Spaces, Mappings, and Mathematical Structures with an Introduction to Proof

The goal of this course is to introduce abstract mathematical thought and formal proof writing.

We begin by introducing logic and proof strategies, with emphasis on proofs related to sets, relations, functions, and elementary number theory.

Then, we study various mathematical structures (such as groups, metric spaces, and topological spaces) that arise in more formal study of various branches of mathematics (algebra, calculus, and topology).