v t e

v t e Common logical connectives
Tautology/True $\top$
Alternative denial (NAND gate) ${\overline {\wedge }}$ Converse implication $\Leftarrow$ Implication (IMPLY gate) $\Rightarrow$ Disjunction (OR gate) $\lor$
Negation (NOT gate) $\neg$ Exclusive or (XOR gate) $\oplus$ Biconditional (XNOR gate) $\odot$ Statement (Digital buffer)
Joint denial (NOR gate) ${\overline {\vee }}$ Nonimplication (NIMPLY gate) $\nRightarrow$ Converse nonimplication $\nLeftarrow$ Conjunction (AND gate) $\land$
Contradiction/False $\bot$
Philosophy portal

v t e Set theory
Overview	Set (mathematics)
Axioms	Adjunction Choice countable dependent global Constructibility (V=L) Determinacy projective Extensionality Infinity Limitation of size Pairing Power set Regularity Union Martin's axiom Axiom schema replacement specification
Operations	Cartesian product Complement (i.e. set difference) De Morgan's laws Disjoint union Identities Intersection Power set Symmetric difference Union
Concepts Methods	Almost Cardinality Cardinal number (large) Class Constructible universe Continuum hypothesis Diagonal argument Element ordered pair tuple Family Forcing One-to-one correspondence Ordinal number Set-builder notation Transfinite induction Venn diagram
Set types	Amorphous Countable Empty Finite (hereditarily) Filter base subbase Ultrafilter Fuzzy Infinite (Dedekind-infinite) Recursive Singleton Subset · Superset Transitive Uncountable Universal
Theories	Alternative Axiomatic Naive Cantor's theorem Zermelo General Principia Mathematica New Foundations Zermelo–Fraenkel von Neumann–Bernays–Gödel Morse–Kelley Kripke–Platek Tarski–Grothendieck
Paradoxes Problems	Russell's paradox Suslin's problem Burali-Forti paradox
Set theorists	Paul Bernays Georg Cantor Paul Cohen Richard Dedekind Abraham Fraenkel Kurt Gödel Thomas Jech John von Neumann Willard Quine Bertrand Russell Thoralf Skolem Ernst Zermelo

v t e Terms in graph theory
Types of graphs	Directed Undirected Acyclic Bipartite Connected Complete Labeled Hypergraph Multigraph Planar Pseudograph Regular Tree Weighted Wheel
Graph elements	Bridge Edge Directed edge Loop Node Strongly connected component Subgraph (graph theory) Vertex
Graph attributes	Edge-connectedness Dominator (graph theory) Girth (graph theory) Order (graph theory) Size (graph theory) Vertex-connectedness
Category Outline Glossary Wikibook Wikiversity

Category theory

Key concepts

Universal constructions

Limits	Terminal objects Products Equalizers Kernels Pullbacks Inverse limit
Colimits	Initial objects Coproducts Coequalizers Cokernels and quotients Pushout Direct limit

Algebraic categories

Constructions on categories

Higher category theory

Key concepts

Categorification

Enriched category

Higher-dimensional algebra

n-categories

Weak `n`-categories	Bicategory (pseudofunctor) Tricategory Tetracategory Kan complex ∞-groupoid ∞-topos
Strict `n`-categories	2-category (2-functor) 3-category

Categorified concepts

v t e Number theory
Fields	Algebraic number theory (class field theory, non-abelian class field theory, Iwasawa theory, Iwasawa–Tate theory, Kummer theory) Analytic number theory (analytic theory of L-functions, probabilistic number theory, sieve theory) Geometric number theory Computational number theory Transcendental number theory Diophantine geometry (Arakelov theory, Hodge–Arakelov theory) Arithmetic combinatorics (additive number theory) Arithmetic geometry (anabelian geometry, p-adic Hodge theory) Arithmetic topology Arithmetic dynamics
Key concepts	Numbers 0 Natural numbers Unity Prime numbers Composite numbers Rational numbers Irrational numbers Algebraic numbers Transcendental numbers p-adic numbers (p-adic analysis) Arithmetic Modular arithmetic Chinese remainder theorem Arithmetic functions
Advanced concepts	Quadratic forms Modular forms L-functions Diophantine equations Diophantine approximation Irrationality measure Simple continued fractions
Category List of topics List of recreational topics Wikibook Wikiversity

