# kb

id: list-of-algorithms-20260505-1
file: data/en.wikipedia.org/wiki/List_of_algorithms-1.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
==== Approximate sequence matching ==== Bitap algorithm: fuzzy algorithm that determines if strings are approximately equal. Phonetic algorithms Daitch–Mokotoff Soundex: a Soundex refinement which allows matching of Slavic and Germanic surnames Double Metaphone: an improvement on Metaphone Match rating approach: a phonetic algorithm developed by Western Airlines Metaphone: an algorithm for indexing words by their sound, when pronounced in English NYSIIS: phonetic algorithm, improves on Soundex Soundex: a phonetic algorithm for indexing names by sound, as pronounced in English String metrics: computes a similarity or dissimilarity (distance) score between two pairs of text strings Damerau–Levenshtein distance: computes a distance measure between two strings, improves on Levenshtein distance Dice's coefficient (also known as the Dice coefficient): a similarity measure related to the Jaccard index Hamming distance: sum number of positions which are different Jaro–Winkler distance: is a measure of similarity between two strings Levenshtein edit distance: computes a metric for the amount of difference between two sequences Trigram search: search for text when the exact syntax or spelling of the target object is not precisely known ==== Selection algorithms ==== Introselect Quickselect ==== Sequence search ==== Linear search: locates an item in an unsorted sequence Selection algorithm: finds the kth largest


id: list-of-algorithms-20260505-2
file: data/en.wikipedia.org/wiki/List_of_algorithms-2.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
Chien search: a recursive algorithm for determining roots of polynomials defined over a finite field Schreier–Sims algorithm: computing a base and strong generating set (BSGS) of a permutation group Todd–Coxeter algorithm: Procedure for generating cosets. === Computer algebra === Buchberger's algorithm: finds a Gröbner basis Cantor–Zassenhaus algorithm: factor polynomials over finite fields Faugère F4 algorithm: finds a Gröbner basis (also mentions the F5 algorithm) Gosper's algorithm: find sums of hypergeometric terms that are themselves hypergeometric terms Knuth–Bendix completion algorithm: for rewriting rule systems Multivariate division algorithm: for polynomials in several indeterminates Pollard's kangaroo algorithm (also known as Pollard's lambda algorithm): an algorithm for solving the discrete logarithm problem Polynomial long division: an algorithm for dividing a polynomial by another polynomial of the same or lower degree Risch algorithm: an algorithm for the calculus operation of indefinite integration (i.e. finding antiderivatives) === Geometry === Closest pair problem: find the pair of points (from a set of points) with the smallest distance between them Collision detection algorithms: check for the collision or intersection of two given solids Cone algorithm: identify surface points Convex hull algorithms: determining the convex hull of a set of points Chan's algorithm Gift wrapping algorithm or Jarvis march


id: list-of-algorithms-20260505-3
file: data/en.wikipedia.org/wiki/List_of_algorithms-3.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
Computation of π: Bailey–Borwein–Plouffe formula: (BBP formula) a spigot algorithm for the computation of the nth binary digit of π Borwein's algorithm: an algorithm to calculate the value of 1/π Chudnovsky algorithm: a fast method for calculating the digits of π Gauss–Legendre algorithm: computes the digits of pi Division algorithms: for computing quotient and/or remainder of two numbers Goldschmidt division Long division Newton–Raphson division: uses Newton's method to find the reciprocal of D, and multiply that reciprocal by N to find the final quotient Q. Non-restoring division Restoring division SRT division Exponentiation: Addition-chain exponentiation: exponentiation by positive integer powers that requires a minimal number of multiplications Exponentiating by squaring: an algorithm used for the fast computation of large integer powers of a number Hyperbolic and Trigonometric Functions: BKM algorithm: computes elementary functions using a table of logarithms CORDIC: computes hyperbolic and trigonometric functions using a table of arctangents Montgomery reduction: an algorithm that allows modular arithmetic to be performed efficiently when the modulus is large Multiplication algorithms: fast multiplication of two numbers Booth's multiplication algorithm: a multiplication algorithm that multiplies two signed binary numbers in two's complement notation Fürer's algorithm: an integer multiplication algorithm for very large numbers possessing a


