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

Fields

Concepts

Orientations

Models

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

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

Entropy type	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 type	Byte pair encoding Lempel–Ziv 842 LZ4 LZJB LZO LZRW LZSS LZW LZWL Snappy
Other types	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 bzip2 (RLE + BWT + MTF + Huffman)

Lossy

Transform type	Discrete cosine transform DCT MDCT DST FFT Wavelet Daubechies DWT SPIHT
Predictive type	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

Mark Adler

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 Kirkpatrick–Reisch sort Timsort Introsort Spreadsort Merge-insertion sort
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
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 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 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	Boolean Bottom type Collection Enumerated type Exception Function type Opaque data type Recursive data type Semaphore Stream Strongly typed identifier Top type Type class Empty type Unit type Void
Related topics	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 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, computer laws are not hard and fast laws, but rules of thumbs or postulations

Artificial intelligence
Part of a series on

Major goals Artificial general intelligence Intelligent Agent Recursive self-improvement Planning Computer vision General game playing Knowledge reasoning Natural language processing Robotics AI safety
Approaches Machine learning Symbolic Deep learning Bayesian networks Evolutionary algorithms Situated approach Hybrid intelligent systems Systems integration
Applications Projects Deepfake Machine translation Generative AI Art Audio Music Healthcare Mental health Government Industry Earth sciences Bioinformatics Physics
Philosophy Chinese room Friendly AI Control problem/Takeover Ethics Existential risk Turing test Regulation
History Timeline Progress AI winter AI boom AI era
Glossary Glossary
v t e

Machine learning and data mining
Part of a series on
Paradigms Supervised learning Unsupervised learning Online learning Batch learning Meta-learning Semi-supervised learning Self-supervised learning Reinforcement learning Curriculum learning Rule-based learning 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
Artificial neural network Autoencoder Cognitive computing Deep learning DeepDream Feedforward neural network Recurrent neural network LSTM GRU ESN reservoir computing Restricted Boltzmann machine GAN Diffusion model SOM Convolutional neural network U-Net Transformer Vision Mamba Spiking neural network Memtransistor Electrochemical RAM (ECRAM)
Reinforcement learning Q-learning SARSA Temporal difference (TD) Multi-agent Self-play
Learning with humans Active learning Crowdsourcing Human-in-the-loop 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
Machine-learning venues 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 Program synthesis
Journals	Evolutionary Computation (journal)

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 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 (language use) Prototype theory Force dynamics Semantic feature Semantic gap Theory of descriptions
Analysis
Latent Computational Machine-learning
Applications
Semantic file system Semantic desktop Semantic matching Semantic parsing Semantic similarity Semantic query Semantic Web Semantic wiki

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 Computational Conversation analysis Corpus linguistics Discourse analysis 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 school Systemic functional Usage-based Structuralism
Topics Autonomy of syntax Compositionality Conservative/innovative forms Descriptivism Etymology Iconicity Internet linguistics LGBT linguistics Origin of language Orthography Philosophy of linguistics Prescriptivism Second-language acquisition Theory of language
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)	Agent Class-based Prototype-based Object-based 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
Dataflow	Flow-based Reactive (Functional reactive) Signals Streams Synchronous
Logic	Abductive logic Answer set Constraint (Constraint logic) Inductive logic Nondeterministic Ontology Probabilistic logic Query
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 APL ArkTS Assembly BASIC C C++ C# Classic Visual Basic COBOL Erlang Forth Fortran Go Haskell Java JavaScript Julia Kotlin Lisp Lua MATLAB ML Object Pascal Pascal Perl PHP Prolog Python R Ruby Rust SQL Scratch Shell Simula Smalltalk Swift Visual Basic more...
Lists: Alphabetical Categorical Generational Non-English-based Category

Program execution
General concepts
Code Translation Compiler Compile time Optimizing compiler Intermediate representation (IR) Execution Runtime system Runtime Executable Interpreter Virtual machine
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
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
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 Turing machine gallery
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

Prefixes for decimal and binary multiples Decimal Value SI 1000 103 k kilo 10002 106 M mega 10003 109 G giga 10004 1012 T tera 10005 1015 P peta 10006 1018 E exa 10007 1021 Z zetta 10008 1024 Y yotta 10009 1027 R ronna 100010 1030 Q quetta Binary Value IEC JEDEC 1024 210 Ki kibi K kilo 10242 220 Mi mebi M mega 10243 230 Gi gibi G giga 10244 240 Ti tebi T tera 10245 250 Pi pebi — 10246 260 Ei exbi — 10247 270 Zi zebi — 10248 280 Yi yobi — — — v t e

