General InformationTextsRequired Texts:Recommended Reference for Writing:Course DescriptionOn ReadingPoster PresentationsCourse AssessmentWriting Initiative Assistant ConferencesCourse GradesAcademic Integrity and Classroom DemeanorClassroom and Learning AccommodationsWriting Intensive Course InformationStudent EligibilityLearning OutcomesMinimum Writing RequirementsGrading PoliciesPlagiarismAssessmentInformationTentative ScheduleHistory of Mathematics1MA 330, Section 002, Spring 2009Contents1 General Information 12 Texts 22.1 Required Texts: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22.2 Recommended Reference for Writing: . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Course Description 24 On Reading 45 Poster Presentations 56 Course Assessment 57 Writing Initiative Assistant Conferences 68 Course Grades 69 Academic Integrity and Classroom Demeanor 610 Classroom and Learning Accommodations 611 Writing Intensive Course Information 711.1 Student Eligibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711.2 Learning Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711.3 Minimum Writing Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711.4 Grading Policies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711.5 Plagiarism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711.6 Assessment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 811.7 Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 812 Tentative Schedule 81 General InformationDr. Benjamin BraunCourse Webpage: www.ms.uky.edu/%7ebraunEmail: [email protected]: 257-6810Class Time/Location: 1:00-1:50 PM, MWF, 213 Funkhouser BuildingOffice Location/Hours: 831 POT, Monday 2PM, Wednesday 10AM, Friday 12PM.1I reserve the right to change or amend this syllabus at any time for any reason.12 Texts2.1 Required Texts:Journey Through Genius: The Great Theorems of Mathematics, by William Dunham. ISBN-10:014014739XThe Calculus Gallery: Masterpieces from Newton to Lebesgue, by William Dunham. ISBN-10:06911362622.2 Recommended Reference for Writing:The Elements of Style, by William Strunk and E. B. White.3 Course DescriptionWe begin with two quotes from John Stillwell.One of the disappointments experienced by most mathematics students is that they never get acourse on mathematics. They get courses in calculus, algebra, topology, and so on, but the divisionof labor in teaching seems to prevent these different topics from being combined into a whole. Infact, some of the most important and natural questions are stifled because they fall on the wrongside of topic boundary lines. Algebraists do not discuss the fundamental theorem of algebrabecause “that’s analysis” and analysts do not discuss Riemann surfaces because “that’s topology,”for example. Thus if students are to feel they really know mathematics by the time they graduate,there is a need to unify the subject.Mathematics and its HistoryJohn StillwellThe best way to teach real mathematics, I believe, is to start deeper down, with the elementaryideas of number and space. . . . in fact, arithmetic, algebra, and geometry can never beoutgrown. . . by maintaining ties between these disciplines, it is possible to present a more unifiedview of mathematics, yet at the same time to include more spice and variety.Numbers and GeometryJohn StillwellA course in the history of mathematics provides an opportunity for students of mathematicsto remedy the disappointment described by Stillwell. We will think seriously about a variety ofthe pillars of mathematics, the truly outstanding theorems, while trying to maintain balance anddialogue among the most fundamental branches of mathematics. In this way, we will hopefully createfor ourselves a cohesive vision of mathematics and establish connections between mathematics andthe non-mathematical world.Our class sessions will consist of discussions based on daily readings. The readings will bestructured around Journey Through Genius and The Calculus Gallery. There will be a variety ofshort assignments, from journal responses to traditional problems, and these will often be a startingpoint for our discussions. The readings and short assignments will be the common material we drawfrom. Students will also complete a major course project.One comment that must be made regarding this course is that there are many possible pathswe could take in our investigation of the pillars of mathematics. For example, how does one choose2the “best” theorems? What does that even mean? What makes a theorem beautiful? Or useful?Though we will be following the path laid out by the course texts, these questions are importantand a large part of our discussions should be dedicated to developing an understanding of our ownmathematical aesthetic and how it differs from those of other people. Consider, for example, thefollowing quote.Beauty and insight – these are words that Erd˝os and his colleagues use freely [in reference tomathematics] but have difficulty explaining. “It’s like asking why Beethoven’s Ninth Symphony isbeautiful,” Erd˝os said. “If you don’t see why, someone can’t tell you. I know numbers arebeautiful. If they aren’t beautiful, nothing is.”The Man Who Loved Only Numbers:The Story of Paul Erd˝os and the Search for Mathematical TruthPaul HoffmanWhile Erd˝os’s thoughts are satisfying in some ways, they fall short in others. There must bereasons why certain theorems are almost universally accepted as profoundly beautiful while othersare considered less important. What drives our sense of mathematical value, both individually andcollectively? How have those values changed over time? These are perhaps the most fundamentalquestions to ask in a history of math course because the mathematicians whose work we are studyingwere inspired by their own values, leading directly to where we are now. So, while we will be readingtexts by experts in the history of mathematics, we must look at the topics they have selected with,simultaneously, the utmost respect and a sharply critical eye. The following passage from Ways ofReading is very relevant to this point.For good reasons and bad, students typically define their skill by reproducing rather thanquestioning or revising the work of