A Project in
Next Century Mathematics
“Advanced Algebra, Trigonometry,
Michael Roy Lansang
Immanuel C. Canoy
Mathematics 10 Teacher
1.1 Reviewing the Cartesian Coordinate Plane
The words, functions, coordinate, abscissa, and ordinate, as now use in mathematics, were introduce by Gottfried Wilhelm Leibniz (1646-1716) of Germany. Leibniz was the great genius of the 17th century. He was also Newton’s rival in the invention of the calculus.
The 14th century was a mathematically barren one. Inclusive of this century was the hundred years’ war and black death which killed more than 1/3 of Europe’s population. However, mathematics during this period did not entirely die out. The greatest mathematician of this period was Nicole Oresme (1323-1282) of Normandy. He wrote five mathematical works. In one of this appears the process of locating points by coordinates, which foreshadowed modern coordinate geometry.
The conventionalization of the functional notation f(x) was contributed by Leonhard Euler of Switzerland.
1.4 Graphs of Functions
The word function was first introduced by Leibniz in 1694 to denote any quantity connected with a curve. In 1718, Johann Bernoulli regarded function as any expression made up of variables and constants. Later Leonhard Euler (1707-1783) considered function as any equation and formula. But it was Lejeune Dirichlet (1805-1859) who first associated the concept of correspondence in the definition of function.
1.5 Operations with Functions
A “chain” process of combining two relations in a given order to produce composite relation is called composition of relations. For instance, the relation “is the mother of” and the relation “is the father of” yield the composite relation “is the mother of the father of,” that is, “ is the paternal grandmother of”....
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