MA 330 002, History of Mathematics1University of Kentucky, Spring 2012Contents1. General Information 12. Course Description 23. Tentative Schedule 5Mathematical origins 5The Pythagorean theorem arises 5Euclid and the process of heroification 5Islamic contributions 6Estimating π, from ancient to contemporary times 6The joy of infinite series 6Leonhard Euler 6The nature of infinity and mathematical progress 6Final discussion meeting time 64. Assessment and Grades 75. Course Expectations 76. Classroom and Learning Accommodations 87. Writing Intensive Course Information 8Student Eligibility 8Learning Outcomes 8Minimum Writing Requirements 8Grading Policies 8Plagiarism 9Assessment 9Information 91. General InformationProf. Benjamin BraunCourse Webpage: www.ms.uky.edu/%7ebraunEmail: [email protected] Phone: 257-6810Class Time/Location: 12:00-12:50PM, MWF, CB 345Office Location/Hours: 831 POT, MW 9AM, F 10AM, and by appointmentCourse Texts:• Journey Through Genius: The Great Theorems of Mathematics, 1991, by William Dunham.ISBN-10: 014014739X1I reserve the right to change or amend this syllabus at any time for any reason.1• Lies My Teacher Told Me: Everything Your American History Textbook Got Wrong, up-dated and revised edition from 2007, by James W. Loewen. ISBN-10: 0743296281• The Crest of the Peacock: Non-European Roots of Mathematics, third edition, by GeorgeGheverghese Joseph. ISBN-10: 06911352662. Course DescriptionIt isn’t at all clear what a course on the History of Mathematics should be. Is it a history coursewith some math in it? Is it a math course where historical tidbits are tossed in? Should it onlycover mathematics that students have already seen, or only mathematics that is new to them, ora blend of both? Should it be an easier course (“the last requirement for my math minor”) or achallenging one (“now I really understand Lebesgue integration”)?For what it’s worth, I don’t have good answers to these questions either, because in my idealworld, this course wouldn’t exist. If mathematics was taught the way I think is best, it wouldalready include enough history, or solid glimpses of history, to make this class irrelevant. Also,these historical glimpses would inform our vision of how mathematics develops, and of who it isthat helps mathematics grow. This line of thought always leads me back to wondering what thepoint of university study is, what you (the student) should gain from coming to this class, fromreading the texts that are offered, from completing the course assignments.So what do you want to get from this course? There are lots of things that I think students canget out of this course, but if I write them down, they won’t mean as much. You can get some ideaof my thoughts from the reading schedule for the course. Instead of telling you what you shouldthink, let’s get our thoughts flowing with the thoughts of others.The most important thing I learned in this class is that I have the ability to com-prehend things that are very difficult, and have not been taught to me.Former MA 330 studentI learned a great deal from taking this course; however, I do not think what I learnedwas exactly what I was supposed to learn.Former MA 330 studentOne of the disappointments experienced by most mathematics students is that theynever get a course on mathematics. They get courses in calculus, algebra, topology,and so on, but the division of labor in teaching seems to prevent these differenttopics from being combined into a whole. In fact, some of the most important andnatural questions are stifled because they fall on the wrong side of topic boundarylines. . . Thus if students are to feel they really know mathematics by the time theygraduate, there is a need to unify the subject.Mathematics and its HistoryJohn StillwellThe principal aim of mathematical education is to develop certain faculties of themind, and among these intuition is not the least precious. It is through it that themathematical world remains in touch with the real world.2It is by logic that we prove, but by intuition that we discover.Science et m´ethodeHenri Poincar´eSo we teach to build intuition, and intuition enables our students to make discoveries.Notice that Poincar´e does not say that the principal aim of teaching is to conveyfacts or theorems. The principal aim of mathematical teaching is to build qualitiesof mind that enable students to make discoveries.Teaching Research, Encouraging DiscoveriesFrancis SuFor good reasons and bad, students typically define their skill by reproducing ratherthan questioning or revising the work of their teachers (or the work of those theirteachers ask them to read). It is important to read generously and carefully and tolearn to submit to projects that others have begun. But it is also important to knowwhat you are doing – to understand where this work comes from, whose interestsit serves, how and where it is kept together by will rather than desire, and whatit might have to do with you. To fail to ask fundamental questions – Where am Iin this? How can I make my mark? Whose interests are represented? What canI learn by reading with and against the grain? – to fail to ask these questions isto mistake skill for understanding, and it is to misunderstand the goals of a liberaleducation.Ways of ReadingDavid Bartholomae and Anthony PetroskyWe must find ways to restore the child-like curiosity of college students. I see that8th graders are more curious, more willing to probe with a “why?,” more willing toask questions if they don’t understand, and more willing to let you know your penis leaking in your front pocket. Somewhere along the path to adulthood, they losethe ability to ask questions.Teaching Research, Encouraging DiscoveriesFrancis SuWe learned that if our students had reading problems when faced with long andcomplex texts, the problems lay in the way they imagined a reader – the role areader plays, what a reader does, why a reader reads (if not simply to satisfy therequirements of a course). When, for example, our students were puzzled by whatthey read, they took this as a sign of failure. (“It doesn’t make any sense,” theywould say, as though sense were supposed to be waiting on the page, ready for themthe first time they read through.) And our students were haunted by the thoughtthat they couldn’t remember everything they had read. . . or if they did rememberbits and pieces, they felt that the fragmented text