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MATHMAA

# Algebra

Algebra and  its Structures Generalized version of Arithmetic that uses variables to stand for unspecified numbers its purpose is to solve algebraic equations or system of equations.

Examples of such solutions are the quadratic formula (for a quadratic equation ) and Gauss Jordan elimination (for solving a system of equations in matrix form) .

In higher Mathematics, it is a structure consisting of a class of objects and set of rules (analogous to addition and multiplication) for combining them . Its structures share two essential characteristics :

1) Calculations involve a finite number of steps and

2) Calculations involve abstract symbols (usually letters) representing more general objects(numbers ).

Higher-algebra (also known as Modern or Abstract-Algebra) includes all of elementary -algebra , as well as Group Theory , Theory of Rings , Field Theory, Manifolds and Vector Spaces.

· Surds

· Logarithms

· Exponents

· Mathematical Induction

· Theory of Equations

· Vector Algebra

· Group Theory

· Ring Theory

· Vector Spaces