Classes of natural numbers

Powers and related numbers
Achilles Power of 2 Power of 3 Power of 10 Square Cube Fourth power Fifth power Sixth power Seventh power Eighth power Perfect power Powerful Prime power

Of the form a × 2^b ± 1
Cullen Double Mersenne Fermat Mersenne Proth Thabit Woodall

Other polynomial numbers
Hilbert Idoneal Leyland Loeschian Lucky numbers of Euler

Recursively defined numbers
Fibonacci Jacobsthal Leonardo Lucas Narayana Padovan Pell Perrin

Possessing a specific set of other numbers
Amenable Congruent Knödel Riesel Sierpiński

Expressible via specific sums
Nonhypotenuse Polite Practical Primary pseudoperfect Ulam Wolstenholme

Figurate numbers

2-dimensional

centered	Centered triangular Centered square Centered pentagonal Centered hexagonal Centered heptagonal Centered octagonal Centered nonagonal Centered decagonal Star
non-centered	Triangular Square Square triangular Pentagonal Hexagonal Heptagonal Octagonal Nonagonal Decagonal Dodecagonal

3-dimensional

centered	Centered tetrahedral Centered cube Centered octahedral Centered dodecahedral Centered icosahedral
non-centered	Tetrahedral Cubic Octahedral Dodecahedral Icosahedral Stella octangula
pyramidal	Square pyramidal

4-dimensional

non-centered	Pentatope Squared triangular Tesseractic

Combinatorial numbers
Bell Cake Catalan Dedekind Delannoy Euler Eulerian Fuss–Catalan Lah Lazy caterer's sequence Lobb Motzkin Narayana Ordered Bell Schröder Schröder–Hipparchus Stirling first Stirling second Telephone number Wedderburn–Etherington

Primes
Wieferich Wall–Sun–Sun Wolstenholme prime Wilson

Pseudoprimes
Carmichael number Catalan pseudoprime Elliptic pseudoprime Euler pseudoprime Euler–Jacobi pseudoprime Fermat pseudoprime Frobenius pseudoprime Lucas pseudoprime Lucas–Carmichael number Perrin pseudoprime Somer–Lucas pseudoprime Strong pseudoprime

Arithmetic functions and dynamics

Divisor functions	Abundant Almost perfect Arithmetic Betrothed Colossally abundant Deficient Descartes Hemiperfect Highly abundant Highly composite Hyperperfect Multiply perfect Perfect Practical Primitive abundant Quasiperfect Refactorable Semiperfect Sublime Superabundant Superior highly composite Superperfect
Prime omega functions	Almost prime Semiprime
Euler's totient function	Highly cototient Highly totient Noncototient Nontotient Perfect totient Sparsely totient
Aliquot sequences	Amicable Perfect Sociable Untouchable
Primorial	Euclid Fortunate

Other prime factor or divisor related numbers
Blum Cyclic Erdős–Nicolas Erdős–Woods Friendly Giuga Harmonic divisor Jordan–Pólya Lucas–Carmichael Pronic Regular Rough Smooth Sphenic Størmer Super-Poulet

Numeral system-dependent numbers

Arithmetic functions
and dynamics

Persistence
- Additive
- Multiplicative

Digit sum	Digit sum Digital root Self Sum-product
Digit product	Multiplicative digital root Sum-product
Coding-related	Meertens
Other	Dudeney Factorion Kaprekar Kaprekar's constant Keith Lychrel Narcissistic Perfect digit-to-digit invariant Perfect digital invariant Happy