id: list-of-algorithms-20260505-4
file: data/en.wikipedia.org/wiki/List_of_algorithms-4.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
=== Optimization algorithms === Hybrid Algorithms Alpha–beta pruning: search to reduce number of nodes in minimax algorithm A hybrid BFGS-Like method (see more https://doi.org/10.1016/j.cam.2024.115857) Branch and bound Bruss algorithm: see odds algorithm Chain matrix multiplication Combinatorial optimization: optimization problems where the set of feasible solutions is discrete Greedy randomized adaptive search procedure (GRASP): successive constructions of a greedy randomized solution and subsequent iterative improvements of it through a local search Hungarian method: a combinatorial optimization algorithm which solves the assignment problem in polynomial time Conjugate gradient methods (see more https://doi.org/10.1016/j.jksus.2022.101923) Constraint satisfaction AC-3 algorithm general algorithms for the constraint satisfaction Chaff algorithm: an algorithm for solving instances of the Boolean satisfiability problem Davis–Putnam algorithm: check the validity of a first-order logic formula Difference map algorithm general algorithms for the constraint satisfaction Davis–Putnam–Logemann–Loveland algorithm (DPLL): an algorithm for deciding the satisfiability of propositional logic formula in conjunctive normal form, i.e. for solving the CNF-SAT problem Exact cover problem Min conflicts algorithm general algorithms for the constraint satisfaction Algorithm X: a nondeterministic algorithm Dancing Links: an efficient implementation of Algorithm X Cross-entropy method: a general Monte Carlo approach to combinatorial and continuous multi-extremal optimization and importance sampling Differential evolution Dynamic Programming: problems


id: list-of-algorithms-20260505-5
file: data/en.wikipedia.org/wiki/List_of_algorithms-5.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
Algorithms for calculating variance: avoiding instability and numerical overflow Approximate counting algorithm: allows counting large number of events in a small register Bayesian statistics Nested sampling algorithm: a computational approach to the problem of comparing models in Bayesian statistics Clustering algorithms Average-linkage clustering: a simple agglomerative clustering algorithm Canopy clustering algorithm: an unsupervised pre-clustering algorithm related to the K-means algorithm Chinese whispers Complete-linkage clustering: a simple agglomerative clustering algorithm DBSCAN: a density based clustering algorithm Expectation-maximization algorithm Fuzzy clustering: a class of clustering algorithms where each point has a degree of belonging to clusters FLAME clustering (Fuzzy clustering by Local Approximation of MEmberships): define clusters in the dense parts of a dataset and perform cluster assignment solely based on the neighborhood relationships among objects Fuzzy c-means k-means clustering: cluster objects based on attributes into partitions k-means++: a variation of this, using modified random seeds k-medoids: similar to k-means, but chooses datapoints or medoids as centers KHOPCA clustering algorithm: a local clustering algorithm, which produces hierarchical multi-hop clusters in static and mobile environments. Linde–Buzo–Gray algorithm: a vector quantization algorithm to derive a good codebook Lloyd's algorithm (Voronoi iteration or relaxation): group data points into a given number of categories, a popular


id: list-of-algorithms-20260505-6
file: data/en.wikipedia.org/wiki/List_of_algorithms-6.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
Asymmetric (public key) encryption: ElGamal Elliptic curve cryptography MAE1 NTRUEncrypt RSA Digital signatures (asymmetric authentication): DSA, and its variants: ECDSA and Deterministic ECDSA EdDSA (Ed25519) RSA Cryptographic hash functions (see also the section on message authentication codes): BLAKE MD5 – Note that there is now a method of generating collisions for MD5 RIPEMD-160 SHA-1 – Note that there is now a method of generating collisions for SHA-1 SHA-2 (SHA-224, SHA-256, SHA-384, SHA-512) SHA-3 (SHA3-224, SHA3-256, SHA3-384, SHA3-512, SHAKE128, SHAKE256) Tiger (TTH), usually used in Tiger tree hashes WHIRLPOOL Cryptographically secure pseudo-random number generators Blum Blum Shub – based on the hardness of factorization Fortuna, intended as an improvement on Yarrow algorithm Linear-feedback shift register (note: many LFSR-based algorithms are weak or have been broken) Yarrow algorithm Key exchange Diffie–Hellman key exchange Elliptic-curve Diffie–Hellman (ECDH) Key derivation functions, often used for password hashing and key stretching Argon2 bcrypt PBKDF2 scrypt Message authentication codes (symmetric authentication algorithms, which take a key as a parameter): HMAC: keyed-hash message authentication Poly1305 SipHash Secret sharing, secret splitting, key splitting, M of N algorithms Blakey's scheme Shamir's secret sharing Symmetric (secret key) encryption: Advanced Encryption Standard (AES), winner of NIST competition, also known as Rijndael Blowfish


