math 461, college geometry i
TRANSCRIPT
Math 461, College Geometry I
Fall 2016
Prerequisites: Math 234.
Class:
Van Vleck B119, 8:00AM-9:15AM, TR.
Professor: Bing Wang, Department of Mathematics,Office Hours in Van Vleck 813, TR 1:00-2:00pm or by appointment,[email protected], 608-263-5148, http://www.math.wisc.edu/∼bwang.
Grade:
Your overall score will be calculated according to the following categories and weights.
• Midterm Exams (20% × 2): Oct 11th and Nov15th. All the midterm examsare in the Tuesday class. Every midterm exam is NOT accumulative.
• Final Exam (40%): Saturday, Dec 17th, 7:25pm-9:25pm, place to be de-termined. Final exam is accumulative.
• Homeworks (20%): Homework assignments are posted on the course web site,which will be updated often. Homework is due at the beginning of the Tuesdayclass each week. It is returned at the next Tuesday class. Late homework is NOTaccepted. Please prepare your written homework according to the following rules:
1. Write your full name at the top of the first page in the order: LAST, FIRST.
2. Put the problems in order, indicating clearly any you have skipped.
3. STAPLE your homework.
You will be graded on a curve.
Attention:
• Acceptable excuses for missing an exam include only official university excuses, witha note from an appropriate university official.
• If you have special exam requirement, please contact me as early as possible. Weneed extra time to find place and people to proctor the special exams.
• Cheating formula sheet, Calculators and computer software are NOT PERMITTEDduring exams and Quizzes. If you engage in any misconduct during the exam, yourexam score will automatically be zero.
1
Textbook:
Geometry for College Students, by I. Martin Issacs.
Course Content:
Math 461 is the College Geometry course. In this course, we shall learn how to provetheorems in the setting of plane geometry. We shall first review some elementary facts oflines, triangles and circles, which was taught in high school. Then we move on to advancedtopics. Based on several obvious axioms, we set up many beautiful and deep theorems ofplane geometry, including Morley’s Theorem, the butterfly Theorem, Ceva’s Theorem, andMenelaus’ Theorem, etc. We shall also discuss the vector methods of proof and investigateinteresting geometric constructions. We emphasize that one of the most important objectof this course is to learn how to understand and write proofs. The materials covered arelisted as follows:
• Review of high-school geometry.
• Special points of triangle.
• The nine-point circle.
• Simson lines.
• The theorem of Ceva and Menelaus.
• Morley’s theorem.
• Vectors techniques of proof.
• Radical axes of circles.
• Compass and straightedge constructions.
2