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Strang's "Introduction to Linear Algebra". This book is a friend!

Garrity's "All the Math You Missed". Brings you up to speed fast, and has great references.

Came here to add Strang's. In the same spirit of Jaynes', a very good exposition for self-study students.

In logic, "Introduction to Logic: and to the Methodology of Deductive Sciences" - Tarski.

I wish that I started studying these three books before college, in order: 1) Tarski's 2) Strang's 3) Jaynes'

Strang's classes are also amazing http://mit.usiu.ac.ke/about/ocw-stories/gilbert-strang/. I haven't read Garrity going to grab it!