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Mathematics As a Humanistic Discipline Elena Anne Marchisotto California State University, Northridge

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Mathematics As a Humanistic Discipline Elena Anne Marchisotto California State University, Northridge Humanistic Mathematics Network Journal Issue 7 Article 9 4-1-1992 Mathematics as a Humanistic Discipline Elena Anne Marchisotto California State University, Northridge Follow this and additional works at: http://scholarship.claremont.edu/hmnj Part of the Logic and Foundations of Mathematics Commons, and the Mathematics Commons Recommended Citation Marchisotto, Elena Anne (1992) "Mathematics as a Humanistic Discipline," Humanistic Mathematics Network Journal: Iss. 7, Article 9. Available at: http://scholarship.claremont.edu/hmnj/vol1/iss7/9 This Article is brought to you for free and open access by the Journals at Claremont at Scholarship @ Claremont. It has been accepted for inclusion in Humanistic Mathematics Network Journal by an authorized administrator of Scholarship @ Claremont. For more information, please contact [email protected]. MATHEMATICS AS A HUMANISTIC DISCIPLINE ElenaAnne Marchisotto ProfessorofMQ1hem1ltics California State University J8Il NordhoffStreet. Nonhridge It is said that the mono which adorned the A conference was held at Williams College in doors of Plato's Academy advised. "Let no one Williamstown. Maryland, in 1982, to evaluate the unversed in mathematics enter here." For the mathematical needs of students in other disciplines Greeks, the study of mathematics furnished the and the implementation of curricula to meet those finest training field for the mind. It occupied an needs. Papers were presented by mathematicians and esteemed place in the curriculum of Plato's mathematics educators identifying requirements for Academy. No person was considerededucated if specific field s: Isaac Greber for Engineering, William he did not know mathematics. ScherlisandMary ShawforComputerScience.Stanley Zionts for Business, Jack Lockhead for the Physical Mathematics hasnotretainedsuch adominant Sciences, and Robert Norman the Social Sciences. position in modem education. However the in­ creasing importance of the discipline in the In Engineering, the required mathematics core twentieth century because of the computer and represents topics that are regarded as fundamental related teehnologieshas generatedrenewedinterest mathematics as wellas those topics which students are in its study. Today's academies universities and expected to know in order to solve engineering colleges - are requiring the study of mathematics problems in other courses. They include the under­ for more students than ever before. In 1983. the standing of limits, functions, complex variables, in­ largest public university system in the country ­ tegral equations, and the calculus of variations. The The CaliforniastateUniversitySystem -established central analytical tool of the engineer is the ability to a mathematics course as a graduation requirement derive, solve, and understand differential equatio ns. for all students at any of its nineteen campuses. Other mathematics courses which are becoming more Liberal ans colleges throughout the United States important to engineeringmajors with the adventofthe are reinstating mathematics requirements for all computer are probability and statistics, Boo lean al­ majors. Mathematics plays a central role in the gebra, and numerical methods. curriculum of most universities and colleges throughout the world today. The requisites for Computer Science are many. The modes of thought which characterize mathemat­ With the exceptionofspecialized univ~ rsitie s ics are crucial to prospective computer scientists. like MIT and CalTech, Mathematics Departments Probably the most important contribution mathemat­ nationwide are considered service departments. ics makes is teaching these students how to reason offering the majority oftheir courses to students in abstractly and problem solve. fields other than mathematics. Such depanments as Engineering, Computer Science, Business, the Until the 1950' s the role of mathematics in Physical Sciences,and the Social Sciencesinclude Business Programs was minimal. Aboutthat time , the a COre of mathematics courses which are essential discipline called Management Science was incorpo­ to meet the mathematical needs of their majors. rated into business schools, and more and more HMN Journal #7 69 quantitative techniques were employed in business that is different from those for whom mathematics is classes. Mathematical applications to management their major field. Non-majors are more interested in problems are abundant. Models that include linear what mathematics can do (within the limited focus programming and computer simulation are widely peculiar to their discipline) than what mathematics used in industry. Students enrolled in