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Special functions: non-elementary functions that have established names and notations due to their importance. Trigonometric functions : relate the angles of a triangle to the lengths of its sides. Nowhere differentiable function called also Weierstrass function : continuous everywhere but not differentiable even at a single point.
Thomae's function: is a function that is continuous at all irrational numbers and discontinuous at all rational numbers. It is also a modification of Dirichlet function and sometimes called Riemann function. Kronecker delta function: is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise.
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).
This object of algebra was called modern algebra or abstract algebra, as established by the influence and works of Emmy Noether. [36] Some types of algebraic structures have useful and often fundamental properties, in many areas of mathematics. Their study became autonomous parts of algebra, and include: [14] group theory; field theory
Functions – mapping that associates a single output value with each input value; Sequences – ordered list of elements either finite or infinite; Systems of equations – finite set of equations; Vectors – element of a vector space; Matrix – two dimensional array of numbers; Vector space – basic algebraic structure of linear algebra
Algebra is the branch of mathematics that studies certain abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic operations other than the standard arithmetic operations, such as addition and multiplication.