P-adic numbers-related

Automorphic
- Trimorphic

Digit-composition related

Digit-permutation related

Divisor-related

Other

Friedman

Binary numbers
Evil Odious Pernicious

Generated via a sieve
Lucky Prime

Sorting related
Pancake number Sorting number

Natural language related
Aronson's sequence Ban

Graphemics related
Strobogrammatic

Mathematics portal

Addition (+)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{term}}\,+\,{\text{term}}\\\scriptstyle {\text{summand}}\,+\,{\text{summand}}\\\scriptstyle {\text{addend}}\,+\,{\text{addend}}\\\scriptstyle {\text{augend}}\,+\,{\text{addend}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{sum}}$
Subtraction (−)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{term}}\,-\,{\text{term}}\\\scriptstyle {\text{minuend}}\,-\,{\text{subtrahend}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{difference}}$
Multiplication (×)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{factor}}\,\times \,{\text{factor}}\\\scriptstyle {\text{multiplier}}\,\times \,{\text{multiplicand}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{product}}$
Division (÷)
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\frac {\scriptstyle {\text{dividend}}}{\scriptstyle {\text{divisor}}}}\\[1ex]\scriptstyle {\frac {\scriptstyle {\text{numerator}}}{\scriptstyle {\text{denominator}}}}\end{matrix}}\right\}\,=\,$	$\scriptstyle \left\{{\begin{matrix}\scriptstyle {\text{fraction}}\\\scriptstyle {\text{quotient}}\\\scriptstyle {\text{ratio}}\end{matrix}}\right.$
Exponentiation
	$\scriptstyle \left.{\begin{matrix}\scriptstyle {\text{base}}^{\text{exponent}}\\\scriptstyle {\text{base}}^{\text{power}}\end{matrix}}\right\}\,=\,$	$\scriptstyle {\text{power}}$
nth root (√)
	$\scriptstyle {\sqrt[{\text{degree}}]{\scriptstyle {\text{radicand}}}}\,=\,$	$\scriptstyle {\text{root}}$
Logarithm (log)
	$\scriptstyle \log _{\text{base}}({\text{anti-logarithm}})\,=\,$	$\scriptstyle {\text{logarithm}}$

v t e Algebra
Outline History
Areas	Abstract algebra Algebraic geometry Algebraic variety Scheme Algebraic number theory Category theory Commutative algebra Elementary algebra Homological algebra K-theory Linear algebra Multilinear algebra Noncommutative algebra Order theory Representation theory Universal algebra
Basic concepts	Algebraic expression Equation (Linear equation, Quadratic equation) Function (Polynomial function) Inequality (Linear inequality) Operation (Addition, Multiplication) Relation (Equivalence relation) Variable
Algebraic structures	Field (theory) Group (theory) Module (theory) Ring (theory) Vector space (Vector)
Linear and multilinear algebra	Basis Determinant Eigenvalues and eigenvectors Inner product space (Dot product) Hilbert space Linear map (Matrix) Linear subspace (Affine space) Norm (Euclidean norm) Orthogonality (Orthogonal complement) Rank Trace
Algebraic maps	Homomorphism (Group homomorphism, Ring homomorphism) Isomorphism Endomorphism Automorphism Kernel (algebra)
Algebraic constructions	Composition algebra Exterior algebra Free object (Free group, ...) Geometric algebra (Multivector) Polynomial ring (Polynomial) Quotient object (Quotient group, ...) Symmetric algebra Tensor algebra
Topic lists	Algebraic structures
Glossaries	Field theory Linear algebra Order theory Ring theory
Category