id: list-of-algorithms-20260505-7
file: data/en.wikipedia.org/wiki/List_of_algorithms-7.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
Hopcroft's algorithm, Moore's algorithm, and Brzozowski's algorithm: algorithms for minimizing the number of states in a deterministic finite automaton Powerset construction: algorithm to convert nondeterministic automaton to deterministic automaton. Tarski–Kuratowski algorithm: a non-deterministic algorithm which provides an upper bound for the complexity of formulas in the arithmetical hierarchy and analytical hierarchy == Information theory and signal processing == === Coding theory === ==== Error detection and correction ==== BCH Codes Berlekamp–Massey algorithm Peterson–Gorenstein–Zierler algorithm Reed–Solomon error correction BCJR algorithm: decoding of error correcting codes defined on trellises (principally convolutional codes) Forward error correction Gray code Hamming codes Hamming(7,4): a Hamming code that encodes 4 bits of data into 7 bits by adding 3 parity bits Hamming distance: sum number of positions which are different Hamming weight (population count): find the number of 1 bits in a binary word Redundancy checks Adler-32 Cyclic redundancy check Damm algorithm Fletcher's checksum Longitudinal redundancy check (LRC) Luhn algorithm: a method of validating identification numbers Luhn mod N algorithm: extension of Luhn to non-numeric characters Parity: simple/fast error detection technique Verhoeff algorithm ==== Lossless compression algorithms ==== Burrows–Wheeler transform: preprocessing useful for improving lossless compression Context tree weighting Delta encoding: aid to compression of data


id: list-of-algorithms-20260505-8
file: data/en.wikipedia.org/wiki/List_of_algorithms-8.md
category: reference
title: List of algorithms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_algorithms
date_saved: 2026-05-05T08:12:49.096714+00:00
instance: kb-cron
parent: list-of-algorithms-20260505-0
summary:
Cache algorithms CHS conversion: converting between disk addressing systems Double dabble: convert binary numbers to BCD Hash function: convert a large, possibly variable-sized amount of data into a small datum, usually a single integer that may serve as an index into an array Fowler–Noll–Vo hash function: fast with low collision rate Pearson hashing: computes 8-bit value only, optimized for 8-bit computers Zobrist hashing: used in the implementation of transposition tables Unicode collation algorithm Xor swap algorithm: swaps the values of two variables without using a buffer == Database algorithms == Algorithms for Recovery and Isolation Exploiting Semantics (ARIES): transaction recovery Join algorithms Block nested loop Hash join Nested loop join Sort-Merge Join The Chase == Distributed systems algorithms == Clock synchronization Berkeley algorithm Cristian's algorithm Intersection algorithm Marzullo's algorithm Consensus (computer science): agreeing on a single value or history among unreliable processors Chandra–Toueg consensus algorithm Paxos algorithm Raft (computer science) Detection of Process Termination Dijkstra-Scholten algorithm Huang's algorithm Lamport ordering: a partial ordering of events based on the happened-before relation Leader election: a method for dynamically selecting a coordinator Bully algorithm Mutual exclusion Lamport's Distributed Mutual Exclusion Algorithm Naimi-Trehel's log(n) Algorithm Maekawa's Algorithm Raymond's Algorithm Ricart–Agrawala Algorithm Snapshot algorithm: record


id: list-of-aperiodic-sets-of-tiles-20260505-0
file: data/en.wikipedia.org/wiki/List_of_aperiodic_sets_of_tiles-0.md
category: reference
title: List of aperiodic sets of tiles
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_aperiodic_sets_of_tiles
date_saved: 2026-05-05T08:12:50.348730+00:00
instance: kb-cron
parent: list-of-aperiodic-sets-of-tiles-20260505-0
summary:
In geometry, a tiling is a partition of the plane (or any other geometric setting) into closed sets (called tiles), without gaps or overlaps (other than the boundaries of the tiles). A tiling is considered periodic if there exist translations in two independent directions which map the tiling onto itself. Such a tiling is composed of a single fundamental unit or primitive cell which repeats endlessly and regularly in two independent directions. An example of such a tiling is shown in the adjacent diagram (see the image description for more information). A tiling that cannot be constructed from a single primitive cell is called nonperiodic. If a given set of tiles allows only nonperiodic tilings, then this set of tiles is called aperiodic. The tilings obtained from an aperiodic set of tiles are often called aperiodic tilings, though strictly speaking it is the tiles themselves that are aperiodic. (The tiling itself is said to be "nonperiodic".) The first table explains the abbreviations used in the second table. The second table contains all known aperiodic sets of tiles and gives some additional basic information about each set. This list of tiles is still incomplete. == Explanations == == List == ==


