Create ReadingList.md

Author: Keno

doc/ReadingList.md

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+This is a list of references I found useful while thinking about Diffractor.
+If you are new to Julia, AD or Diffractor and are primarily intersted in
+Diffractor, how it works, how to use it, or even there general Diffractor
+theory, this is probably not the list for you. As always in the literature,
+some of these references use terms differently from how they are used in
+Diffractor (as well as being inconsistent with each other). Additionally,
+many of these references are quite dense and though I've found small nuggets
+of insight in each, excavating those took many hours. Also, these are not
+introductory texts. If you've not taken an introductory differential
+geometry course, I would recommend looking for that first. Don't feel bad if
+some of these references read like like nonsense. It often reads that way to me to.
+
+# Reading on Optics
+
+- "Categories of Optics" - Mitchell Riley - https://arxiv.org/abs/1809.00738
+
+The original paper on optics. Good background for understanding the optics terminology.
+
+# Readings on First Order Differential Geometry
+
+- "Introduction to Smooth Manifolds" John M. Lee
+
+Chapter 11 "The Cotangent Bundle" is useful for a reference on the theory of cotangent bundles,
+which corresponds to the structure of reverse mode AD through the optical equivalence. Also a
+useful general reference for Differential Geomtry.
+
+- "Natural Operations in Differential Geometry" - Ivan Kolář
+
+I recommend Chapter IV. "Jets and Natural bundles"
+
+# Readings on Higher Order Differential Geometry
+
+- "Second Order Tangent Vectors in Riemannian Geometry", Fisher and Laquer, J. Korean Math Soc 36 (1999)
+
+This one is quite good. I recommend reading the first half at least and tracing through the definitions.
+This corresponds fairly closely to notion of iterated tangent spaces as implemented in Diffractor.
+
+- "The Geometry of Jet Bundles" D. J. Saunders
+
+I recommend reading Chapter 5 "Second order Jet bundles", though of course some earlier chapters
+may be useful to understand this chapter. I'm not 100% happy with the notation, but it gives good
+intuition.
+