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How to Prove It: A Structured Approach
87% of respondents would recommend this to a friend
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This bestselling text's third edition helps students transition from solving problems to proving theorems by teaching them the techniques needed to read and write proofs.
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Product Details
- Bestselling text's third edition helps students transition from solving problems to proving theorems
- Introduces students to advanced mathematics through mastery of proofs and includes over 150 new exercises
- New chapter on number theory and begins with basic concepts of logic and set theory
- Teaches techniques needed to read and write proofs and build up complex proofs step by step
- Assumes no background beyond standard high school mathematics and will be useful to various disciplines
- Provides detailed 'scratch work' sections to expose the machinery of proofs about numbers, sets, relations, and functions
| Publisher | Cambridge University Press |
| Publication date | August 29, 2019 |
| Edition | 3rd |
| Language | English |
| Print length | 468 pages |
| ISBN-10 | 1108439535 |
| ISBN-13 | 978-1108439534 |
| Item Weight | 1.7 pounds (770 grams) |
| Dimensions | 6 x 1.18 x 9 inches (15.2 x 3 x 22.9 cm) |
Who Should Buy?
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Undergraduate Students
Ideal for undergraduate mathematics students learning proof techniques and logical reasoning in their coursework.
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Self-Learners
Great for individuals who wish to independently study mathematical proofs and require a structured learning approach.
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Instructors
Useful for educators seeking a comprehensive resource to teach proof strategies and mathematics reasoning effectively.
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Non-Math Majors
Not suitable for those pursuing degrees outside of mathematics, as the focus is heavily on proof techniques.
Product Description
How to Prove It: A Structured Approach
Product Buying Guide
How to Prove It: A Structured Approach 3rd Edition is a bestselling text that helps students transition from solving problems to proving theorems. This comprehensive guide introduces students to the techniques needed to read and write proofs in advanced mathematics and theoretical computer science.
Product Specifications
- Title: How to Prove It: A Structured Approach 3rd Edition
- New edition featuring over 150 new exercises
- Includes a new chapter on number theory
- Covers basic concepts of logic and set theory
- Teaches techniques for building complex proofs step by step
- Suitable for beginners with no background beyond standard high school mathematics
- Ideal for computer scientists, philosophers, linguists, and mathematicians
Key Features
- Comprehensive guide for transitioning from problem-solving to proving theorems
- Teaches essential techniques for reading and writing proofs
- Features over 150 new exercises for practice
- Includes a new chapter on number theory
- Covers basic concepts of logic and set theory as a foundation
- Ideal for beginners with no advanced mathematics background
- Suitable for various disciplines: computer science, philosophy, linguistics, and mathematics
Usage Scenarios
- Students taking courses in advanced mathematics or theoretical computer science
- Individuals interested in logic and proof techniques
- Professionals in computer science, philosophy, linguistics, or mathematics seeking to enhance their understanding of proofs
Some User Review
- I found this book incredibly helpful in transitioning from problem-solving to proof-writing. The explanations are clear, and the examples and exercises provide excellent practice.
- As someone with no background in advanced mathematics, this book was a great starting point for me. The step-by-step approach and scratch work sections really helped me understand the process of building proofs.
- The new chapter on number theory was a valuable addition. It deepened my understanding of proofs and provided new challenges to test my skills.
- I recommend this book to any student or professional looking to improve their proof-writing abilities. It's a comprehensive guide that covers all the essential techniques.
- The concepts are explained well, and the exercises are a good mix of easy and challenging. I feel much more confident in my ability to read and write proofs after using this book.
- The author does an excellent job of breaking down complex proofs into manageable steps. This book is a must-have for anyone serious about learning how to prove theorems.
Competitors
- The price of How to Prove It: A Structured Approach 3rd Edition is competitive and offers great value considering the comprehensive content and additional exercises provided in the new edition. It is worth the investment for students and professionals interested in advancing their proof-writing skills.
Buying Considerations
- Consider your level of mathematical background before purchasing this book. It is designed for beginners with no advanced mathematics experience, but it may not be suitable for individuals already proficient in proof-writing.
- If you are specifically interested in number theory, the new chapter included in this edition makes it an even more valuable resource for you.
- Think about your future goals and disciplines of interest. This book caters to a range of professionals, including computer scientists, philosophers, linguists, and mathematicians.
- The new exercises in this edition offer ample practice opportunities. If you are looking for additional exercises to strengthen your proof-writing skills, this book is a great choice.
Conclusion
How to Prove It: A Structured Approach 3rd Edition is the go-to guide for students and professionals looking to transition from problem-solving to proving theorems. With its comprehensive content, step-by-step approach, and additional exercises, this book is an excellent investment for anyone interested in logic, proof techniques, and advanced mathematics.
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Logic Editorial Review
Velleman's book, "How to Prove It: A Structured Approach," presents an introduction to the art of creating mathematical proofs. The book is praised for offering an abundance of exercises with many solutions provided to challenge students to apply their newly acquired knowledge. In addition, the book is said to contain many examples to support the text and make the material more accessible to beginners. However, there are Cons with some customers feeling that the text is "verbose" and "confusing," with the explanations lacking clarity in certain areas, making it unsuitable as a primary text for beginners. However, many others felt differently, indicating the book is the best one they have ever read on this topic.
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Pros
- Lots of exercises with many solutions
- Plenty of examples to aid understanding
- Comprehensive and in-depth coverage of proving skill-building
- Good physical quality
Cons
- Explanations are confusing and lack clarity
Product Price History
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OMR 21
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Features & Benefits
- Bestselling text on proofs in mathematics and computer science
- Over 150 new exercises and a new chapter on number theory
- Teaches techniques to read and write proofs
- Assumes no background beyond standard high school mathematics
- Ideal for computer scientists, philosophers, linguists, and mathematicians
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