So a friend here at the Utah REU named Douglas has 8 GB of textbooks on a thumb drive.  Eight gigabytes!!  Needless to say, I also now have many textbooks in my dropbox.  I only picked the really good ones that are actually worth reading.  I have found that the overwhelming majority of textbooks are pure garbage, so it’s nice to find some that are actually pretty good.  If I take one thing away from this REU, it’s the collection of textbooks recommended by very smart people who read a lot of textbooks and know which ones are useful.  These aren’t only Mathematics Textbooks, mind you.  I also have two or three Physics textbooks (I’m looking at you, Ethan).  These Physics textbooks approach Physics from the mathematical side, which makes doing a lot of physics a LOT easier.  Instead of trying to learn Physics and getting confused by all the bullshit, the books teach the mathematics that the physics is actually built upon so that one may do physics like a physicist rather than like an undergraduate.  That being said, intuition is important.  However, I think I have gained enough intuition from my introductory physics courses to start reading about “real physics.”  For instance, I’m told that mathematical constructions called Clifford Algebras make much of Quantum Mechanics much easier.  Anyway, the books are:


Introduction to Smooth Manifolds

Algebraic Topology


Linear Algebra Done Right

Mathematical Methods to Classical Mechanics (Physics)

Principles of Quantum Mechanics (Physics)

…and a couple of others.


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