Syllabus Math 592: Introduction to AdvancedMathematicsGeometry, Proof and Understanding:John T. BaldwinAugust 17, 2007Fall 2007Class meets in 214 Douglas Hall at 5-8 on Monday. Call Number: 24695Office hours M at 3-4 or W: 11-12 or Th at 4-5 or by appointment in 327SEO. (Subject to change)Feel free to e-mail me at [email protected] or phone to make an appointmentto discuss any difficulties that arise.Office:327SEO.Office phone:312-413-2149e-mail:[email protected]: http://www2.math.uic.edu/∼jbaldwin/math592/indexMost assignments will be made only on the website, so check it frequently.Text: The Language of First-order Logic by Barwise and Etchmendy avail-able used on line at Amazon and athttp://www-csli.stanford.edu/hp/#LOFOLHighly recommended: Euclid’s elements - Heath translation. Also availablefree on-line.Prerequisites: Approval of the instructor.DescriptionGeometry, Proof and Understanding: The goal of this course is to under-stand the role of ‘proof’ as an organizing principle to enable secondary studentsto retain the diverse content of plane geometry. We will adopt an historical viewof the teaching of geometry with short readings from Euclid, Descartes, Hilbert,Moise, some notes on the evolution of geom etry books in the 20th centrury andcontemporary secondary geometry textbooks (Glencoe, UCSMP, Discovering1Geometry). Comparison of these readings will demonstate the immense peda-gogical impact of decisions about the exact formalization of geometry adapted inthe secondary classroom. We will also analyze the role of discourse in the geom-etry classroom consulting such mathematics educators as Chval-Khisty, ZalmanUsiskin, Harel-Souder, and Ball-Bass. In order to organize this discussion wewill consider some basic concepts from mathematical logic using such tools asBarwise-Etchemendy’s computer simulation: Tarski’s world. The aim will beunderstand the complementary role of syntax and and semantics and how thisis reflected in organizing a geometry course.Resources Material for this course will be disseminated via the text, theclassroom assignments and lectures, doing the problems and exams, and sup-plemental material handed out in class or on the web. These four modes aresupplementary and you are responsible for material presented in any of theforms.Computer use: Owning a computer is not a prerequisite for this course. Butwe will be making use of the internet and of some software. If you don’t haveeasy access please let me know and we try to get the appropriate software onsome departmental machines. For copyright purposes you should buy a copy ofTarski’s World.214 Douglas Hall is equipped with audio-visual equipment. Any studentcan log on to the internet with a laptop if they get Odyssey software (freeto download at the computer center webpage under networking). Warning:Odyssey will disable your windows software for using other networks. Thesimplest solution seems to be to turn Odyssey off except when you are at UIC. Ihope that several of you can bring laptops (with Tarski’s World) and we can justwork together for the perio ds when we want to use that material. 2nd warning:the room is not well-equipped with electrical outlets so charge your laptop first.Reading Assignments The weekly reading assignment is on the web. Youare expected to read the assignment before class and there may be quick quizzeson the reading assignment.Homework: There will be (weekly?) problem assignments. Some will begraded; others you just will be expected to do. I am willing to check over anyof your work.Grading: Your overall performance will be evaluated by the instructor.Contributing to that assessment, there will be a midterm exam and/or an essay,homework and a final exam.2Students with Disabilities: Students with disabilities who require accom-modations for access and participation in this course must be registered withthe Office of Disability Services (ODS). Please contact ODS at (312)413-2103(voice) or (312)413-0123 (TTY).MSCS POLICY ON INCOMPLETE GRADES: The last day to dropthe course without penalty is September 5. Incomplete grades are for hardshipsthat occur at the time of the final. IN grades must be approved by the Depart-ment. IN grades are normally made up during the first two weeks of the nextsemester.Drop Policy Consult MSCS and grad