# Algebra

## 2000 B.C. - Babylon

Stone tablets were made which depicted images of people who were exploring the fundamental ideas of algebra.

## Diophantus 200-300 A.D.

• "The Father of Algebra"
• Negative and Irrational numbers did not exist
• Author of "Arithmetica," which was a series of books containing equations with one solution or many solutions
• Known for introducing mathematical notations into symbols
• Only proposed solutions to exact problems, but not general solutions

## Brahmagupta 600 A.D.

• Mathematician and Astronomer
• Established rules for finding the cube and square roots of integers
• Zero is a number rather than a representation of nothing
• Developed means of using negative numbers for representing debt
• Developed rules for operations with negative numbers

## Al-Karaji 11th Century

• Produced rules for algebraic operations with real numbers that exclude the use of geometric figures
• Developed rules for dealing with exponents
• Currently known as the law of exponents

## Leonardo Fibonacci 13th Century

• Developed the Fibonacci Sequence
• The first example of recurrence series
• Used today in computer science
• Also used in number theory and to count mathematical objects
• Exposed the Western Culture to Hindu-Arabic Mathematics
Arthur Benjamin: The magic of Fibonacci numbers

## Rene Descartes 17th Century

• Accomplishments were in analytical geometry
• This allowed algebraic formulas to be visualized
• Developed a coordinate plane to locate points on a Cartesian plane
• The development of the coordinate plane was crucial to breakthroughs in the development of physics and calculus as well

## Carl Gauss 18th Century

• Made contributions to many mathematical fields
• Main contributions involved in work with complex numbers
• Developed the fundamental theorem of algebra, which says, "Every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number is a complex number with an imaginary part equal to zero.

## Algebra In The Classroom

SC State Department of Education includes standards on:

• linear functions
• arithmetic sequences
• Geometry
• Functions
Each of these standards incorporates algebraic aspects and multiple branches of mathematics. For example, abstract algebra incorporates concepts of sets which relates directly with discrete mathematics. Since sets have to be defined by some arithmetic sequence, it involves a rich assortment of algebraic structure. Another example is a unit focused on functions and graphing. In order to graph a linear function, one must first input values (x) to obtain the output value (y). This is a great time to stress the importance of modern algebra. There are many ways to incorporate algebra into the classroom in relation to other branches of mathematics.