Business is. They generally study mathematics only because Programs need a mathematics background which it is useful in preparation for their fields, and this includes algebra, beginning differential andintegral sometimes impairs their enthusiasm for the subject. calculus. matrix algebra, linear programming, and simulation, all with applications in the field. Is utility sufficient as a motivation for learn­ ing? Some mathematicians (like c.F. Gauss whohas Mathematics is the language of the Physical been credited with boasting that pure mathematics is Sciences and has traditionally been at the center of useless) will ask if utility is even a necessary con­ all programs in those fields. Calculus is essential to ditionfor study.Others(like Philip Davis and Reuben the study ofthe physical sciences. What students in Hersh) will question if utility can be measured: those disciplines need most from their mathematics preparation is a basic understanding ofvariables and . ..the meanin gs of the expression functions and how to express them in mathematical "mathematical utility" embrace aesthetic, language. philosophical , historic, psychologica l, commercial, scientific, technological, and Mathematicspreparation for the SocialSciences mathematical elements. Even this does not is somewhat different from that for prospective include all possible meanings... One can physical science. mathematics, or engineering ma­ distinguish between utility within the field jors. In fact, unlike these disciplines, there is no itself and utility to other fields. Even with generally accepted body of mathematics that every these subdivisions, the notion of utility is social science student is expected to know. Yet exceedingly slippery (1981, p. 80). social scientists, when questioned, win indicate a wide range of mathematics that they find useful in Measuring the mathematical utility ofa course their field s. These include probability, manipulative is often not a realistic task. However, even if one algebra, computing, statistics, calculus and differ­ determines that what is presented in a mathematics ential equations, combinatorics.Hnear algebra, sets class is useful for some purpose. the learnin g ex­ and relations. perience is incomplete if utility is the only focus. A fixed goal of learning a specified syllabus may be In each of the above-me nt ioned fields the va­ pursued, and perhaps attained. But if at no time the lidity of prerequisite courses in mathematics is un­ issues of how and why the goal is important are questioned to provide the appropriate background discussed in the classroom , the students get no for students to pursue subsequent coursework in .perspective on the mathematics being taught. They their disciplines.The service functionofmathematics focus only on the mechanics ofthe discipline. They is clearly defined and well justified . have no real interest in concepts, in learning what mathematics is in addition to what it does. For However, teaching mathematics as a service students in Engineering, Computer Science, Busi­ course has some built-in liabilities. The experience ness, and the Physical and Social Sciences, prereq­ of teaching mathematics to students for whom the uisite mathematics coursework should serve, ill subjectisnot theirmajorfield is often less satisfactory addition to itsutilitarian goal ofprep aration forw(Jli: than teaching mathematics majors. Non-mathemat­ in the field, to provide them with some context of ics majors approach the subject from a perspective how the mathematics they find useful has come to al l l 70 HMN Joum be, how it relates to disciplinesotherthan theirs, and journalsregularly include articles with this perspec­ how it affects their lives. rive. For example, the American Mathematical Monthly (April, 1982) featured an article in the Thesegoalsbecomeevenmoreimponantwhen section entitled "The Teaching of Mathematics" mathematics course requirements are extended to edited by Mary and Roben Wardrop which places students in non-math related fields: the humanities, mathematics squarely in the center of human de­ the arts, etc. As Lynn Anhur Steen indicates in the velopment: January, 1986 issue of Focus, the newsletter of the Mathematical AssociationofAmerica:"Forstudents Mathematics has played a central role in the intheartsandhumaniti~mathematicsisaninvisible development of modem civilization. It has culture - feared, avoided, and consequently been essential not only to the growth of misunderstood.n These students see no utility in scienceand technology, but has hadprofound learning mathematics. The biggest challenge in effects on philosophy and other forms of teaching liberal ans students is enabling them to thought as well (Page 270). recognize mathematics as a creative, human en­ deavor, as a "humanistic discipline". Mathematics has a place in history. It is pan of the human experience. There are few who will
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