v t e Linear algebra
Outline Glossary Template:Matrix classes
Linear equations	Linear equation System of linear equations Determinant Minor Cauchy–Binet formula Cramer's rule Gaussian elimination Gauss–Jordan elimination Overcompleteness Strassen algorithm
Matrices	Matrix Matrix addition Matrix multiplication Basis transformation matrix Characteristic polynomial Spectrum Trace Eigenvalue, eigenvector and eigenspace Cayley–Hamilton theorem Jordan normal form Weyr canonical form Rank Inverse, Pseudoinverse Adjugate, Transpose Dot product Symmetric matrix, Skew-symmetric matrix Orthogonal matrix, Unitary matrix Hermitian matrix, Antihermitian matrix Positive-(semi)definite Pfaffian Projection Spectral theorem Perron–Frobenius theorem Diagonal matrix, Triangular matrix, Tridiagonal matrix Block matrix Sparse matrix Hessenberg matrix, Hessian matrix Vandermonde matrix Stochastic matrix, Toeplitz matrix, Circulant matrix, Hankel matrix (0,1)-matrix List of matrices
Matrix decompositions	Cholesky decomposition LU decomposition QR decomposition Polar decomposition Spectral theorem Singular value decomposition Higher-order singular value decomposition Schur decomposition Schur complement Haynsworth inertia additivity formula Reducing subspace
Relations and computations	Matrix equivalence Matrix congruence Matrix similarity Matrix consimilarity Row equivalence Elementary row operations Householder transformation Least squares Linear least squares Gram–Schmidt process Woodbury matrix identity
Vector spaces	Vector space Linear combination Linear span Linear independence Basis, Hamel basis Change of basis Dimension theorem for vector spaces Hamel dimension Examples of vector spaces Linear map Shear mapping Squeeze mapping Linear subspace Row and column spaces, Null space Rank–nullity theorem Nullity theorem Cyclic subspace Dual space, Linear functional Category of vector spaces
Structures	Topological vector space Normed vector space Inner product space Euclidean space Orthogonality Orthogonal complement Orthogonal projection Orthogonal group Pseudo-Euclidean space Null vector Indefinite orthogonal group Orientation Improper rotation Symplectic structure
Multilinear algebra	Multilinear algebra Tensor Tensors (classical) Component-free treatment of tensors Outer product Tensor algebra Exterior algebra Symmetric algebra Clifford algebra Geometric algebra Bivector Multivector Gamas's theorem
Affine and projective	Affine space Affine transformation, Affine group, Affine geometry Affine coordinate system, Flat (geometry) Cartesian coordinate system Euclidean group Poincaré group Galilean group Projective space Projective transformation Projective geometry Projective linear group Quadric
Numerical linear algebra	Numerical linear algebra Floating-point arithmetic Numerical stability Basic Linear Algebra Subprograms Sparse matrix Comparison of linear algebra libraries
Category

Calculus

Precalculus

Limits

Differential calculus

Integral calculus

Vector calculus

Derivatives
Basic theorems
- Line integrals
- Green's
- Stokes'
- Gauss'

Multivariable calculus

Sequences and series

Arithmetico-geometric sequence
Types of series
- Alternating
- Binomial
- Fourier
- Geometric
- Harmonic
- Infinite
- Power
  - Maclaurin
  - Taylor
- Telescoping
Tests of convergence

Special functions
and numbers

History of calculus

Lists

Integrals	rational functions irrational algebraic functions exponential functions logarithmic functions hyperbolic functions inverse trigonometric functions inverse Secant Secant cubed
List of limits List of derivatives

Miscellaneous topics

Complex calculus
- Contour integral
Differential geometry
- Manifold
- Curvature
- of curves
- of surfaces
- Tensor
Euler–Maclaurin formula
Gabriel's horn
Integration Bee
Proof that 22/7 exceeds π
Regiomontanus' angle maximization problem
Steinmetz solid

Statistics

Descriptive statistics

Continuous data

Center	Mean Arithmetic Arithmetic-Geometric Contraharmonic Cubic Generalized/power Geometric Harmonic Heronian Heinz Lehmer Median Mode
Dispersion	Average absolute deviation Coefficient of variation Interquartile range Percentile Range Standard deviation Variance
Shape	Central limit theorem Moments Kurtosis L-moments Skewness

Count data

Index of dispersion

Summary tables

Dependence

Graphics

Data collection

Study design	Effect size Missing data Optimal design Population Replication Sample size determination Statistic Statistical power
Survey methodology	Sampling Cluster Stratified Opinion poll Questionnaire Standard error
Controlled experiments	Blocking Factorial experiment Interaction Random assignment Randomized controlled trial Randomized experiment Scientific control
Adaptive designs	Adaptive clinical trial Stochastic approximation Up-and-down designs
Observational studies	Cohort study Cross-sectional study Natural experiment Quasi-experiment

Statistical inference

Statistical theory

Frequentist inference

Point estimation	Estimating equations Maximum likelihood Method of moments M-estimator Minimum distance Unbiased estimators Mean-unbiased minimum-variance Rao–Blackwellization Lehmann–Scheffé theorem Median unbiased Plug-in
Interval estimation	Confidence interval Pivot Likelihood interval Prediction interval Tolerance interval Resampling Bootstrap Jackknife
Testing hypotheses	1- & 2-tails Power Uniformly most powerful test Permutation test Randomization test Multiple comparisons
Parametric tests	Likelihood-ratio Score/Lagrange multiplier Wald