Computer architecture bit widths
Bit
1 4 8 12 16 18 24 26 28 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
- CSS
- 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 Systems on Chip (SoCs) Energy consumption (Green computing) Electronic design automation Hardware acceleration
Computer systems organization	Computer architecture Computational complexity Dependability Embedded system Real-time computing
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 variable 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 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
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–computer interaction	Interaction design Social computing Ubiquitous computing Visualization Accessibility
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 Mixed reality Virtual reality 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
Category Outline WikiProject Commons

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

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 {\text{base))^{\text{exponent))\,=\,

\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 Important publications in science
Mathematics	Mathematics Statistics
Natural science	Astronomy Biology Chemistry Geology Physics
Social science	Anthropology Economics Sociology
Related	Antiquarian science books Philosophy

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

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 Linear Multilinear Universal Homological
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 Differential Discrete Euclidean Finite
Number theory	Arithmetic Algebraic number theory Analytic number theory Diophantine geometry
Topology	General Algebraic Differential Geometric Homotopy 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
Mathematics portal Category Commons WikiProject

?

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

Category:Mathematics templates

Category:Wikipedia outlines

v t e Common logical connectives
Tautology/True $\top$
Alternative denial (NAND gate) $\uparrow$ Converse implication $\leftarrow$ Implication (IMPLY gate) $\rightarrow$ Disjunction (OR gate) $\lor$
Negation (NOT gate) $\neg$ Exclusive or (XOR gate) $\not \leftrightarrow$ Biconditional (XNOR gate) $\leftrightarrow$ Statement (Digital buffer)
Joint denial (NOR gate) $\downarrow$ Nonimplication (NIMPLY gate) $\nrightarrow$ Converse nonimplication $\nleftarrow$ Conjunction (AND gate) $\land$
Contradiction/False $\bot$
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v t e Set theory
Overview	Set (mathematics)
Axioms	Adjunction Choice countable dependent global Constructibility (V=L) Determinacy 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 Weighted edge
Graph attributes	Edge-connectedness Dominator (graph theory) Girth (graph theory) Multiplicity (graph theory) Order (graph theory) Size (graph theory) Vertex-connectedness
Category Outline Glossary Wikibook Wikiversity

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 Continued fractions
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v t e Algebra
Outline History
Areas	Abstract algebra Algebraic geometry 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 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
Basic concepts	Scalar Vector Vector space Scalar multiplication Vector projection Linear span Linear map Linear projection Linear independence Linear combination Basis Change of basis Row and column vectors Row and column spaces Kernel Eigenvalues and eigenvectors Transpose Linear equations
Matrices	Block Decomposition Invertible Minor Multiplication Rank Transformation Cramer's rule Gaussian elimination
Bilinear	Orthogonality Dot product Hadamard product Inner product space Outer product Kronecker product Gram–Schmidt process
Multilinear algebra	Determinant Cross product Triple product Seven-dimensional cross product Geometric algebra Exterior algebra Bivector Multivector Tensor Outermorphism
Vector space constructions	Dual Direct sum Function space Quotient Subspace Tensor product
Numerical	Floating-point Numerical stability Basic Linear Algebra Subprograms Sparse matrix Comparison of linear algebra libraries
Category

v t e Calculus
Precalculus	Binomial theorem Concave function Continuous function Factorial Finite difference Free variables and bound variables Graph of a function Linear function Radian Rolle's theorem Secant Slope Tangent
Limits	Indeterminate form Limit of a function One-sided limit Limit of a sequence Order of approximation (ε, δ)-definition of limit
Differential calculus	Derivative Second derivative Partial derivative Differential Differential operator Mean value theorem Notation Leibniz's notation Newton's notation Rules of differentiation linearity Power Sum Chain L'Hôpital's Product General Leibniz's rule Quotient Other techniques Implicit differentiation Inverse functions and differentiation Logarithmic derivative Related rates Stationary points First derivative test Second derivative test Extreme value theorem Maximum and minimum Further applications Newton's method Taylor's theorem Differential equation Ordinary differential equation Partial differential equation Stochastic differential equation
Integral calculus	Antiderivative Arc length Riemann integral Basic properties Constant of integration Fundamental theorem of calculus Differentiating under the integral sign Integration by parts Integration by substitution trigonometric Euler Tangent half-angle substitution Partial fractions in integration Quadratic integral Trapezoidal rule Volumes Washer method Shell method Integral equation Integro-differential equation
Vector calculus	Derivatives Curl Directional derivative Divergence Gradient Laplacian Basic theorems Line integrals Green's Stokes' Gauss'
Multivariable calculus	Divergence theorem Geometric Hessian matrix Jacobian matrix and determinant Lagrange multiplier Line integral Matrix Multiple integral Partial derivative Surface integral Volume integral Advanced topics Differential forms Exterior derivative Generalized Stokes' theorem Tensor calculus
Sequences and series	Arithmetico-geometric sequence Types of series Alternating Binomial Fourier Geometric Harmonic Infinite Power Maclaurin Taylor Telescoping Tests of convergence Abel's Alternating series Cauchy condensation Direct comparison Dirichlet's Integral Limit comparison Ratio Root Term
Special functions and numbers	Bernoulli numbers e (mathematical constant) Exponential function Natural logarithm Stirling's approximation
History of calculus	Adequality Brook Taylor Colin Maclaurin Generality of algebra Gottfried Wilhelm Leibniz Infinitesimal Infinitesimal calculus Isaac Newton Fluxion Law of Continuity Leonhard Euler Method of Fluxions The Method of Mechanical Theorems
Lists	Differentiation rules List of integrals of exponential functions List of integrals of hyperbolic functions List of integrals of inverse hyperbolic functions List of integrals of inverse trigonometric functions List of integrals of irrational functions List of integrals of logarithmic functions List of integrals of rational functions List of integrals of trigonometric functions Secant Secant cubed List of limits Lists of integrals
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

