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Algebra is the branch of mathematics that studies algebraic structures and the operations they use. [1] An algebraic structure is a non-empty set of mathematical objects, such as the integers, together with algebraic operations defined on that set, like addition and multiplication.
Elementary algebra, also known as high school algebra or college algebra, [1] encompasses the basic concepts of algebra. It is often contrasted with arithmetic : arithmetic deals with specified numbers , [ 2 ] whilst algebra introduces variables (quantities without fixed values).
2.1 Mathematics. 2.2 Physics. ... This is a list of equations, ... Dirac equation. Dirac equation in the algebra of physical space;
Abel–Ruffini theorem (theory of equations, Galois theory) Abhyankar–Moh theorem (algebraic geometry) Absolute convergence theorem (mathematical series) Acyclic models theorem (algebraic topology) Addition theorem (algebraic geometry) Adiabatic theorem ; Ado's theorem (Lie algebra) Akhiezer's theorem (complex analysis)
To solve equations from either family, one uses algorithmic or geometric techniques that originate from linear algebra or mathematical analysis. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general ...
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
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