Introduction to Proofs and Proof Strategies

This conversational textbook encourages students to approach mathematics problems without relying on traditional proof templates or classifications. It covers familiar topics from a theoretical perspective and then applies these strategies to more advanced topics, using over 370 problems and illustrations. It is ideal for first- and second-year students in mathematics, statistics, and computer science.

Format: Paperback / softback
Length: 349 pages
Publication date: 22 June 2023
Publisher: Cambridge University Press

Discovering a proof is an exhilarating journey that requires a creative mindset and a willingness to explore new approaches. This conversational textbook is designed to guide students through this process, emphasizing the artistic nature of mathematics. Rather than imposing a rigid classification of proof types or providing pre-determined proof templates, it empowers students to develop the critical thinking skills necessary to tackle complex mathematical problems when no clear algorithm or recipe exists.

The book begins by delving into familiar and fundamental topics from a theoretical perspective, providing a solid foundation for the subsequent chapters. From there, it progresses to inequalities, induction, relations, cardinality, and elementary number theory, covering essential concepts that form the backbone of mathematics.

To enhance the learning experience, the book is packed with over 370 problems, illustrations, discussions, and minimal prerequisites. These elements not only reinforce the theoretical concepts but also encourage students to apply their knowledge in real-world scenarios. Additionally, the inclusion of 200 worked examples allows students to see mathematical concepts in action, further deepening their understanding and mastery.

This course is particularly valuable for first- and second-year students in mathematics, statistics, and computer science. It offers a comprehensive and engaging approach to proof-based mathematics, equipping students with the tools they need to excel in their academic pursuits. Instructors will find the book's resources, including solutions to select problems, extremely helpful in facilitating classroom discussions and guiding students through the learning process.

So, embark on this mathematical adventure, and let your creativity soar as you discover the beauty and power of proof. With this textbook as your guide, you will embark on a journey of discovery, challenging your mind and expanding your mathematical horizons.

Weight: 722g
Dimension: 253 x 179 x 21 (mm)
ISBN-13: 9781009096287