Wikipedia's contents: Mathematics and logic
Mathematics is the study of topics such as quantity (numbers), structure, space, and change. It evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to a specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. Since the mid-nineteenth century formal logic has been studied in the context of the foundations of mathematics.
Information theory • Logic • Statistics • Theoretical computer science
Methodology • Graphical methods • Mathematics-based methods • Rules of inference
Mathematical statements • Algorithms • Axioms • Conjectures • Erdős conjectures • Combinatorial principles • Equations • Formulae involving pi • Mathematical identities • Inequalities • Lemmas • Mathematical proofs • NP-complete problems • Statements undecidable in ZFC • Mathematical symbols • Undecidable problems • Theorems ( Fundamental theorems)
General concepts • Dualities • Transforms • Recursion
Mathematical objects • Mathematical examples • Curves • Complex reflection groups • Complexity classes • Examples in general topology • Finite simple groups • Fourier-related transforms • Mathematical functions • Mathematical knots and links • Manifolds • Mathematical shapes • Matrices • Numbers • Polygons, polyhedra and polytopes • Regular polytopes • Simple Lie groups • Small groups • Special functions and eponyms • Algebraic surfaces • Surfaces • Table of Lie groups• Areas of mathematics • Arithmetic and Diophantine geometry • Calculus • Category theory • Cryptographic key types • Differential geometry and topology ( Topology) • Field theory • Game theory • Graph theory • Group theory • Mathematical jargon • Mathematical symbols • Linear algebra • Order theory • Probability and statistics • Riemannian and metric geometry • Ring theory • Scheme theory • Semisimple groups • Shapes with metaphorical names
• Tensor theory
Wikipedia's contents: Mathematics and logic
Mathematics is the study of topics such as quantity (numbers), structure, space, and change. It evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Mathematicians explore such concepts, aiming to formulate new conjectures and establish their truth by rigorous deduction from appropriately chosen axioms and definitions.
Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason or principle) is the study of the principles and criteria of valid inference and demonstration. As a formal science, logic investigates and classifies the structure of statements and arguments, both through the study of formal systems of inference and through the study of arguments in natural language. The field of logic ranges from core topics such as the study of fallacies and paradoxes, to a specialized analysis of reasoning using probability and to arguments involving causality. Logic is also commonly used today in argumentation theory. Since the mid-nineteenth century formal logic has been studied in the context of the foundations of mathematics.
Information theory • Logic • Statistics • Theoretical computer science
Methodology • Graphical methods • Mathematics-based methods • Rules of inference
Mathematical statements • Algorithms • Axioms • Conjectures • Erdős conjectures • Combinatorial principles • Equations • Formulae involving pi • Mathematical identities • Inequalities • Lemmas • Mathematical proofs • NP-complete problems • Statements undecidable in ZFC • Mathematical symbols • Undecidable problems • Theorems ( Fundamental theorems)
General concepts • Dualities • Transforms • Recursion
Mathematical objects • Mathematical examples • Curves • Complex reflection groups • Complexity classes • Examples in general topology • Finite simple groups • Fourier-related transforms • Mathematical functions • Mathematical knots and links • Manifolds • Mathematical shapes • Matrices • Numbers • Polygons, polyhedra and polytopes • Regular polytopes • Simple Lie groups • Small groups • Special functions and eponyms • Algebraic surfaces • Surfaces • Table of Lie groups• Areas of mathematics • Arithmetic and Diophantine geometry • Calculus • Category theory • Cryptographic key types • Differential geometry and topology ( Topology) • Field theory • Game theory • Graph theory • Group theory • Mathematical jargon • Mathematical symbols • Linear algebra • Order theory • Probability and statistics • Riemannian and metric geometry • Ring theory • Scheme theory • Semisimple groups • Shapes with metaphorical names
• Tensor theory