Algebra is the base of every advanced math function.  It’s techniques and equations are absolutely essential to solving later forms of math.  There are over 7 different types of algebra, but here are the most used in everyday college/high school courses:

Elementary algebra- This form of algebra typically is taught and mastered at the high school level and at the University level under the title of the same name.  Elementary algebra is typically where the idea of a variable is introduced to the student.  The order of operations is also taught for the correct order to work a problem.  Say for instance: 23(X-4)= 17.  Order of operations would have us do parenthesis first, so we would distributed the 23.  23X – 92= 17.   Then move the 92 over to get 23x = 109. x= 4.73

College Algebra- At the university level these courses are known as College Algebra 1 and 2 or simply Algebra 1 and 2.  In this form of algebra the true basis of algebra begins, graphing is stressed.  The line formula is introduced of:
 y= mx + b.  
m= the slope
x= X intercept
b= Y intercept
From the line formula, we can derive the midpoint formula and the formula to solve for slope.
Midpoint formula= (x1 +x2) /2 , (y1 + y2) /2
Slope formula = y2- y1/ x2 – x1

Abstract Algebra-
Abstract is a much more complicated algebra than simple college or elementary.  It introduces the concepts of imaginary numbers, complex numbers and is considered the beginning of calculus.  It sprang forth from the concept of matrices to solve a system of linear equations.  Although they originally challenged comprehension, hyper complex numbers had kinetic motivation.  The theme that served a core around the results tended to be grouped, which made it become a unified set of common concepts.

Algebraic Geometry-
Algebraic geometry is type of mathematics that combines several types of algebra including abstract and commutative.  The basic concepts in algebraic geometry are algebraic varieties, geometric manifestations of solutions of systems of polynomial equations.  More objects of study include plane curves, circles, lemniscates, parabolas, lines, and Cassini ovals.

Linear Algebra-
Linear algebra is one of the types of algebra that studies the idea of vector spaces, basically where linear functions input one vector and output a whole different one.  They are represented by matrices and are often called linear maps.  As such, matrix theory is thought to be a main part of linear algebra.
The history of linear algebra can be traced back to the beginning of the 20th century.  At the time, many of the concepts of linear algebra was being referred to as abstract algebra.  It wasn’t until the end of the nineteenth century that the idea and concepts and matrices and tensors were added.

Several of these are enough to make you say, “Someone take my algebra class!” 


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