1. General Information2. Texts2.1. Required Texts:2.2. Recommended Reference for Writing:3. Course Description4. On Reading5. Special Presentation by David Bressoud6. Poster Presentations7. Course Assessment8. Course Grades9. Academic Integrity and Classroom Demeanor10. Classroom and Learning Accommodations11. Tentative ScheduleHistory of Mathematics1MA 330, Sections 001 & 002, Spring 20081. General InformationDr. Benjamin BraunCourse Webpage: www.ms.uky.edu/%7ebraun/MA330 Spring2008/MA330 Spring2008.htmlEmail: [email protected]: 257-6810Section 001: 8:00-8:50 AM: MWF, 347 Whitehall Classroom BuildingSection 002: 1:00-1:50 PM: MWF, 213 Funkhouser Biological SciencesOffice Location/Hours: 831 POT, Mon: 9-10AM and 3-4PM, Wed: 2-3PM, Fri: 9-10AM.2. Texts2.1. Required Texts: Journey Through Genius: The Great Theorems of Mathematics, byWilliam Dunham. ISBN-10: 014014739XMath Through The Ages: A Gentle History for Teachers and Others, Expanded Edition,by William P. Berlinghoff and Fernando Q. Gouva. ISBN-10: 0883857367A Source Book in Mathematics, by D. E. Smith. ISBN-10: 04866469042.2. Recommended Reference for Writing: The Elements of Style, by William Strunkand 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 neverget 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 different topics from beingcombined into a whole. In fact, some of the most important and natural questions arestifled because they fall on the wrong side of topic boundary lines. Algebraists do notdiscuss the fundamental theorem of algebra because “that’s analysis” and analysts do notdiscuss Riemann surfaces because “that’s topology,” for example. Thus if students are tofeel they really know mathematics by the time they graduate, there is a need to unify thesubject.Mathematics and its HistoryJohn StillwellThe best way to teach real mathematics, I believe, is to start deeper down, with theelementary ideas of number and space. . . . in fact, arithmetic, algebra, and geometry cannever be outgrown. . . by maintaining ties between these disciplines, it is possible topresent a more unified view of mathematics, yet at the same time to include more spiceand variety.Numbers and GeometryJohn Stillwell1I reserve the right to change or amend this syllabus at any time for any reason.1A course in the history of mathematics is a great opportunity for students of mathematicsto remedy the disappointment described by Stillwell. We will think seriously about a varietyof the pillars of mathematics, the truly outstanding theorems, while trying to maintainbalance and dialogue among the most fundamental branches of mathematics. In this way, wewill hopefully create for ourselves a cohesive vision of mathematics and establish connectionsbetween mathematics and the non-mathematical world.Our class sessions will consist of discussions based on daily readings. The readings willbe structured around Journey Through Genius, with additional material taken from theother course texts. There will be a variety of short assignments, from journal responsesto traditional problems, and these will often be a starting point for our discussions. Thereadings and short assignments will be the common material we draw from. Students willalso be responsible for writing one biographical paper and completing one course project.These are described in detail in a following section, and will be the work we do as individualspursuing our own interests.One comment that must be made regarding this course is that there are many possiblepaths we could take in our investigation of the pillars of mathematics. For example, howdoes one choose the “best” theorems? What does that even mean? What makes a theorembeautiful? Or useful? Though we will be following the path laid out by the course texts, thesequestions are important and a large part of our discussions should be dedicated to developingan understanding of our own mathematical aesthetic and how it differs from those of otherpeople. Consider, for example, the following quote from Paul Erd˝os.Beauty and insight – these are words that Erd˝os and his colleagues use freely [in referenceto mathematics] but have difficulty explaining. “It’s like asking why Beethoven’s NinthSymphony is beautiful,” Erd˝os said. “If you don’t see why, someone can’t tell you. I knownumbers are beautiful. 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 E rd˝os’s thoughts are satisfying in some ways, they fall short in others. There mustbe reasons why certain theorems are almost universally accepted as profoundly beautifulwhile others are considered less important. What drives our sense of mathematical value,both individually and collectively? How have those values changed over time? These areperhaps the most fundamental questions to ask in a history of math course because themathematicians whose work we are studying were inspired by their own values, leadingdirectly to where we are now. So, while we will be reading texts by experts in the historyof mathematics, we must look at the topics they have selected with, simultaneously, theutmost respect and a sharply critical eye. The following passage from Ways of Reading isvery relevant to this point.For good reasons and bad, students typically define their skill by reproducing rather thanquestioning or revising the work of their teachers (or the work of those their teachers askthem to read). It is important to read generously and carefully and to learn to submit toprojects that others have begun. But it is also important to know what you are doing – tounderstand where this work comes from, whose interests it serves, how and where it iskept together by will rather than desire, and what it might have to do with you. To fail toask fundamental questions – Where am I in this? How can I make my mark? Whoseinterests are represented? What can I learn by reading with and against the grain? – tofail to ask these questions is to mistake skill for understanding, and it is to misunderstandthe goals of a liberal education.Ways of ReadingDavid Bartholomae and Anthony Petrosky4. On ReadingWe learned that if our students had reading problems when faced with long and