# The Art of Proof: Basic Training for Deeper Mathematics

Basic Training Deeper Mathematics: The Art of Proof is an undergraduate text for students learning to write and understand mathematical proofs. Designed for a one-semester or two-quarter course after calculus, it covers discrete and continuous topics, with short essays for seminar-style discussion at the end.

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- Rating: 4.2 / 5
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## At a glance

- Teaches axioms, theorems, and proofs while developing mathematical topics rather than treating proof methods in isolation.
- Topics include integers, induction, algorithms, real and rational numbers, modular arithmetic, limits, and uncountable sets.
- Divided into discrete and continuous material, which the authors recommend giving equal attention.
- Concludes with short seminar-style essays on subjects including continuity, cryptography, groups, complex numbers, ordinal numbers, and generating functions.

## Pros

- Combines proof instruction with examples across both discrete and continuous mathematics.
- Detailed proofs and proofs with hints can support either independent work or instructor-led courses.
- The closing essays provide options for small-group presentations or mathematics club discussion.

## Specifications

### Publication details
- Publisher: Springer
- Publication date: August 31, 2010
- Edition: 2010th
- Language: English
- Print length: 203 pages
- ISBN-10: 1441970223
- ISBN-13: 978-1441970220
### Dimensions and installation
- Weight listed: 1.25 pounds
- Dimensions: 7 x 0.5 x 10 inches

## Before you buy

- The book is intended for readers who have studied calculus with reasonable success. Linear algebra may also be part of their background, but is not presented as a requirement.

## A good fit for

- Undergraduate students transitioning from calculus to rigorous mathematical reasoning.
- Instructors planning a one-semester or two-quarter introduction to proof.
- Small groups seeking short topics for seminar-style mathematical presentations.

## Less suited to

- Readers seeking a book that starts before calculus-level mathematical study.
- Readers looking for a single-topic reference focused only on one area such as analysis or algebra.

## Customer feedback

The listing provides aggregate ratings but no written customer feedback, so these figures do not identify specific strengths, concerns, or reasons for opinions. They indicate a generally favorable but not unanimous response, which is limited guidance for deciding whether the book's proof-focused course structure and stated calculus background fit your needs.

## Frequently asked questions

### What background does the book assume?
The listing describes it for students who have studied calculus with reasonable success. It notes that students may also have studied linear algebra.
### What topics does it cover?
Topics include integers, induction, algorithms, real and rational numbers, modular arithmetic, limits, and uncountable sets. The book also includes essays on further mathematical topics.
### Can it suit a course or group presentation?
It is designed for a one-semester or two-quarter course. Its final essays are described as suitable for small-team seminar presentations in class or at a mathematics club.
### How long is the listed edition?
The product details list a print length of 203 pages.

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## Add-ons

- [Introduction to Mathematical Structures and Proofs \(Undergraduate Texts in Mathematics\)](https://best-deals.pro/visit/the-art-of-proof-basic-training-deeper-mathematics)

## Images

![The Art of Proof: Basic Training for Deeper Mathematics — 1](https://best-deals.pro/i/iTepAwRuRZ_R0pTcNhTK0eTWDLjyALvN0PDhrJc0h2JvwtLs-8jnZKe-E6moezpKF61sHvq3ocKZKJbEhOVbNFJCn4IUHvPVnnxvb5BKZVsSMx0xSOUJ.jpg)