I started this blog for myself as a tool to improve my ability to explain mathematical concepts. While I do not expect many people to read what I post, I still want the material to be accessible by a general audience. There's a saying that you really don't know something until you teach it. I agree. In my career as a graduate student, I have never felt more comfortable with material than when I am teaching it. Unfortunately, our department doesn't offer courses in all the areas my research touches. I hope that this blog will then allow me to "teach" material that I find interesting or that I wish to understand better.
Why "Tangent Bundle"? A tangent bundle is a concept from differential geometry, but I also envision this blog as being a collection of posts from various branches of mathematics. The posts here will not all be related; I will write about any topic I feel like explaining. Some posts will be quick thoughts or puzzles; others will be longer series that explore ideas in greater detail.
If you have any feedback on my posts, please leave a comment. If something is unclear, I would always welcome the opportunity to clarify. In addition you can use the form on this page to suggest topics that would you like to see explained. On the off-chance that anyone makes such a suggestion, I will probably be excited enough to actually comply with the request.
For anybody out there reading this: enjoy! I hope that I can teach you something new.
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