WHAT IS ALGEBRA lgebra has often been described as arith metic with letters Unlike arithmetic which deals with specific numbers algebra introduces variables that greatly extend the generality and scope of arithmetic This book will focus on the algebra taught in middle schools and high schools often referred to as elementary algebra which deals with the gen eral properties of numbers and the relations between them sin ALGEBRAIC QUANTITIES The principal distinguishing characteristic of algebra is the use of letters to represent numeri cal quantities and simple symbols to represent 10 Sin
WHAT IS ALGEBRA mathematical operations Following a system that originated with the 17th century French thinker René Descartes letters especially x y and 2 represent unknown quantities or vari ables The and signs indicate addition and subtraction of these quantities but multipli cation is simply indicated by adjacent letters Thus ax represents the product of a by x This simple expression can be interpreted for example as the interest earned in one year by a sum of a dollars invested at an annual rate of x It can also be interpreted as the distance traveled in a hours by a car moving at x miles per hour Such flexibility of representation is what gives algebra its great utility THE BEGINNINGS OF ALGEBRA More than 3 500 years ago an Egyptian named Ahmes collected a set of mathematical prob lems and their solutions About 2 500 years ago the Greek mathematician Pythagoras started a religious mathematical brother hood Intensely interested in geometry they classified numbers according to geometri cal properties The famous Greek geometer 11 R a costs
Algebra Euclid discovered important properties of numbers through a study of geometry Diophantus another famous early Greek mathematician has been called the father of algebra He treated algebra from a purely numerical point of view He made a special study of certain types of equations that are today called Diophantine equations Our modern word algebra comes from the Arabic al Jabr which appeared in the title of an algebra text written in about 825 CE by the Arab astronomer and mathematician al Khwarizmi The word algorithm is derived from his name MODERN ALGEBRA The study of the algebra of real numbers and the recent recognition of the fundamental importance of the basic principles have led to the development of what is now called mod ern algebra or abstract algebra The concepts of modern algebra have been found to be extremely useful in other branches of mathematics as well as in the physical and social sciences A chemist may use modern algebra in a study of the structure 12
WHAT IS ALGEBRA DIOPHANTUS Diophantus of Alexandria C 250 CE was a Greek mathematician famous for his work in algebra One mathematical work he is believed to have written is a large and extremely influential treatise called Arithmetica continued on the next page Pierre de Fermat extended the work of Diophantus by marking up a copy of the earlier mathematician s treatise Arithmetica Courtesy of De Agostini Picture Library Getty Images 13 R a costs
