A Gentle Introduction to the Art of Mathematics, version 3.1 by Joe Fields (PDF)

Description

GIAM (a Gentle Introduction to the Art of Mathematics) is a free, open-source textbook — the current version is 3.1. GIAM covers several topics in the foundations of mathematics (logic, sets, relations, functions and cardinality) and introduces the reader to many techniques of mathematical proof (direct, indirect, contradiction, contrapositive, mathematical induction, combinatorial proofs and magic).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I had this textbook assigned for an introductory proofs class nearly 10 years ago, and found it to be pleasant to read (much more so than a typical math textbook), and with a note of fun in the writing that clearly communicates the author’s joy of mathematics. I have since used sections of the book when teaching proof techniques to High School Geometry students and higher grades, with great success.The open-source nature of this text means it has had a great deal of community feedback and most (if not all) wrinkles have been ironed out. The fact that it’s still given away freely (in digital form) on the author’s website is also a bonus. Very generous, well-written, and informative. I don’t know what more I could ask for!

⭐I have used this book twice in my transitions/introduction-to-proof course. Having taught such a course for 35 years, I find that this open-source book is superior to comparable books available from the regular press. It shares with them a thorough coverage of “foundations” topics such as sets, logic, functions relations, etc as well as proof/disproof techniques: direct, contradiction, contrapositive, cases, induction (strong and weak), etc. However, it is superior in several ways:1) The author’s writing style is engaging and enthusiastic. He is not just writing about proofs, he is writing about doing mathematics and you can tell he loves the subject and invites the reader to join him. His writing is playful. e.g.He invites the reader to “monkey around” with a problem until the outlines of its solution become apparent.2) His style and structure are gentle in that he revisits each topic several times at levels calculated to be accessible, but to stretch the reader just a bit each time. I advise my students to read it like a novel rather than a recipe book.3) Chapter 1 contains the foundational material for a wide variety to topics about which one might write proofs. The course could be organized around any one of these or any group of these.4) Since the book is open-source, he is able to incorporate suggestions and exercises from readers and users of the book. In version 3, it is now becoming quite well rounded with lots of exercises ranging from routine practice problems to problems designed to delight the successful solver.5) The book carries the reader from naive calculation-style mathematics to full rigor.

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