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Everything about Initial algebra
Mathematical object
In mathematics, an initial algebra is an initial object in the category of F-algebras for a given endofunctor F. This initiality provides a general framework for induction and recursion. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Initial algebraA 5-minute orientation
- Skim a recent paper: Initial Optimization Techniques for the Cube Algebra Query LanguageInfluential work since 2022
- Pick up a classic book: Numerical solution of initial-value problems in differential-algebraic equationsThe most-reprinted book on the subject
- Read the landmark paper: Initial Algebra Semantics and Continuous AlgebrasCited 566 times
- Go sideways: F-algebraA closely related topic
- Go sideways: F-coalgebraA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Initial Algebra Semantics and Continuous Algebras
Difficulties in initial algebra learning in Indonesia
Initial and Final Algebra Semantics for Data Type Specifications: Two Characterization Theorems
Computer algebra derives correct initial conditions for low-dimensional dynamical models
Space and frequency-multiplexed optical linear algebra processor: fabrication and initial tests
Improving Grade 7 Students’ Achievement in Initial Algebra Through a Technology-Based Intervention
A presentation of the initial lift-algebra
Development and Initial Evaluation of the ClearSpeak Style for Automated Speaking of Algebra
🆕 Influential since 2022
Initial Optimization Techniques for the Cube Algebra Query Language
Irish 14-year-old students’ knowledge of initial algebra
A unifying logical foundation for initial algebra semantics and induction
Analysis of Students' Mathematical Communication Ability in Solving Algebra Problems by Considering Initial Ability and Habits of Mind
Solution of a nonlinear fractional-order initial value problem via a $\mathscr{C}^{*}$-algebra-valued $\mathcal{R}$-metric space
📚 Books worth reading
Numerical solution of initial-value problems in differential-algebraic equationsKathryn Eleda Brenan · 1989- 📕ODE methods for the solution of differential/algebraic systemC. William Gear · 1982
- 📕Approximation methods for the consistent initialization of differential-algebraic equationsB. Leimkuhler · 1988
Nordsieck's methodHartmut W. Roseke · 1973- 📕On obtaining a consistent set of initial values for a system of differential-algebraic equationsB. Leimkuhler · 1987
- 📕A panorama of mathematicsCarlos M. da Fonseca · 2016
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- F-algebra In mathematics, specifically in category theory, F-algebras generalize the notion of algebraic structure. Rewriting the algebraic laws in terms of morphisms…
- F-coalgebra In mathematics, specifically in category theory, an F-coalgebra is a structure defined according to a functor F, with specific properties as defined below…
- Coinduction In computer science, coinduction is a technique for defining and proving properties of systems of concurrent interacting objects. Coinduction is the mathematica…
- Catamorphism In functional programming, the concept of catamorphism (from the Ancient Greek: κατά "downwards" and μορφή "form, shape") denotes the unique homomorphism…
- Anamorphism In computer programming, an anamorphism is a function that generates a sequence by repeated application of the function to its previous result. You begin…
- Corecursion In computer science, corecursion is a type of operation that is dual to (structural) recursion. Whereas recursion consumes a data structure by first handling…
- Inductive type In type theory, a system has inductive types if it has facilities for creating a new type from constants and functions that create terms of that type.…
- Monad (category theory) In category theory, a branch of mathematics, a monad is a triple (T,η,μ) consisting of a functor T from a category to itself and two natural transformations…