Specific tests

Z-test (normal) Student's t-test F-test
Goodness of fit	Chi-squared G-test Kolmogorov–Smirnov Anderson–Darling Lilliefors Jarque–Bera Normality (Shapiro–Wilk) Likelihood-ratio test Model selection Cross validation AIC BIC
Rank statistics	Sign Sample median Signed rank (Wilcoxon) Hodges–Lehmann estimator Rank sum (Mann–Whitney) Nonparametric anova 1-way (Kruskal–Wallis) 2-way (Friedman) Ordered alternative (Jonckheere–Terpstra) Van der Waerden test

Bayesian inference

Correlation	Pearson product-moment Partial correlation Confounding variable Coefficient of determination
Regression analysis (see also Template:Least squares and regression analysis	Errors and residuals Regression validation Mixed effects models Simultaneous equations models Multivariate adaptive regression splines (MARS)
Linear regression	Simple linear regression Ordinary least squares General linear model Bayesian regression
Non-standard predictors	Nonlinear regression Nonparametric Semiparametric Isotonic Robust Homoscedasticity and Heteroscedasticity
Generalized linear model	Exponential families Logistic (Bernoulli) / Binomial / Poisson regressions
Partition of variance	Analysis of variance (ANOVA, anova) Analysis of covariance Multivariate ANOVA Degrees of freedom

Categorical / multivariate / time-series / survival analysis

Categorical

Multivariate

Time-series

General	Decomposition Trend Stationarity Seasonal adjustment Exponential smoothing Cointegration Structural break Granger causality
Specific tests	Dickey–Fuller Johansen Q-statistic (Ljung–Box) Durbin–Watson Breusch–Godfrey
Time domain	Autocorrelation (ACF) partial (PACF) Cross-correlation (XCF) ARMA model ARIMA model (Box–Jenkins) Autoregressive conditional heteroskedasticity (ARCH) Vector autoregression (VAR) (Autoregressive model (AR))
Frequency domain	Spectral density estimation Fourier analysis Least-squares spectral analysis Wavelet Whittle likelihood

Survival

Survival function	Kaplan–Meier estimator (product limit) Proportional hazards models Accelerated failure time (AFT) model First hitting time
Hazard function	Nelson–Aalen estimator
Test	Log-rank test

Applications

Biostatistics	Bioinformatics Clinical trials / studies Epidemiology Medical statistics
Engineering statistics	Chemometrics Methods engineering Probabilistic design Process / quality control Reliability System identification
Social statistics	Actuarial science Census Crime statistics Demography Econometrics Jurimetrics National accounts Official statistics Population statistics Psychometrics
Spatial statistics	Cartography Environmental statistics Geographic information system Geostatistics Kriging

Chaos theory

Concepts

Core	Attractor Bifurcation Fractal Limit set Lyapunov exponent Orbit Periodic point Phase space
Anosov diffeomorphism Arnold tongue axiom A dynamical system Bifurcation diagram Box-counting dimension Correlation dimension Conservative system Ergodicity False nearest neighbors Hausdorff dimension Invariant measure Lyapunov stability Measure-preserving dynamical system Mixing Poincaré section Recurrence plot SRB measure Stable manifold Topological conjugacy
Theorems	Ergodic theorem Liouville's theorem Krylov–Bogolyubov theorem Poincaré–Bendixson theorem Poincaré recurrence theorem Stable manifold theorem Takens's theorem

Theoretical
branches

Chaotic
maps (list)

Discrete	Arnold's cat map Baker's map Complex quadratic map Coupled map lattice Duffing map Dyadic transformation Dynamical billiards outer Exponential map Gauss map Gingerbreadman map Hénon map Horseshoe map Ikeda map Interval exchange map Irrational rotation Kaplan–Yorke map Langton's ant Logistic map Standard map Tent map Tinkerbell map Zaslavskii map
Continuous	Double scroll attractor Duffing equation Lorenz system Lotka–Volterra equations Mackey–Glass equations Rabinovich–Fabrikant equations Rössler attractor Three-body problem Van der Pol oscillator

