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MAT 3272: Geometry IIProfessor: Charles Delman Professor’s Office: M3351Phone: 581-6274 (O) 348-7786 (H, before 9pm, please) Office Hours: MW, 3-51. Course ContentMajor theorems of neutral geometry, including an introduction to number systems,continuity, and measurement; the metric approach to geometry; major theorems of Eu-clidean geometry; history of the discovery of hyperbolic geometry; major theorems ofhyperbolic geometry; models and the proof of the relative consistency of hyperbolicgeometry; introduction to geometric transformations and symmetry (time permitting);spherical and elliptic geometry (time permitting); projective geometry as a unifyingframework for the three classical geometries (time permitting).2. Objectives(1) The student will be able to write clear and logically sound proofs and developproofs of geometric theorems on her/his own.(2) The student will be able to verify that the axioms of a system hold in a modelof that system.(3) The student will be able to use models to prove the relative consistency of anaxiom system.(4) The student will be able to discuss the cultural and historical context of mathe-matics and the philosophical controversies about the foundations of mathematics.(5) Without reference to outside sources, the student will be able• to define the major concepts of geometry which have been covered and statetheir purpose;• to state and prove the major theorems of geometry which have been coveredand discuss their consequences and the relationships among them.(6) The student will be able to explore an open-ended question by positing conjec-tures and either proving them or finding counterexamples.3. RequirementsClass participation: You are expected to be in class every day and to be preparedto discuss the reading or present your progress toward a solution of any of the assignedproblems. In borderline cases, participation may affect your grade.Homework: Written homework problems will be regularly assigned and graded (withcomments). I encourage you to discuss the course material with your classmates. Youmay hand in joint papers; just give credit at the top to all of the authors of a homeworkpaper. The authors of a joint paper will receive the same grade.In-term Exams: There will be two exams during the class term (in addition to thefinal), which may be partly or wholly given as take-homes. Make-up exams will be givenonly under extraordinary circumstances or in case of serious emergency; prior permissionto miss an exam must be obtained from the professor if at all possible.Final exam: The final exam will be comprehensive. It may be partly or wholly givenas a take-home, and it may have an oral component.Exams may not be done jointly!14. GradingI do not grade on a “curve”. Under no circumstances will your grade directly dependon how how your fellow students do. If you do a good job of learning the material, youwill receive a good grade, regardless of how well the other members of the class perform.Don’t forget that the reverse is also true: if you do a poor job of learning the material,you will receive a poor grade, regardless of how poorly everyone else does.I will assign letter (rather than numerical) grades, based on the objectives statedabove and standards clarified in class. Grades correspond to my judgement of quality asfollows:• A Excellent. The work exhibits mastery of nearly all important ideas, includingthose which are subtle or difficult, much insight and originality, highly coherentorganization and fine expository style. Errors and omissions, if any, are minor.• B Good. The work exhibits substantial understanding of most important ideas,including some which are subtle or difficult, some insight and originality, co-herent organization and correct usage, grammer and spelling. There are somesubstantive errors or omissions.• C Fair. The work exhibits basic understanding of many fundamental ideas, al-though not those which are subtle or difficult, and demonstrates some coherence.The presentation is readable, with at most minor errors of usage, grammer orspelling. There are many substantive errors or omissions.• D Poor. The work exhibits some understanding of a few fundamental ideas, butnot those which are subtle or difficult, and it fails to demonstrate coherence. Us-age, grammar and spelling are mostly correct. There are a great many subtantiveerrors or omissions.• F No credit. The work exhibits to o few of the positive qualities noted above tobe worthy of credit.Each requirement will count toward your final grade according to the scheme below(possibly subject to slight modification):Homework: 40%In-term Exams: 40%Final Exam: 20%Complete honesty on assignments and exams is expected of all students. Any instancesof cheating will be prosecuted according to university


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EIU MAT 3272 - syllabus

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