Foundations of Euclidean Geometry

Instructor -- Pavel Guerzhoy

The class meets Mondays, Wednesdays and Fridays 2:30 - 3:20pm at 404, Keller Hall


Office: 501, Keller Hall (5-th floor)
tel: (808)-956-6533
e-mail: pavel(at)math(dot)hawaii(dot)edu (usually, I respond to e-mail messages within a day)
Office hours: Mondays, Wednesdays and Fridays 1:30-2:20
Reading
In this class we use the book
  • COLLEGE GEOMETRY, A Discovery Approach by David C. Kay Addisopn Wesley Longman, Inc.
    The book is really unavoidable, and cannot be replaced with another textbook.
    Course Objective
    To develop proof-writing skills by the means of axiomatic Euclidean Geometry and the axiomatic method in general. To learn basic concepts and ideas of axiomatic method, Euclidean geometry, transformation theory. The course is run in part as a seminar, with relatively few lectures. Every student will present certain assignment(s) in class.
    Prerequisites
    Math 243 or 253, and Math 321 (or concurrent); or consent.
    Grading Policy
    The final grade reflects the student's understanding of the concepts of axiomatic method, its applications to Euclidean geometry, and transformation theory. To understand these concepts means to be able to produce mathematically correct rigorous proofs of certain propositions. As this is a writing-intensive course, certain proofs will be produced by students in writing as homework assignments and on the exams, and will serve as a basis for grading.

    Final Grade comes out from

  • Final exam on Friday, Dec, 15, from 12 to 2 pm
  • Midterm exam
  • Homework consists of the problems from the list below and counts for 50% of the final grade. The problems marked by W should be submitted and will be graded. Other problems are considered as suggested exercises which help both to solve W-problems and to perform well on the tests. The W-problems must be submitted in a properly written form. In particular, the text solutions should be written in clear and grammatically correct language. Poorly written assignments will be returned back (with remarks); these remarks must be addressed and the homework must be resubmitted until it is considered as "accepted". The grade for the homework comes out of the number of "accepted" assignments. In order to simplify these iterations it is highly recommended to have your homework printed, not hand-written. Note that no partial credit will be given for a particular assignment.



    Contents


    and Homework assignments 


     

     CHAPTER 2   Foundations of Geometry 1    
     
2.1 A:1-10, B:11-13, C:14
2.2 A:1,4,6,7a,7b, C12W,C13W
2.3 A:1-4, B:5,6,7,9,10, C12W
2.4 A:3, B:15,18,19W
2.5 B:12,13,15,16, C:19W


     CHAPTER 3  Foundations of Geometry 2   
     
3.1 C:17W
3.3 A:7,8, B:14,15,16,20,21a; 
Read section 3.2 and explain, in writing, what is the difference between taxicab and
usual geometry? Pay particular attention at how the notion of "distance" showed up in the previous axiomatic development of geometry, and how does it work in section 3.3 in the connection with SAS postulate. 
3.4 A:9, B:15,17


     CHAPTER 4  Euclidean Geometry: Trigonometry, Coordinates and Vectors   
     
4.7 A:2,3,4,5,6,7, B:10a,15,12W,18W



     CHAPTER 5 Transformations in Geometry   
    
5.1 A:1-6, B:7-10, C:12,13W,14W,16W
5.2 A:1-7, B:12 C18W
5.3 A:5,6, B:14,17, C19W