History and the Importance of Calculus Calculus can be summed up as "the study of mathematically defined change"5, or the study of infinity and the infinitesimal. The basic concepts of it include: limits, derivatives, differentiation and integrals. The word "calculus" means "rock"; the reason behind the naming of it is that rocks were used to used to carry out arithmetic. This branch of mathematics is able to be rooted all the way back to around 450 B.C., when Zeno of Elea discovered infinite numbers and distances. Later, in 225 B.C., Archimedes developed a formula for a sum of infinite series and also created the area of a circle and the volume of a sphere by using "calculus thinking". Not much progress took place until the 17th century, Pierre de Fermat looked at parabolas' maximum and minimum and discovered the tangent. Mathematicians Torricelli and Barrow then decided to put that tangent on a curved line, which can be used to calculate instantaneous rate of change. Although all of these steps are relating to calculus, the branch was not officially introduced to the world until the 1640's. It has been said that it was specifically founded by two people--Isaac Newton and Gottfried Wilhelm Leibniz. Despite this synonymous finding, both mathematicians came up with completely different methods and notations. Newton had ideas that were based on limits and concrete concepts while Leibniz's views were built upon the infinite and the abstract. However, these two were unaware with one another's ideas, and Leibniz was accused of plagiarizing Newton, which stirred up a huge controversy. It was proved false in the end, and they both were given the title of being the inventors of calculus; but today, Leibniz's abstracts and notations are the essential uses in calculus while Newton's theories and laws have been adopted by physics. Some people believe calculus is a difficult branch of mathematics to master because of the many new abstract concepts and methods that are