What you will learn here is to reason, write, and read like a mathematician. The book we follow is Velleman's "How To Prove It", which provides a systematic attempt to reason with proofs. The book will cover Logic, Sets, Proofs, Relations, Functions, Induction, and Infinite Sets, and they are the basis for all mathematical literature. The background of calculus is not needed rather only algebra & trigonometry, and a determined, and humble, spirit.