id: outline-of-arithmetic-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_arithmetic-0.md
category: reference
title: Outline of arithmetic
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_arithmetic
date_saved: 2026-05-05T08:12:51.611767+00:00
instance: kb-cron
parent: outline-of-arithmetic-20260505-0
summary:
The following outline is provided as an overview of and topical guide to arithmetic: Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms, and the use of such operations to perform more complicated calculations. Arithmetic is fundamental for both pure mathematics and its practical application to science and daily life. In pure mathematics, arithmetic is defined formally for various types of numbers, such as integers, fractions of integers (rational numbers), and real numbers. In practical application, arithmetic is usually approximate, operating on decimal or binary numbers, with rounding. == Essence of arithmetic == Elementary arithmetic Decimal arithmetic Decimal point Numeral Place value == History of arithmetic == == Arithmetic operations and related concepts == Order of operations Addition Summation – Answer after adding a sequence of numbers Additive inverse Subtraction – Taking away numbers Multiplication – Repeated addition Multiple – Product of multiplication Least common multiple Multiplicative inverse Division – Repeated subtraction Modulo – The remainder of division Quotient – Result of division Quotition and partition – How many parts are there, and what is the size


id: list-of-mathematical-artists-20260505-0
file: data/en.wikipedia.org/wiki/List_of_mathematical_artists-0.md
category: reference
title: List of mathematical artists
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_mathematical_artists
date_saved: 2026-05-05T08:12:52.917714+00:00
instance: kb-cron
parent: list-of-mathematical-artists-20260505-0
summary:
This is a list of artists who actively explored mathematics in their artworks. Art forms practised by these artists include painting, sculpture, architecture, textiles and origami. Some artists such as Piero della Francesca and Luca Pacioli went so far as to write books on mathematics in art. Della Francesca wrote books on solid geometry and the emerging field of perspective, including De Prospectiva Pingendi (On Perspective for Painting), Trattato d’Abaco (Abacus Treatise), and De corporibus regularibus (Regular Solids), while Pacioli wrote De divina proportione (On Divine Proportion), with illustrations by Leonardo da Vinci, at the end of the fifteenth century. Merely making accepted use of some aspect of mathematics such as perspective does not qualify an artist for admission to this list. The term "fine art" is used conventionally to cover the output of artists who produce a combination of paintings, drawings and sculptures. == List == == References == == External links == Saint Louis University: List of mathematical artists, by field


id: list-of-axioms-20260505-0
file: data/en.wikipedia.org/wiki/List_of_axioms-0.md
category: reference
title: List of axioms
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_axioms
date_saved: 2026-05-05T08:12:54.221468+00:00
instance: kb-cron
parent: list-of-axioms-20260505-0
summary:
This is a list of axioms as that term is understood in mathematics. In epistemology, the word axiom is understood differently; see axiom and self-evidence. Individual axioms are almost always part of a larger axiomatic system. == ZF (the Zermelo–Fraenkel axioms without the axiom of choice) == Together with the axiom of choice (see below), these are the de facto standard axioms for contemporary mathematics or set theory. They can be easily adapted to analogous theories, such as mereology. Axiom of extensionality Axiom of empty set Axiom of pairing Axiom of union Axiom of infinity Axiom schema of replacement Axiom of power set Axiom of regularity Axiom schema of specification See also Zermelo set theory. == Axiom of choice == With the Zermelo–Fraenkel axioms above, this makes up the system ZFC in which most mathematics is potentially formalisable. === Equivalents of AC === Hausdorff maximality theorem Well-ordering theorem Zorn's lemma === Stronger than AC === Axiom of global choice === Weaker than AC === Axiom of countable choice Axiom of dependent choice Boolean prime ideal theorem Axiom of uniformization === Alternates incompatible with AC === Axiom of real determinacy == Other axioms of mathematical logic == Von Neumann–Bernays–Gödel axioms Continuum


id: list-of-banach-spaces-20260505-0
file: data/en.wikipedia.org/wiki/List_of_Banach_spaces-0.md
category: reference
title: List of Banach spaces
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Banach_spaces
date_saved: 2026-05-05T08:12:55.569651+00:00
instance: kb-cron
parent: list-of-banach-spaces-20260505-0
summary:
In the mathematical field of functional analysis, Banach spaces are among the most important objects of study. In other areas of mathematical analysis, most spaces which arise in practice turn out to be Banach spaces as well. == Classical Banach spaces == According to Diestel (1984, Chapter VII), the classical Banach spaces are those defined by Dunford & Schwartz (1958), which is the source for the following table. Glossary of symbols for the table below: F {\displaystyle \mathbb {F} } denotes the field of real numbers R {\displaystyle \mathbb {R} } or complex numbers C . {\displaystyle \mathbb {C} .} K {\displaystyle K} is a compact Hausdorff space. p , q ∈ R {\displaystyle p,q\in \mathbb {R} } are real numbers with 1 < p , q < ∞ {\displaystyle 1<p,q<\infty } that are Hölder conjugates, meaning that they satisfy 1 q + 1 p = 1 {\displaystyle {\frac {1}{q}}+{\frac {1}{p}}=1} and thus also q = p p − 1 . {\displaystyle q={\frac {p}{p-1}}.} Σ {\displaystyle \Sigma } is a σ {\displaystyle \sigma } -algebra of sets. Ξ {\displaystyle \Xi } is an algebra of sets (for spaces only requiring finite additivity, such as the ba space). μ {\displaystyle \mu


