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Basic Math
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- Snippet from Wikipedia: Mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics with the major subdisciplines of number theory, algebra, geometry, and analysis, respectively. There is no general consensus among mathematicians about a common definition for their academic discipline.
Most mathematical activity involves the discovery of properties of abstract objects and the use of pure reason to prove them. These objects consist of either abstractions from nature or—in modern mathematics—entities that are stipulated to have certain properties, called axioms. A proof consists of a succession of applications of deductive rules to already established results. These results include previously proved theorems, axioms, and—in case of abstraction from nature—some basic properties that are considered true starting points of the theory under consideration.
Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent from any scientific experimentation. Some areas of mathematics, such as statistics and game theory, are developed in close correlation with their applications and are often grouped under applied mathematics. Other areas are developed independently from any application (and are therefore called pure mathematics), but often later find practical applications.
Historically, the concept of a proof and its associated mathematical rigour first appeared in Greek mathematics, most notably in Euclid's Elements. Since its beginning, mathematics was primarily divided into geometry and arithmetic (the manipulation of natural numbers and fractions), until the 16th and 17th centuries, when algebra and infinitesimal calculus were introduced as new fields. Since then, the interaction between mathematical innovations and scientific discoveries has led to a correlated increase in the development of both. At the end of the 19th century, the foundational crisis of mathematics led to the systematization of the axiomatic method, which heralded a dramatic increase in the number of mathematical areas and their fields of application. The contemporary Mathematics Subject Classification lists more than sixty first-level areas of mathematics.
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Math: Outline of mathematics, Mathematics research, Mathematical anxiety, Pythagorean Theorem, Scientific Notation, Algebra (Pre-algebra, Elementary algebra, Abstract algebra, Linear algebra, Universal algebra), Arithmetic (Essence of arithmetic, Elementary arithmetic, Decimal arithmetic, Decimal point, numeral system, Place value, Face value), Applied mathematics, Binary operation, Classical mathematics, Control theory, Cryptography, Definitions of mathematics, Discrete mathematics (Outline of discrete mathematics, Combinatorics), Dynamical systems, Engineering mathematics, Financial mathematics, Fluid mechanics (Mathematical fluid dynamics), Foundations of mathematics, Fudge (Mathematical fudge, Renormalization), Game theory, Glossary of areas of mathematics, Graph theory, Graph operations, Information theory, Language of mathematics, Mathematical economics, Mathematical logic (Model theory, Proof theory, Set theory, Type theory, Recursion theory, Theory of Computation, List of logic symbols), Mathematical optimization, Mathematician, Modulo, Mathematical notation (List of logic symbols, Notation in probability and statistics, Physical constants, Mathematical alphanumeric symbols, ISO 31-11), Numerical analysis, Operations research, Philosophy of mathematics, Probability (Outline of probability), Statistics, Mathematical structure, Ternary operation, Unary operation, Variable (mathematics), Glossary, Bibliography (Math for Data Science and DataOps, Math for Machine Learning and MLOps, Math for Programmers and Software Engineering), Courses, Mathematics GitHub. (navbar_math - see also navbar_variables)
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