I've been looking to expand my knowledge in geometry as it's not covered in my undergraduate curriculum.
For some reason I'm repelled by the classical approach (hopefully it will pass) as I feel it's not very connected to what we study but I could be wrong as I've only began recently.
Recently, in my "intro to proofs" course we studied plane isometries from a classical approach, and found it piqued my interest. I assume it has a modern treatment somewhere and generalizations?
Thus, I'm looking for literature involving:
- Analytic Geometry (formal treatment of $n=2$ and $n=3$ would suffice). Atleast containing derivations of conics, quadratic surfaces, vector treatment of plane/space geometry. (to my understanding it's sometimes studied in highschool, perhaps there's a treatment an undergrad would enjoy?).
- Transformations(*) and their derivations in euclidean space such as dilations, rotations, reflections, shear etc from coordinates point of view. Their derivations using matrices or complex numbers (as mentioned in wiki articles).
(*) Linear Algebra books which contains these applications in geometry are acceptable. I have browsed the table of contents of several reccomended introductory books on linear algebra but they don't seem to cover the geometric perspective. Correct me if I'm wrong.
Edit: One book is out of reach, the other seems above my current level, so I've changed the requested literature slightly.