A Gentle Introduction to the Art of Mathematics

A Gentle Introduction to the Art of Mathematics (GIAM for short) is a textbook for a "transitions" course. Transitions courses (also known as "foundations" or "intro to proofs" courses) are typically taken after the Calculus sequence and before upper-division coursework in the mathematics major. Their purpose is to acclimatize the student to some of the culture and terminology of mathematics and to begin developing in them a proficiency at reading and writing mathematical proofs. GIAM has chapters on Logic, Set theory, Relations and Cardinality interspersed with chapters on proofs -- direct and indirect arguments, induction, combinatorial reasoning and "magic". Also, there are amusing quotations at the start of every chapter.