Proofs 101

An Introduction to Formal Mathematics

By: Joseph Kirtland

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Paperback | 20 November 2020 | Edition Number 1

At a Glance

Paperback
198 Pages

Dimensions(cm)
23.4 x 15.6 x 1.07

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Proofs 101: An Introduction to Formal Mathematics serves as an introduction to proofs for mathematics majors who have completed the calculus sequence (at least Calculus I and II) and a first course in linear algebra.

The book prepares students for the proofs they will need to analyze and write the axiomatic nature of mathematics and the rigors of upper-level mathematics courses. Basic number theory, relations, functions, cardinality, and set theory will provide the material for the proofs and lay the foundation for a deeper understanding of mathematics, which students will need to carry with them throughout their future studies.

Features

Designed to be teachable across a single semester
Suitable as an undergraduate textbook for Introduction to Proofs or Transition to Advanced Mathematics courses
Offers a balanced variety of easy, moderate, and difficult exercises

Industry Reviews

"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

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