# Non-Euclidean Geometries

### The class meets Mondays, Wednesdays and Fridays 8:30 - 9:20pm at 414, 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 9:30-10:20, 11:30-12:30

In this class we use the book
• GEOMETRY, by David A. Brannan, Mattheew F. Esplen, Jeremy J. Gray Cabmbridge University Press, ISBN 0 521 59787 0(paperback) 0 521 59193 7 (hardback)
The book is really unavoidable, and cannot be replaced with another textbook.
Course Objective
To develop a solid background for understanding non-Euclidean geometries. To systematically develop the transformational point of view on geometry. To learn basic concepts of affine and inversive geometry.
Prerequisites
Math 351 or consent. Math 311, although is not formally required, would be highly desirable.
The final grade reflects the student's understanding of the concepts of geometry which we discuss in this class. To understand these concepts means to understand the proofs of theorems, namely, to be able to solve problems which illustrate steps of these proofs, and to write the solutions down in a mathematically correct way. Certain solutions will be produced by students in writing as homework and quizzes assignments and on the exams, and will serve as a basis for grading.

• Final exam on Monday, May 7, from 7:30 to 9:30 am
The exam counts for 30% of the final grade.

• Midterm exam covers the material of Chapters 1 and 2
The exam counts for 20% of the final grade.
• Quizzes
count for 50% of the final grade. Homework is assigned on a regular basis. Please find the list of assignements below. Quizzes consist of problems which are pretty similar to those from the homework assignments, and thus allow to check the homework.

### Contents

and Homework assignments

```
CHAPTER 1   Conics
1.1.1 -- 1.1.4 1.5(1.1) 1-5
1.2            1.5(1.2) 1-6

Appendix 2, Appendix 1 ... I review the necessary material in class, and assign special problems for homework.

CHAPTER 2  Affine Geometry
2.1           2.6(2.1) 1-5
2.2.1         2.6(2.2) 1-6
2.2.2
2.3           2.6(2.3) 1-5
2.4
2.5           2.6(2.5) 1,2

CHAPTER 5  Inversive Geometry
5.1           5.6(5.1) 1-4
A primer on complex numbers ... I review the necessary material in class, and assign special problems for homework.
5.2.1-5.2.3   5.6(5.2) 1-4
5.3           5.6(5.3) 1-5
5.4           5.6(5.4) 1-4
5.5           5.6(5.5) 1-3

If time allows, we then consider as much of Chapter 6 as we will be able to.

```