Math Algebra

NAME
TUTOR
COURCE
DATE
ALGEBRA
This is a branch of pure mathematics that is concerned with the study of rules relations and operations. This basically deals with the concepts arising from these operations and relations, they include: polynomials (it’s an expression formed from one or more variables and has a single constant), equations, terms and algebraic structures (Cohn, 11)
There are different types of algebra, namely: Abstract algebra, elementary algebra, algebraic geometry, linear algebra, algebraic number theory, algebraic combinations and universal algebra.
Abstract algebra: Instead of the use of numbers systems, it deals with deal with structures linked to abstract algebra for example the use of rings, vectors, fields, group actions, linear algebra and groups (Steege & Bailey, 24). It can further be divided into
Sets: this is a collection of all elements which are specific for the said set (familiar number types). They can also be said to be, matrices, polynomials e.g. ax2 + bx + c, vectors sets, cyclic groups etc.
Inverse elements: this where one uses a negative number to bring about the theory of an inverse element. For example, when adding a number, one can say that the inverse of “b” is “-b” to describe the same number (Cohn, 13). Another example of a inverse expression could be for the multiplication sign for example, “b” to denote inverse, it would be “1/b”.
The general rule here is, “b*b-1”= e and that “b-1*b= e”.
Binary operations: here, one must define the set of that particular operation for instance; “x and y” are two elements in a set S while another element in the set can be said to be “x*y” ( Steege, & Bailey 59). Linear algebra: This is the analysis of the linear equations. One tries to solve the linear equations as well as analyzing them. Generally, they deal with vector spaces like vectors. For example, (x+1) (y -2). Linear algebra is used in various areas of our day to day lives, for example in businesses, in economics, chemistry, computers etc. it gives a clear balance between theory and the mathematical comp...