Shay Fuchs

Introduction to Proofs and Proof Strategies (eBook, PDF)

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Cambridge University Press
• Erscheinungstermin: 10. Juli 2023
• Englisch
• ISBN-13: 9781009115490
• Artikelnr.: 68948577

Autorenporträt

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.

Inhaltsangabe

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.