id: list-of-works-by-nikolay-bogolyubov-20260505-0
file: data/en.wikipedia.org/wiki/List_of_works_by_Nikolay_Bogolyubov-0.md
category: reference
title: List of works by Nikolay Bogolyubov
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_works_by_Nikolay_Bogolyubov
date_saved: 2026-05-05T08:12:56.878536+00:00
instance: kb-cron
parent: list-of-works-by-nikolay-bogolyubov-20260505-0
summary:
List of some published works of Nikolay Bogolyubov in chronological order: == 1924 == N. N. Bogolyubov (1924). On the behavior of solutions of linear differential equations at infinity (Russian: О поведении решений линейных дифференциальных уравнений на бесконечности). == 1934 == N. M. Krylov and N. N. Bogolyubov (1934). On various formal expansions of non-linear mechanics (in Ukrainian). Kiev: Izdat. Zagal'noukr. Akad. Nauk. == 1937 == N. N. Bogoliubov and N. M. Krylov (1937). "La theorie generalie de la mesure dans son application a l'etude de systemes dynamiques de la mecanique non-lineaire" (in French). Ann. Math. II 38: 65–113. Zbl. 16.86. == 1945 == Боголюбов Н. Н. (1945). О некоторых статистических методах в математической физике (in Russian). Киев: Изд-во АН УССР. N. N. Bogoliubov (1945). On Some Statistical Methods in Mathematical Physics (in Russian). Kyiv: Izdatelstvo AN USSR. == 1946 == N. N. Bogoliubov (1946). "Kinetic Equations" (in Russian). Journal of Experimental and Theoretical Physics 16 (8): 691–702. N. N. Bogoliubov (1946). "Kinetic Equations" (in English). Journal of Physics 10 (3): 265–274. == 1947 == N. N. Bogoliubov, K. P. Gurov (1947). "Kinetic Equations in Quantum Mechanics" (in Russian). Journal of Experimental and Theoretical Physics 17 (7): 614–628. N. N.


id: list-of-boolean-algebra-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_Boolean_algebra_topics-0.md
category: reference
title: List of Boolean algebra topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_Boolean_algebra_topics
date_saved: 2026-05-05T08:12:58.151075+00:00
instance: kb-cron
parent: list-of-boolean-algebra-topics-20260505-0
summary:
This is a list of topics around Boolean algebra and propositional logic. == Articles with a wide scope and introductions == Algebra of sets Boolean algebra (structure) Boolean algebra Field of sets Logical connective Propositional calculus == Boolean functions and connectives == Ampheck Analysis of Boolean functions Balanced Boolean function Bent function Boolean algebras canonically defined Boolean function Boolean matrix Boolean-valued function Conditioned disjunction Evasive Boolean function Exclusive or Functional completeness Logical biconditional Logical conjunction Logical disjunction Logical equality Logical implication Logical negation Logical NOR Majority function Material conditional Minimal axioms for Boolean algebra Peirce arrow Read-once function Sheffer stroke Sole sufficient operator Symmetric Boolean function Symmetric difference Zhegalkin polynomial == Examples of Boolean algebras == Boolean domain Complete Boolean algebra Interior algebra Two-element Boolean algebra == Extensions of Boolean algebras == Derivative algebra (abstract algebra) Free Boolean algebra Monadic Boolean algebra == Generalizations of Boolean algebras == De Morgan algebra First-order logic Heyting algebra Lindenbaum–Tarski algebra Skew Boolean algebra == Syntax == Algebraic normal form Boolean conjunctive query Canonical form (Boolean algebra) Conjunctive normal form Disjunctive normal form Formal system == Technical applications == And-inverter graph Logic gate Boolean analysis == Theorems and specific laws == Boolean prime ideal


