Book Description

The book is somewhat unusual in bringing together its two main subjects, usually addressed in separate courses. The first of these subjects is an introduction to the notion of proofs and proof methods, and the second one is basic analysis.

The first two chapters, Logic and Proof and Sets and Functions, are typically covered in a “Transition to Higher Mathematics” class. They are usually discussed in in books whose goal is either simply to teach students to prove statements, or to teach students how to prove statements and introduce them to discrete mathematics. In this book, however, the chapters that follow (Real Numbers, Sequences, Limits) slowly lead to Analysis, at the level of precision that is normally seen in Advanced Calculus classes taken by upper-level undergraduates.

The book fills an existing gap by matching these two topics, proofs and analysis, which are usually not taught in the same course. This is great if your students need such a class, but in many places, it can create overlaps — if most students in the class already took a “Transition to Higher Mathematics” class, then they will not need the first two chapters of the book. Another concern is that if we teach students how to prove statements, and all statements we prove in the next three months come from Analysis, then we might send the message that proofs are something used only in Analysis. If you can allay these concerns, then the book may be a good choice for your class.

Book Details