Modern Geometry

In this course we shall:

• establish the Euclidean space (in two dimensions)

• investigate finite geometries synthetically and analytically

• illustrate algebraic notions using geometric interpretations and vice-versa

• utilize electronic tools to aid the study of Euclidean and non-Euclidean geometry

This course shall cover four chapters namely:

1. Plane Euclidean geometry

2. Affine transformations in the Euclidean plane

3. Finite geometries

4. Non-Euclidean geometries

For most of the course familiarity of topics from Linear Algebra and Abstract Algebra are needed. The analytic approach in Chapter 1 would be expressed through the language of vectors while in topics starting from Chapter 2, several algebraic structures will be used for geometric concepts.

Technology will be used extensively for the whole semester. Hence, the availability of electronic devices (such as smartphones or laptops) and internet connectivity will be advantageous.

• 16 Lecture Exercises (one from each lecture)

• 4 Quizzes (one from each chapter)

• 2 Major Examinations (one from each term period)

• 1 Project

Cut-off score is 50% for all course requirements.

Answers to lecture exercises and quizzes shall be written in sheets of 1/4 of short-sized bond paper. Take a photo of each page and send them as attachment to my e-mail address jdselle@ctu.edu.ph with subject properly indicating which course requirement is being submitted (for example "Math 4213 Quiz No. 1"). Then, in the body of the mail, write your full name, course, year, and block section (I encourage you to do this in formal and complete sentences). The reason why it is required to write in 1/4 sheets is to enhance visibility. (Photos of whole-sized paper are sometimes difficult to read). You are allowed to use as many 1/4 sheets as you would need.

Subject to circumstances, major exams will be conducted in the campus. This shall be properly arranged and instructions shall be announced to you.

• Ryan (2012). Euclidean and Non-Euclidean Geometry. Cambridge University Press

• Cederberg (2001). A course in the modern geometries. Springer

• Batten (1997). Combinatorics of finite geometries. Cambridge University Press