Product guide

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.

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.

Price

$34.42Save 23%

Reference price: ~~$44.99~~

Price checked: Nov 14, 2026

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Often bought together

Introduction to Mathematical Structures and Proofs (Undergraduate Texts in Mathematics)

$33.20

Pros and cons

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.

Technical specifications

9 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

What to know before buying

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.

Who is it for?

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 reviews on Amazon

4.2 / 5 · 36 ratings

5 stars68%68%
4 stars14%14%
3 stars2%2%
2 stars8%8%
1 star8%8%

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.