Proofs 101

"""An ideal curriculum textbook, Proofs 101: An Introduction to Formal Mathematics is exceptionally well organized and presented. A core and essential addition to college and university library Mathematics collections"" – Midwest Book Review "" I wished I had Proofs 101: An Introduction to Formal Mathematics as a textbook when I was a student!"" – Luise-Charlotte Kappe, Professor Emerita, Binghamton University ""As undergraduate students mature in their study of mathematics, they face learning the writing of proofs. From his extensive classroom experience, Kirtland has fashioned a guide to these new levels of maturity. This book presents a carefully constructed tour whose sights include the foundations and most useful techniques of proof, as well as visits to the houses of number theory and set theory where these methods support results. The presentation is conversational, like a good proof can be, and focuses on what proofs reveal instead of the mechanics of writing them. Students can develop as mathematicians with this book as a guide."" – John McCleary, Vassar College ""I greatly enjoy the way that the author speaks so directly and freely to the reader (student). The text does a good job of taking hard mathematical concepts and making them into bite-size, easy to digest pieces of information whose purpose and uses are explicitly stated. I also appreciate how the author warns the reader about common misconceptions rather than leading them into a trap through a contrived example. This book not only goes through all of the information and definitions one would need to write a clear and concise statement or proof in mathematics, but also explains the reasoning behind why it's important to do so. It’s an excellent introduction to higher-level mathematical thinking and writing."" – Jennifer Crodelle, Middlebury College"