Wikipedia's contents: Mathematics and logic

Mathematics is the science of quantization. It is also the study of patterns and relationships, including concepts such as quantity, structure, space, uncertainty, and change. It evolved through the use of abstraction and logical reasoning, from counting, calculation, measurement, and the systematic study of positions, 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 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 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.

The Mathematics Portal The Logic PortalMore about Mathematics and Logic...

Mathematics and logic: Overview Lists Outlines Portals Categories Glossaries Indexesedit watch

Overview (see for all subject areas)Formal sciences Information theory Logic Statistics Theoretical computer scienceMathematics Algebra Applied mathematics Arithmetic Calculus Equations Geometry Mathematical analysis Mathematics education Mathematical practice Measurement Numbers Philosophy of mathematics Probability Proofs Theorems Trigonometry Unsolved problems in mathematicsedit watch

Outlines (see for all subject areas)Formal sciences branches of knowledge that are concerned with formal systems. Unlike other sciences, the formal sciences are not concerned with the validity of theories based on observations in the real world, but instead with the properties of formal systems based on definitions and rules.

Mathematics study of quantity, structure, space, and change. Mathematicians seek out patterns, and formulate new conjectures. (See also: Lists of mathematics topics)

Arithmetic oldest and most elementary branch of mathematics, involving the study of quantity, especially as the result of combining numbers. The simplest arithmetical operations include addition, subtraction, multiplication and division.

Algebra branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures.

Algebraic structures

Analysis/Calculus branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations.

Category theory

Discrete mathematics study of mathematical structures that are fundamentally discrete rather than continuous. In contrast to real numbers that have the property of varying "smoothly", the objects studied in discrete mathematics such as integers, graphs, and statements in logic do not vary smoothly in this way, but have distinct, separated values.

Combinatorics branch of mathematics concerning the study of finite or countable discrete structures.

Geometry one of the oldest branches of mathematics, it is concerned with questions of shape, size, relative position of figures, and the properties of space.

Trigonometry branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves.