Here's my list: Basic 1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos) Linear Algebra 1. Finite-Dimensional Vector Space (Paul Halmos) 2

Here's my list: Basic 1. Chapter Zero (Carol Schumacher) 2. Naive Set Theory (Paul Halmos) Linear Algebra 1. Finite-Dimensional Vector Space (Paul Halmos) 2. Linear Algebra Done Right (Steven Axler) Real Analysis 1. Real Mathematical Analysis (Charles Pugh) 2. Introduction to Analysis (Maxwell Rosenlicht) Algebra 1. A first course in abstract algebra (John Fraleigh) These books are better for self-directed reading compared to some of the classics like Rudin or Herstein. These should keep you busy for a while.