I am going to use this blog to record some of my mathematical thoughts. Modern mathematics has a pretty steep learning curve and I don't really want to spend my time writing about the basics. What are the basics? I could say something like everything you learn in a standard mathematics undergraduate degree, but that is vague. On this site we shall use the following convention: basic mathematics is the material contained in the Appendices of Introduction to Smooth Manifolds by John M Lee. I don't have any strong opinions about the book as a whole, but the Appendices line up closely with what I would call basic mathematics and they are very well organized. From these basics, you can develop a lot of interesting mathematics in a relatively short time period.