Chapter Zero: Fundamental Notions of Abstract Mathematics

by Carol Schumacher

This book is designed for the sophomore/junior level Introduction to Advanced Mathematics course. Written in a modified R.L. Moore fashion, it offers a unique approach in which readers construct their own understanding. However, while readers are called upon to write their own proofs, they are also encouraged to work in groups. There are few finished proofs contained in the text, but the author offers “proof sketches” and helpful technique tips to help readers as they develop their proof writing skills. This book is most successful in a small, seminar style class. Logic, Sets, Induction, Relations, Functions, Elementary Number Theory, Cardinality, The Real Numbers For all readers interested in abstract mathematics.

Genres: Mathematics, Reference, Nonfiction

256 pages, Paperback

First published October 3, 1995

Reviews

[piper · Rating 5 out of 5]

I'll start with the disclaimer that I'm predisposed to thinking this book is God's gift to baby mathematicians because Carol Schumacher taught the class in which I used this textbook, and she's an incredible professor. I can't speak on the number theory chapter nor the appendices because we did not use them in the course.

I think this book could be good for both classroom and self-teaching settings. The letter to the student got me so excited for the class and the textbook, and I think the initial enthusiasm made the readings and problems much more informative—Chapter Zero is very much a book where you get out as much as you put in. The structure is laid out really wonderfully to get the reader acquainted with the core ideas underlying formal math in the logic chapter before the set theory chapter where readers can apply the skills they just learned to make their first proofs. From there, really anything else in the book is accessible. I highlighted the definitions a bright orange so I could find them quickly, and that definitely helped when going through problem sets and take-home exams. Really good first taste of abstract math!