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The Unique Effects of Including History in College Algebra - The Modules (2)

D. Goodwin (Black Hills State University) and G. W. Hagerty (Black Hills State University) and S. Smith (Black Hills State University)

Introduction to Polynomials: Looks at the efforts put forth in finding zeros of polynomials and includes a brief introduction to the lives of Niels Henrik Abel and Evariste Galois. This historical module excerpt illustrates the difficulties Abel and Galois had in breaking into the mathematical circles of their time. “Niels Henrik Abel, at the age of sixteen, proved that a general formula for solving a quintic (fifth degree) polynomial did not exist…. However, since he was largely self taught, leading mathematicians in Paris, such as Cauchy, largely ignored him… Evariste Galois had equally important discoveries. At sixteen, Galois had the desire to enter the most prestigious engineering school of the day, the École Polytechnique… [W]hen Galois submitted a paper to the school as part of the admission process, Cauchy lost the paper. He attended another school for the purpose of training to become a teacher. However, he kept his mathematical studies up and submitted a second paper to the École Polytechnique. This paper also appears to have been lost.” (Hagerty and Smith, 2006).

Polynomials: Looks at theoretical methods to help find zeros of polynomials. The module looks at Horner’s method and how information traveled in eras prior to modern-day technology. It includes a discussion of the difficulty of crediting the correct civilization with the development of a topic as it is believed that Horner did not develop the method credited to him; in fact, the Ancient Chinese knew of this method (Eves, 1992).

Technology: Looks at methods to use technology to find zeros of polynomials, and discusses the rapid changes in technology. The goal is to have the students take a look at when the Internet was developed and realize that instant messages were not always possible. The students need to realize that their parents enjoyed “Pong” and “Pacman” and their grandparents had the radio. Thus, the students need to revaluate the question “My parents didn’t need math, why do I?”