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The logarithmic spiral of the nautilus shell is a classical image used to depict the growth and change related to calculus. Calculus is used in every branch of the physical sciences, [54]: 1 actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be ...
Lambda calculus is Turing complete, that is, it is a universal model of computation that can be used to simulate any Turing machine. [3] Its namesake, the Greek letter lambda (λ), is used in lambda expressions and lambda terms to denote binding a variable in a function.
Discrete calculus is used for modeling either directly or indirectly as a discretization of infinitesimal calculus in every branch of the physical sciences, actuarial science, computer science, statistics, engineering, economics, business, medicine, demography, and in other fields wherever a problem can be mathematically modeled. It allows one ...
In type theory, the general idea of a type system in computer science is formalized into a specific algebra of types. For example, when writing f : X → Y {\displaystyle f\colon X\to Y} , the intent is that X {\displaystyle X} and Y {\displaystyle Y} are types , while the arrow → {\displaystyle \to } is a type constructor , specifically, the ...
First-order logic—also called predicate logic, predicate calculus, quantificational logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses quantified variables over non-logical objects, and allows the use of sentences that contain variables.
The book provides mathematical knowledge and skills for computer science, especially for the analysis of algorithms. According to the preface, the topics in Concrete Mathematics are "a blend of CONtinuous and disCRETE mathematics". Calculus is frequently used in the explanations and exercises.
In computer science, the process calculi (or process algebras) are a diverse family of related approaches for formally modelling concurrent systems.Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes.
In mathematical logic, category theory, and computer science, kappa calculus is a formal system for defining first-order functions. Unlike lambda calculus, kappa calculus has no higher-order functions; its functions are not first class objects. Kappa-calculus can be regarded as "a reformulation of the first-order fragment of typed lambda ...