Physical
systems

Chaos
theorists

Game theory

Traditional game theory

Definitions	Asynchrony Bayesian regret Best response Bounded rationality Cheap talk Coalition Complete contract Complete information Complete mixing Confrontation analysis Conjectural variation Contingent cooperator Coopetition Cooperative game theory Dynamic inconsistency Escalation of commitment Farsightedness Game semantics Hierarchy of beliefs Imperfect information Incomplete information Information set Move by nature Mutual knowledge Non-cooperative game theory Non-credible threat Outcome Perfect information Perfect recall Ply Preference Rationality Sequential game Simultaneous action selection Spite Strategic complements Strategic dominance Strategic form Strategic interaction Strategic move Strategy Subgame Succinct game Topological game Tragedy of the commons Uncorrelated asymmetry
Equilibrium concepts	Backward induction Bayes correlated equilibrium Bayesian efficiency Bayesian game Bayesian Nash equilibrium Berge equilibrium Bertrand–Edgeworth model Coalition-proof Nash equilibrium Core Correlated equilibrium Cursed equilibrium Edgeworth price cycle Epsilon-equilibrium Gibbs equilibrium Incomplete contracts Inequity aversion Individual rationality Iterated elimination of dominated strategies Markov perfect equilibrium Mertens-stable equilibrium Nash equilibrium Open-loop model Pareto efficiency Payoff dominance Perfect Bayesian equilibrium Price of anarchy Program equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Rational agent Rationalizability Rationalizable strategy Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfect equilibrium Trembling hand equilibrium
Strategies	Appeasement Bid shading Cheap talk Collusion Commitment device De-escalation Deterrence Escalation Fictitious play Focal point Grim trigger Hobbesian trap Markov strategy Max-dominated strategy Mixed strategy Pure strategy Tit for tat Win–stay, lose–switch
Games	All-pay auction Battle of the sexes Nash bargaining game Bertrand competition Blotto game Centipede game Coordination game Cournot competition Deadlock Dictator game Trust game Diner's dilemma Dollar auction El Farol Bar problem Electronic mail game Gift-exchange game Guess 2/3 of the average Keynesian beauty contest Kuhn poker Lewis signaling game Matching pennies Obligationes Optional prisoner's dilemma Pirate game Prisoner's dilemma Public goods game Rendezvous problem Rock paper scissors Stackelberg competition Stag hunt Traveler's dilemma Ultimatum game Volunteer's dilemma War of attrition
Theorems	Arrow's impossibility theorem Aumann's agreement theorem Brouwer fixed-point theorem Competitive altruism Folk theorem Gibbard–Satterthwaite theorem Gibbs lemma Glicksberg's theorem Kakutani fixed-point theorem Kuhn's theorem One-shot deviation principle Prim–Read theory Rational ignorance Rational irrationality Sperner's lemma Zermelo's theorem
Subfields	Algorithmic game theory Behavioral game theory Behavioral strategy Compositional game theory Contract theory Drama theory Graphical game theory Heresthetic Mean-field game theory Negotiation theory Quantum game theory Social software
Key people	Albert W. Tucker Alvin E. Roth Amos Tversky Antoine Augustin Cournot Ariel Rubinstein David Gale David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Herbert Scarf Hervé Moulin Jean Tirole Jean-François Mertens Jennifer Tour Chayes Ken Binmore Kenneth Arrow Leonid Hurwicz Lloyd Shapley Martin Shubik Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Aumann Robert Axelrod Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey

Combinatorial game theory

Core concepts	Combinatorial explosion Determinacy Disjunctive sum First-player and second-player win Game complexity Game tree Impartial game Misère Partisan game Solved game Sprague–Grundy theorem Strategy-stealing argument Zugzwang
Games	Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs
Mathematical tools	Mex Nimber On Numbers and Games Star Surreal number Winning Ways for Your Mathematical Plays
Search algorithms	Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Key people	Claude Shannon John Conway John von Neumann

Evolutionary game theory

Core concepts	Bishop–Cannings theorem Evolution and the Theory of Games Evolutionarily stable set Evolutionarily stable state Evolutionarily stable strategy Replicator equation Risk dominance Stochastically stable equilibrium Weak evolutionarily stable strategy
Games	Chicken Stag hunt
Applications	Cultural group selection Fisher's principle Mobbing Terminal investment hypothesis
Key people	John Maynard Smith Robert Axelrod