id: list-of-calculus-topics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_calculus_topics-0.md
category: reference
title: List of calculus topics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_calculus_topics
date_saved: 2026-05-05T08:12:59.314130+00:00
instance: kb-cron
parent: list-of-calculus-topics-20260505-0
summary:
This is a list of calculus topics. == Limits == Limit (mathematics) Limit of a function One-sided limit Limit of a sequence Indeterminate form Orders of approximation (ε, δ)-definition of limit Continuous function == Differential calculus == Derivative Notation Newton's notation for differentiation Leibniz's notation for differentiation Simplest rules Derivative of a constant Sum rule in differentiation Constant factor rule in differentiation Linearity of differentiation Power rule Chain rule Local linearization Product rule Quotient rule Inverse functions and differentiation Implicit differentiation Stationary point Maxima and minima First derivative test Second derivative test Extreme value theorem Differential equation Differential operator Newton's method Taylor's theorem L'Hôpital's rule General Leibniz rule Mean value theorem Logarithmic derivative Differential (calculus) Related rates Regiomontanus' angle maximization problem Rolle's theorem == Integral calculus == Antiderivative/Indefinite integral Simplest rules Sum rule in integration Constant factor rule in integration Linearity of integration Arbitrary constant of integration Cavalieri's quadrature formula Fundamental theorem of calculus Integration by parts Inverse chain rule method Integration by substitution Tangent half-angle substitution Differentiation under the integral sign Trigonometric substitution Partial fractions in integration Quadratic integral Proof that 22/7 exceeds π Trapezium rule Integral of the secant function Integral of secant cubed Arclength Solid of revolution


id: outline-of-calculus-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_calculus-0.md
category: reference
title: Outline of calculus
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_calculus
date_saved: 2026-05-05T08:13:00.609028+00:00
instance: kb-cron
parent: outline-of-calculus-20260505-0
summary:
Calculus is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of contemporary mathematics education. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient. == Branches of calculus == Differential calculus Integral calculus Multivariable calculus Fractional calculus Differential Geometry == History of calculus == History of calculus Important publications in calculus == General calculus concepts == Continuous function Derivative Fundamental theorem of calculus Integral Limit Non-standard analysis Partial derivative Infinite Series == Calculus scholars == Sir Isaac Newton Gottfried Leibniz Leonhard Euler == Calculus lists == List of calculus topics == See also == Glossary of calculus Table of mathematical symbols == References == == External links == Weisstein, Eric W. "Calculus". MathWorld. Topics on Calculus at PlanetMath. Calculus Made Easy (1914) by Silvanus P. Thompson Full text in PDF Calculus.org: The Calculus page at University of California, Davis – contains resources and links to other sites COW: Calculus on the Web Archived 2007-10-14 at the Wayback Machine at Temple University - contains resources ranging from pre-calculus and associated algebra Online Integrator (WebMathematica) from Wolfram Research The Role of


id: outline-of-category-theory-20260505-0
file: data/en.wikipedia.org/wiki/Outline_of_category_theory-0.md
category: reference
title: Outline of category theory
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Outline_of_category_theory
date_saved: 2026-05-05T08:13:01.794317+00:00
instance: kb-cron
parent: outline-of-category-theory-20260505-0
summary:
The following outline is provided as an overview of and guide to category theory: Category theory is a general theory of mathematical structures and their relations. It was introduced by Samuel Eilenberg and Saunders Mac Lane in the mid-20th century in their foundational work on algebraic topology. Category theory can be used in most areas of mathematics. In particular, many constructions of new mathematical objects from previous ones that appear similarly in several contexts are conveniently expressed and unified in terms of categories. Examples include quotient spaces, direct products, completion, and duality. Many areas of computer science also rely on category theory, such as functional programming and semantics. == Essence of category theory == Category Functor Natural transformation == Branches of category theory == Homological algebra Diagram chasing Topos theory Enriched category theory Higher category theory Categorical logic Applied category theory == Specific categories == Category of sets Concrete category Category of small categories Category of vector spaces Category of graded vector spaces Category of chain complexes Category of finite dimensional Hilbert spaces Category of sets and relations Category of topological spaces Category of metric spaces Category of preordered sets Category of groups Category of abelian groups Category of rings


