Introduction to Proofs and Proof Strategies

With a conversational style and no prerequisites, this transition to advanced mathematics emphasizes creative thinking and problem-solving.

Shay Fuchs (Author)

9781009096287, Cambridge University Press

Paperback / softback, published 22 June 2023

349 pages
25.3 x 17.8 x 1.7 cm, 0.73 kg

'This textbook is easy to read and designed to enhance students' problem-solving skills in their first year of university. The book really stands out due to the variety and quality of exercises at the end of each chapter. The latter chapters dive into more advanced topics for interested students.' Marina Tvalavadze, University of Toronto Mississauga

Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality, and elementary number theory. The final supplementary chapters allow students to apply these strategies to the topics they will learn in future courses. With its focus on 'doing mathematics' through 200 worked examples, over 370 problems, illustrations, discussions, and minimal prerequisites, this course will be indispensable to first- and second-year students in mathematics, statistics, and computer science. Instructor resources include solutions to select problems.

Contents
Preface
Part I. Core Material
1. Numbers, Quadratics and Inequalities
2. Sets, Functions and the Field Axioms
3. Informal Logic and Proof Strategies
4. Mathematical Induction
5. Bijections and Cardinality
6. Integers and Divisibility
7. Relations
Part II. Additional Topics
8. Elementary Combinatorics
9. Preview of Real Analysis – Limits and Continuity
10. Complex Numbers
11. Preview of Linear Algebra
Notes
References
Index.

Subject Areas: Mathematical foundations [PBC]