I'm a 3rd year undergrad Math student and totally confused right now on what field I'm gonna choose in my thesis next semester. We we're introduced in Transformation Geometry (Introduction to Symmetries by George Martin, used by our professor as a reference). I'm amazed at how the book approaches geometry algebraically tho seems hard. Really, I'm interested in this topic yet I'm disappointed while searching through the Google if this field really exist for research. I found only that this is a new approach in geometry for highschool. Currently, I already read about half of the book. It's a beautiful book.
- Is this a good field to study?
- If this is not a good field to study (i.e., just a new approach in geometry), are there any field of mathematics related to this?