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.
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By Rick Poach
Feb 22, 2011
As an older student returning to college for a B.S. in Mathematics, one constant source of frustration I find is the presentation style of course material in the textbooks. Many authors, very intelligent people, make the mistake of forgetting that their target audience does not have the wealth of context which comes from the years of experience which they themselves have. As such, the authors either try to explain each excruciating nuance through ultimately confusing and inappropriate proofs, or they explain nothing while dropping equally confusing forward references. In the worst cases they actually do both. I am convinced that when students complain that they "can't do Math" they are really stating that they couldn't understand the obscure tomes with which they were burdened. Dr. Fields made none of these mistakes in his book, "A Gentle Introduction to the Art of Mathematics". I took Dr. Fields' class in Foundations when this book was a version 1.x pdf file. I... More > have since looked over the version 2.0 book. The material is presented naturally, often humorously, stating problems in contexts which I found approachable, accessible, and ultimately enjoyable. I consider it to be one of those surprising books which speaks to the curiosity which drives people to study a subject in the first place, that same curiosity often worn down by a poorly presented text. In short, an excellent prof wrote an excellent book, so if you are looking for an introduction to Mathematical Proof, or if just trying to reaffirm that Math doesn't have to be a soul-grinding chore, I'd like to recommend "A Gentle Introduction to the Art of Mathematics".< Less
This is a fantastic and highly recommended book. I used this book in my Foundations of Math class (Introduction to proofs) and found it to be extremely useful for working through homework sets. More importantly, the book is written in a friendly, joke-filled style that greatly helped to lessen the anxiety normally associated with texts covering these topics - of which I've gone through several. The book is stocked with tons of excellent examples, many of which are both fun and interesting especially in the books later chapters. Studying GIAM has made transitioning to upper level math classes simple for me - where many upper division classmates have struggle mightily with these more abstract concepts and their applications. Joseph Fields is definitely one of my math heroes!