v t e Topics of game theory
Definitions	Congestion game Cooperative game Determinacy Escalation of commitment Extensive-form game First-player and second-player win Game complexity Graphical game Hierarchy of beliefs Information set Normal-form game Preference Sequential game Simultaneous game Simultaneous action selection Solved game Succinct game Mechanism design
Equilibrium concepts	Bayes correlated equilibrium Bayesian Nash equilibrium Berge equilibrium Core Correlated equilibrium Coalition-proof Nash equilibrium Epsilon-equilibrium Evolutionarily stable strategy Gibbs equilibrium Mertens-stable equilibrium Markov perfect equilibrium Nash equilibrium Pareto efficiency Perfect Bayesian equilibrium Proper equilibrium Quantal response equilibrium Quasi-perfect equilibrium Risk dominance Satisfaction equilibrium Self-confirming equilibrium Sequential equilibrium Shapley value Strong Nash equilibrium Subgame perfection Trembling hand equilibrium
Strategies	Appeasement Backward induction Bid shading Collusion Cheap talk De-escalation Deterrence Escalation Forward induction Grim trigger Markov strategy Dominant strategies Pure strategy Mixed strategy Strategy-stealing argument Tit for tat
Classes of games	Auction Bargaining problem Global game Intransitive game Mean-field game n-player game Perfect information Large Poisson game Potential game Repeated game Screening game Signaling game Strictly determined game Stochastic game Symmetric game Zero-sum game
Games	Go Chess Infinite chess Checkers All-pay auction Prisoner's dilemma Gift-exchange game Optional prisoner's dilemma Traveler's dilemma Coordination game Chicken Centipede game Lewis signaling game Volunteer's dilemma Dollar auction Battle of the sexes Stag hunt Matching pennies Ultimatum game Rock paper scissors Pirate game Dictator game Public goods game Blotto game War of attrition El Farol Bar problem Fair division Fair cake-cutting Bertrand competition Cournot competition Stackelberg competition Deadlock Diner's dilemma Guess 2/3 of the average Kuhn poker Nash bargaining game Induction puzzles Trust game Princess and monster game Rendezvous problem
Theorems	Aumann's agreement theorem Folk theorem Minimax theorem Nash's theorem Negamax theorem Purification theorem Revelation principle Sprague–Grundy theorem Zermelo's theorem
Key figures	Albert W. Tucker Amos Tversky Antoine Augustin Cournot Ariel Rubinstein Claude Shannon Daniel Kahneman David K. Levine David M. Kreps Donald B. Gillies Drew Fudenberg Eric Maskin Harold W. Kuhn Herbert Simon Hervé Moulin John Conway Jean Tirole Jean-François Mertens Jennifer Tour Chayes John Harsanyi John Maynard Smith John Nash John von Neumann Kenneth Arrow Kenneth Binmore Leonid Hurwicz Lloyd Shapley Melvin Dresher Merrill M. Flood Olga Bondareva Oskar Morgenstern Paul Milgrom Peyton Young Reinhard Selten Robert Axelrod Robert Aumann Robert B. Wilson Roger Myerson Samuel Bowles Suzanne Scotchmer Thomas Schelling William Vickrey
Miscellaneous	Alpha–beta pruning Bounded rationality Combinatorial game theory Confrontation analysis Coopetition Evolutionary game theory Glossary of game theory List of game theorists List of games in game theory No-win situation Topological game Tragedy of the commons

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

v t e Complexity classes
Considered feasible	DLOGTIME AC⁰ ACC⁰ 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 PR R RE ALL
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

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