Introduction to Proofs and Proof Strategies

Erscheinungsjahr 2023
ISBN: 978-1-009-09628-7
Verlag: Cambridge University Press

Buch, Englisch, 349 Seiten, Format (B × H): 184 mm x 251 mm, Gewicht: 736 g

Reihe: Cambridge Mathematical Textbooks

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.

Autoren/Hrsg.

Fuchs, Shay

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Grundlagen der Mathematik

Inhaltsverzeichnis

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.

Über Autor(innen)

Fuchs, Shay
Shay Fuchs is Associate Professor (Teaching Stream) in the Department of Mathematical and Computational Sciences at the University of Toronto, Mississauga, Canada, and a Mathematical Association of America member. He has been a mathematics educator for more than twenty-five years. His course based on this text has been taken by more than 1500 students and used by dozens of his colleagues in the past three years.