Mechanism design

Core concepts	Algorithmic mechanism design Bayesian-optimal mechanism Incentive compatibility Market design Monotonicity Participation constraint Revelation principle Strategyproofness Vickrey–Clarke–Groves mechanism
Theorems	Myerson–Satterthwaite theorem Revenue equivalence
Applications	Digital goods auction Knapsack auction Truthful cake-cutting

Other topics
Bertrand paradox Chainstore paradox Computational complexity of games Helly metric Multi-agent system PPAD-complete

v t e Complementarity problems and algorithms
Complementarity Problems	Linear programming (LP) Quadratic programming (QP) Linear complementarity problem (LCP) Mixed linear (MLCP) Mixed (MCP) Nonlinear (NCP)
Basis-exchange algorithms	Simplex (Dantzig) Revised simplex Criss-cross Lemke

Optimization: Algorithms, methods, and heuristics

Unconstrained nonlinear

Functions

Gradients

Convergence	Trust region Wolfe conditions
Quasi–Newton	Berndt–Hall–Hall–Hausman Broyden–Fletcher–Goldfarb–Shanno and L-BFGS Davidon–Fletcher–Powell Symmetric rank-one (SR1)
Other methods	Conjugate gradient Gauss–Newton Gradient Mirror Levenberg–Marquardt Powell's dog leg method Truncated Newton

Hessians

Newton's method

Constrained nonlinear

General	Barrier methods Penalty methods
Differentiable	Augmented Lagrangian methods Sequential quadratic programming Successive linear programming

Convex optimization

Convex
minimization

Linear and
quadratic

Interior point	Affine scaling Ellipsoid algorithm of Khachiyan Projective algorithm of Karmarkar
Basis-exchange	Simplex algorithm of Dantzig Revised simplex algorithm Criss-cross algorithm Principal pivoting algorithm of Lemke Active-set method

Combinatorial

Paradigms

Graph
algorithms

Minimum spanning tree	Borůvka Prim Kruskal

Shortest path	Bellman–Ford SPFA Dijkstra Floyd–Warshall

Network flows

Metaheuristics
Evolutionary algorithm Hill climbing Local search Parallel metaheuristics Simulated annealing Spiral optimization algorithm Tabu search

Software

v t e Major subfields of optimization
Convex programming Fractional programming Integer programming Quadratic programming Nonlinear programming Stochastic programming Robust optimization Combinatorial optimization Infinite-dimensional optimization Metaheuristics Constraint satisfaction Multiobjective optimization Simulated annealing

v t e Complexity classes
Considered feasible	DLOGTIME AC⁰ ACC⁰ TC TC⁰ L SL RL FL NL NL-complete NC SC CC P P-complete ZPP RP BPP BQP APX FP
Suspected infeasible	UP NP NP-complete NP-hard co-NP co-NP-complete TFNP FNP AM QMA PH ⊕P PP #P #P-complete IP PSPACE PSPACE-complete
Considered infeasible	EXPTIME NEXPTIME EXPSPACE 2-EXPTIME ELEMENTARY NONELEMENTARY PR R RE ALL
Other complexity classes	polyL QP
Class hierarchies	Polynomial hierarchy Exponential hierarchy Grzegorczyk hierarchy Arithmetical hierarchy Boolean hierarchy
Families of classes	DTIME NTIME DSPACE NSPACE Probabilistically checkable proof Interactive proof system
List of complexity classes

Category:Wikipedia outlines

[edit]

v t e Types of programming languages
Level	Machine Assembly Compiled Interpreted Low-level High-level Very high-level Esoteric
Generation	First Second Third Fourth Fifth

v t e Types of programming languages
Level	Machine Assembly Compiled Interpreted Low-level High-level Very high-level Esoteric
Generation	First Second Third Fourth Fifth

v t e Units of information
Platform-independent units	bit hextet octet
Platform-dependent units	nibble byte syllable word
Metric bit units	kilobit megabit
Metric byte units	kilobyte megabyte gigabyte

?

f ( x ) = y 1 1 {\displaystyle f(x)={\frac {y^{1}}{1}}}

Category:Mathematics templates

Category:Wikipedia outlines

$f(x)={\frac {y^{1}}{1}}$