Study Material

  Mathematical  astronomy The sexagesimal method developed by the Babylonians has a far greater computational potential than what was actually needed for the older problem texts. With the development of mathematical astronomy in the  Seleucid  period, however, it became indispensable. Astronomers sought to predict future occurrences of important phenomena, such as lunar eclipses and critical points in planetary cycles (conjunctions, oppositions, stationary points, and first and last visibility). They devised a technique for computing these positions (expressed in terms of degrees of latitude and longitude, measured relative to the path of the Sun’s apparent annual motion) by successively adding appropriate terms in arithmetic progression. The results were then organized into a table listing positions as far ahead as the scribe chose. (Although the method is purely arithmetic, one can interpret it graphically: the tabulated values form a linear “zigzag” approximation ...

  Ancient mathematical sources It is important to be aware of the character of the sources for the study of the history of mathematics. The history of Mesopotamian and Egyptian mathematics is based on the  extant  original documents written by scribes. Although in the case of Egypt these documents are few, they are all of a type and leave little doubt that Egyptian mathematics was, on the whole, elementary and profoundly practical in its orientation. For Mesopotamian mathematics, on the other hand, there are a large number of clay tablets, which reveal mathematical achievements of a much higher order than those of the Egyptians. The tablets indicate that the Mesopotamians had a great deal of remarkable mathematical knowledge, although they offer no evidence that this knowledge was organized into a deductive system. Future research may reveal more about the early development of mathematics in Mesopotamia or about its influence on Greek mathematics, but it seems likely that...

  In the 17th century,   Isaac Newton   in England and Gottfried Leibniz in Germany independently developed the foundations for calculus, Carl B. Boyer, a science historian, explained in " The History of the Calculus and Its Conceptual Development (opens in new tab) " (Dover Publications, 1959). Calculus development went through three periods: anticipation, development and rigorization.  In the anticipation stage, mathematicians attempted to use techniques that involved infinite processes to find areas under curves or maximize certain qualities. In the development stage, Newton and Leibniz brought these techniques together through the derivative (the curve of mathematical function) and integral (the area under the curve). Though their methods were not always logically sound, mathematicians in the 18th century took on the rigorization stage and were able to justify their methods and create the final stage of calculus. Today, we define the derivative and integral in te...

The word mathematics comes from the ancient Greeks and is derived from the word máthēma, meaning "that which is learnt," according to Douglas R. Harper, author of the "Online Etymology Dictionary(opens in new tab)." The ancient Greeks built on other ancient civilizations’ mathematical studies, and they developed the model of abstract mathematics through geometry.  Greek mathematicians were divided into several schools, as outlined by G. Donald Allen, professor of Mathematics at Texas A&M University in his paper, "The Origins of Greek Mathematics(opens in new tab)": In addition to the Greek mathematicians listed above, a number of other ancient Greeks made an indelible mark on the history of mathematics, including Archimedes, most famous for the Archimedes' principle around the buoyant force; Apollonius, who did important work with parabolas; Diophantus, the first Greek mathematician to recognize fractions as numbers; Pappus, known for his hexagon t...

  Why Study Mathematics? Because it's fun and can prepare you for a variety of excellent careers! If you like solving puzzles and figuring things out, then a mathematics major may interest you. In addition, applications of mathematics are everywhere and a strong background in mathematics can help you in many different careers. The sections below provide information about careers in mathematics and the opportunities available to our mathematics majors.

  What is Mathematics?   Mathematics  is the science and study of quality, structure, space, and change. Mathematicians seek out patterns, formulate new conjectures, and establish truth by rigorous deduction from appropriately chosen axioms and definitions. There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics "the science that draws necessary conclusions". Albert Einstein, on the other hand, stated that "as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality." Through abstraction and logical reasoning mathematics evolved from counting, calculation, measurement, and the systematic study of the shapes and motions of physical objects. Practical mathematics has been a human activity for as far back as written records exist. Rigorous arguments first appeared in Greek mathematic...