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Approved by University Studies Sub-Committee. A2C2 action pending.

**University Studies Course Approval Proposal**

Unity and Diversity – Multicultural Perspectives

The Department of Mathematics and Statistics proposes the following course for inclusion in University Studies, Unity and Diversity, Multicultural Perspectives at Winona State University. This was approved by the full department on Thursday, January 4, 2001.

Course: History of Mathematics (MATH 410), 3 s.h.

Catalog Description: General view of the historical development of the elementary branches of mathematics. This is a University Studies course satisfying requirements in Multicultural Perspectives. Prerequisites: MATH 160 and MATH 210. Offered fall semester.

This is an existing course, previously approved by A2C2.

Department Contact Person for this course:

Jeffrey R. Anderson, Mathematics and Statistics Department Chair

Email janderson@winona.edu

General Discussion of University Studies – Multicultural Perspectives in relation to MATH 410:

**University Studies: Multicultural Perspectives**

The purpose of the Multicultural Perspectives requirement in University Studies is to develop students� understanding of diversity (gender, ethnicity, race, etc.) within and between societies. Courses in this area will help students employ a multicultural perspective for examining historical events; contemporary social, economic, and political issues; and artistic, literary, and philosophical expressions. Courses that fulfill the Multicultural Perspectives requirement must address at least three of the following outcomes. These courses must include requirements and learning activities that promote students' abilities to...

a. demonstrate knowledge of diverse patterns and similarities of thought, values, and beliefs as manifest in different cultures;

In MATH 410, students are required to repeat mathematical calculations from eras of history, utilizing the same sorts of notations and methodologies as originally used. The reason for this is partly to give students a better sense of the true development of mathematics, through fits and starts (as opposed to a neatly written out theorem from start to finish). Often these calculations are tedious and use ancient or arcane notations and techniques. For example, the Greek, Archimedes, determined areas via a method of exhaustion. The problem is simple for a first-year calculus student to determine by integration, but the method of exhaustion is truly exhausting. When required to do such work, which students prefer to relegate to mathematics having nothing to do with the real world, the reason and motivation for this work naturally is posed. Why is the method of exhaustion required when integration will do the job faster? Why did the Egyptians use such strange symbols for calculation when the regular numbers are much better? What is the purpose for using base 2 or base 16 or any other base? Why must all the calculations done by Viete be labored over when roots of a polynomial may be approximated by a calculator? Coming from the perspective of MATH 410 students, these questions are well-motivated, and these students generally become very interested in the fact that the answers lie "outside of mathematics" and in the particular culture and societal influences of the time studied. By the end of the semester, students develop the ability to see the many ways a culture provided motivation for the mathematics of the time. It is interesting to see the many different ways mathematicians through the millennia approached the same problems; it is, however, haunting to see that, despite all the cultural differences of the Egyptians, Greeks, Chinese, Mayas, Incas, Arabians, Russians, Europeans, and Americans, the majority of mathematics is still very similar.

b. understand the extent to which cultural differences influence the interpretation and expression of events, ideas, and experiences;

In some cultures, such as the Romans, mathematics was largely non-expressive and confined to applications of immediate benefit to society. In others, such as the Greeks, mathematics did have an aspect of application, but was more focussed upon the development of an absolute truth. Societies allowing more open argumentation cause the development of more of the pure forms of mathematics, while in closed societies, the old Soviet Union, for example, mathematics centered around the needs of the state and was highly monitored. In many ways, it has been war providing a catalyst for the exchange of ideas and the proliferation of new ways of thinking. An example of this is the Crusades causing the spread of Arabic mathematics (algebra and algorithm – names take from an Arab author) to Europe and ultimately giving rise to the Renaissance. In MATH 410, students investigate these differences through comparison and also by examining the effect of the influence of mathematics of one culture on another upon its introduction. Through individual projects, students are able to further study the effects of sub-cultures, within the European continent, for example.

c. understand the extent to which cultural differences influence the interactions between individuals and/or groups;

d. examine different cultures through their various expressions; and/or

The mathematics, its notation, and calculational methods provide a useful and interesting comparison of cultures. Students in MATH 410 study the mathematical inductionism of the Egyptians and the question of why the mathematics of this culture was so content with using examples as proof. Greek society is, of course, famous for giving rise to deductive reasoning and the belief in an absolute truth. Middle Eastern societies, such as the Arabs, were generally interested in creating methods for solving entire classes of problems and essentially gave rise to what we know of as algebra. It is also useful to examine the opposite point-of-view: the effect of mathematics on society. During its time of greatest activity, projective geometry developed out the Italian desire to draw and paint in correct 3-D perspective. In turn, the existence of projective geometry had much effect on some of histories most famous artwork. In the middle 1600's, the lifestyle of most people was dismal at best. Hunger, disease, and a short life were the most common elements in Europe of the time. Beginning in the 1700's, mathematicians, physicists, and astronomers began exploring the use of a newly developed mathematical tool: the calculus. Since that time, calculus as applied to the motion of the planets, the flow of fluids, and the movement of electricity are but a few examples that have had profound impact on society at large. Students in History of Mathematics undergo the investigation of such effects and come to better understand the interconnected nature of mathematics, sciences in general, and societal and cultural influences.

**e. possess the skills necessary for interaction with someone from a
different culture or cultural group.**