id: list-of-chaotic-maps-20260505-0
file: data/en.wikipedia.org/wiki/List_of_chaotic_maps-0.md
category: reference
title: List of chaotic maps
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_chaotic_maps
date_saved: 2026-05-05T08:13:03.039151+00:00
instance: kb-cron
parent: list-of-chaotic-maps-20260505-0
summary:
In mathematics, a chaotic map is a map (an evolution function) that exhibits some sort of chaotic behavior. Maps may be parameterized by a discrete-time or a continuous-time parameter. Discrete maps usually take the form of iterated functions. Chaotic maps often occur in the study of dynamical systems. Chaotic maps and iterated functions often generate fractals. Some fractals are studied as objects themselves, as sets rather than in terms of the maps that generate them. This is often because there are several different iterative procedures that generate the same fractal. See also Universality (dynamical systems). == List of chaotic maps == == List of fractals == Cantor set de Rham curve Gravity set, or Mitchell-Green gravity set Julia set - derived from complex quadratic map Koch snowflake - special case of de Rham curve Lyapunov fractal Mandelbrot set - derived from complex quadratic map Menger sponge Newton fractal Nova fractal - derived from Newton fractal Quaternionic fractal - three dimensional complex quadratic map Sierpinski carpet Sierpinski triangle == References ==


id: list-of-mathematical-topics-in-classical-mechanics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_mathematical_topics_in_classical_mechanics-0.md
category: reference
title: List of mathematical topics in classical mechanics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_mathematical_topics_in_classical_mechanics
date_saved: 2026-05-05T08:13:04.549140+00:00
instance: kb-cron
parent: list-of-mathematical-topics-in-classical-mechanics-20260505-0
summary:
This is a list of mathematical topics in classical mechanics, by Wikipedia page. See also list of variational topics, correspondence principle. == Newtonian physics == Newton's laws of motion Inertia, Kinematics, rigid body Momentum, kinetic energy Parallelogram of force Circular motion Rotational speed Angular speed Angular momentum torque angular acceleration moment of inertia parallel axes rule perpendicular axes rule stretch rule centripetal force, centrifugal force, Reactive centrifugal force Laplace–Runge–Lenz vector Euler's disk elastic potential energy Mechanical equilibrium D'Alembert's principle Degrees of freedom (physics and chemistry) Frame of reference Inertial frame of reference Galilean transformation Principle of relativity == Conservation laws == Conservation of momentum Conservation of linear momentum Conservation of angular momentum Conservation of energy Potential energy Conservative force Conservation of mass == Law of universal gravitation == Projectile motion Kepler's laws of planetary motion Escape velocity Potential well Weightlessness Lagrangian point N-body problem Kolmogorov–Arnold–Moser theorem Virial theorem Gravitational binding energy Speed of gravity Newtonian limit Hill sphere Roche lobe Roche limit == Hamiltonian mechanics == Phase space Symplectic manifold Liouville's theorem (Hamiltonian) Poisson bracket Poisson algebra Poisson manifold Antibracket algebra Hamiltonian constraint Moment map Contact geometry Analysis of flows Nambu mechanics == Lagrangian mechanics == Action (physics) Lagrangian Euler–Lagrange


id: list-of-textbooks-on-classical-mechanics-and-quantum-mechanics-20260505-0
file: data/en.wikipedia.org/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics-0.md
category: reference
title: List of textbooks on classical mechanics and quantum mechanics
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/List_of_textbooks_on_classical_mechanics_and_quantum_mechanics
date_saved: 2026-05-05T08:13:06.136598+00:00
instance: kb-cron
parent: list-of-textbooks-on-classical-mechanics-and-quantum-mechanics-20260505-0
summary:
This is a list of notable textbooks on classical mechanics and quantum mechanics arranged according to level and surnames of the authors in alphabetical order. == Undergraduate == === Classical mechanics === Feynman, Richard P. (2005). The Feynman Lectures on Physics. Vol. 1 (2nd ed.). Addison-Wesley. ISBN 978-0-8053-9065-0. Halliday, David; Resnick, Robert (1970). Fundamentals of Physics. John Wiley & Sons. Chapters 1–21. Numerous subsequent editions. Hamill, Patrick (2014). A Student's Guide to Lagrangians and Hamiltonians. Cambridge University Press. ISBN 978-1107617520. Hand, Louis; Finch, Janet (1998). Analytical Mechanics. Cambridge University Press. ISBN 0521573270. Kibble, T. W.; Berkshire, F. H. (2004). Classical Mechanics. Imperial College Press. ISBN 1860944248. Kleppner, Daniel; Kolenkow, Robert (1973). An Introduction to Mechanics. McGraw-Hill. ISBN 0-07-035048-5. Marion, Jerry; Thornton, Stephen (2003). Classical Dynamics of Particles and Systems (5th ed.). Brooks Cole. ISBN 0534408966. Morin, David (2005). Introduction to Classical Mechanics: With Problems and Solutions. Cambridge University Press. ISBN 9780521876223. Müller-Kirsten, Harald J.W. (2024). Classical Mechanics and Relativity (2nd ed.). World Scientific. ISBN 9789811287114. Taylor, John (2005). Classical Mechanics. University Science Books. ISBN 978-981-12-8711-4. Young, Hugh D.; Freedman, Roger A. (2019). University Physics with Modern Physics (15th ed.). Pearson. ISBN 978-0135159552. === Quantum mechanics === Eisberg, Robert; Resnick, Robert


