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Discrete mathematics and Mathematical logic

Difference between Discrete mathematics and Mathematical logic

Discrete mathematics vs. Mathematical logic

Discrete mathematics is the study of mathematical structures that are fundamentally discrete rather than continuous. Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

Similarities between Discrete mathematics and Mathematical logic

Alan Turing

Alan Mathison Turing, OBE, FRS (23 June 1912 – 7 June 1954) was a British pioneering computer scientist, mathematician, logician, cryptanalyst, theoretical biologist, and marathon and ultra distance runner.

Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

Analysis

Analysis is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it.

Arithmetic

Arithmetic or arithmetics (from the Greek ἀριθμός arithmos, "number") is the oldest and most elementary branch of mathematics.

Automated theorem proving

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs.

Axiom

An axiom or postulate is a premise or starting point of reasoning.

Computability

Computability is the ability to solve a problem in an effective manner.

Countable set

In mathematics, a countable set is a set with the same cardinality (number of elements) as some subset of the set of natural numbers.

David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

Formal verification

In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.

Function (mathematics)

In mathematics, a function is a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output.

Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1.

Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that establish inherent limitations of all but the most trivial axiomatic systems capable of doing arithmetic.

Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

Hilbert's problems

Hilbert's problems are a list of twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.

Hilbert's tenth problem

Hilbert's tenth problem is the tenth on the list of Hilbert's problems of 1900.

Infinitary logic

An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs.

Integer

An integer (from the Latin ''integer'' meaning "whole")Integer&#x2009;'s first, literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

Intuitionistic logic

Intuitionistic logic, sometimes more generally called constructive logic, is a system of symbolic logic that differs from classical logic by replacing the traditional concept of truth with the concept of constructive provability.

Mathematical analysis

Mathematical analysis is a branch of mathematics that studies continuous change and includes the theories of differentiation, integration, measure, limits, infinite series, and analytic functions.

Mathematical proof

In mathematics, a proof is a deductive argument for a mathematical statement.

Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

NP (complexity)

In computational complexity theory, NP is one of the most fundamental complexity classes.

Programming language

A programming language is a formal constructed language designed to communicate instructions to a machine, particularly a computer.

Proof theory

Proof theory is a branch of mathematical logic that represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques.

Set (mathematics)

In mathematics, a set is a collection of distinct objects, considered as an object in its own right.

Theoretical computer science

Theoretical computer science is a division or subset of general computer science and mathematics that focuses on more abstract or mathematical aspects of computing and includes the theory of computation.

Truth value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

Well-formed formula

In mathematical logic, a well-formed formula, shortly wff, often simply formula, is a word (i.e. a finite sequence of symbols from a given alphabet) that is part of a formal language.

Yuri Matiyasevich

Yuri Vladimirovich Matiyasevich, (Ю́рий Влади́мирович Матиясе́вич; born March 2, 1947, in Leningrad) is a Russian mathematician and computer scientist.

The list above answers the following questions

• What Discrete mathematics and Mathematical logic have in common
• What are the similarities between Discrete mathematics and Mathematical logic

Discrete mathematics and Mathematical logic Comparison

Discrete mathematics has 213 relations, while Mathematical logic has 263. As they have in common 30, the Jaccard index is 6.30% = 30 / (213 + 263).

References

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