id: classification-of-low-dimensional-real-lie-algebras-20260505-0
file: data/en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras-0.md
category: reference
title: Classification of low-dimensional real Lie algebras
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras
date_saved: 2026-05-05T08:13:07.603621+00:00
instance: kb-cron
parent: classification-of-low-dimensional-real-lie-algebras-20260505-0
summary:
This mathematics-related list provides Mubarakzyanov's classification of low-dimensional real Lie algebras, published in Russian in 1963. It complements the article on Lie algebra in the area of abstract algebra. An English version and review of this classification was published by Popovych et al. in 2003. == Mubarakzyanov's Classification == Let g n {\displaystyle {\mathfrak {g}}_{n}} be n {\displaystyle n} -dimensional Lie algebra over the field of real numbers with generators e 1 , … , e n {\displaystyle e_{1},\dots ,e_{n}} , n ≤ 4 {\displaystyle n\leq 4} . For each algebra g {\displaystyle {\mathfrak {g}}} we adduce only non-zero commutators between basis elements. === One-dimensional === g 1 {\displaystyle {\mathfrak {g}}_{1}} , abelian. === Two-dimensional === 2 g 1 {\displaystyle 2{\mathfrak {g}}_{1}} , abelian R 2 {\displaystyle \mathbb {R} ^{2}} ; g 2.1 {\displaystyle {\mathfrak {g}}_{2.1}} , solvable a f f ( 1 ) = { ( a b 0 0 ) : a , b ∈ R } {\displaystyle {\mathfrak {aff}}(1)=\left\{{\begin{pmatrix}a&b\\0&0\end{pmatrix}}\,:\,a,b\in \mathbb {R} \right\}} , [ e 1 , e 2 ] = e 1 . {\displaystyle [e_{1},e_{2}]=e_{1}.} === Three-dimensional === 3 g 1 {\displaystyle 3{\mathfrak {g}}_{1}} , abelian, Bianchi I; g 2.1 ⊕ g 1 {\displaystyle {\mathfrak {g}}_{2.1}\oplus


id: classification-of-low-dimensional-real-lie-algebras-20260505-1
file: data/en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras-1.md
category: reference
title: Classification of low-dimensional real Lie algebras
tags: science, encyclopedia
source_url: https://en.wikipedia.org/wiki/Classification_of_low-dimensional_real_Lie_algebras
date_saved: 2026-05-05T08:13:07.603621+00:00
instance: kb-cron
parent: classification-of-low-dimensional-real-lie-algebras-20260505-0
summary:
g 4.1 {\displaystyle {\mathfrak {g}}_{4.1}} , indecomposable nilpotent, [ e 2 , e 4 ] = e 1 , [ e 3 , e 4 ] = e 2 ; {\displaystyle [e_{2},e_{4}]=e_{1},\quad [e_{3},e_{4}]=e_{2};} g 4.2 {\displaystyle {\mathfrak {g}}_{4.2}} , indecomposable solvable, [ e 1 , e 4 ] = β e 1 , [ e 2 , e 4 ] = e 2 , [ e 3 , e 4 ] = e 2 + e 3 , β ≠ 0 ; {\displaystyle [e_{1},e_{4}]=\beta e_{1},\quad [e_{2},e_{4}]=e_{2},\quad [e_{3},e_{4}]=e_{2}+e_{3},\quad \beta \neq 0;} g 4.3 {\displaystyle {\mathfrak {g}}_{4.3}} , indecomposable solvable, [ e 1 , e 4 ] = e 1 , [ e 3 , e 4 ] = e 2 ; {\displaystyle [e_{1},e_{4}]=e_{1},\quad [e_{3},e_{4}]=e_{2};} g 4.4 {\displaystyle {\mathfrak {g}}_{4.4}} , indecomposable solvable, [ e 1 , e 4 ] = e 1 , [ e 2 , e 4 ] = e 1 + e 2 , [ e 3 , e 4 ] = e 2 + e 3 ; {\displaystyle [e_{1},e_{4}]=e_{1},\quad [e_{2},e_{4}]=e_{1}+e_{2},\quad [e_{3},e_{4}]=e_{2}+e_{3};} g 4.5 {\displaystyle {\mathfrak {g}}_{4.5}} , indecomposable solvable, [ e 1 , e 4 ] = α e 1 , [ e 2 , e 4


