Introduction to proofs and proof strategies /
Fuchs, Shay,
Introduction to proofs and proof strategies / Shay Fuchs, University of Toronto. - Cambridge, United Kingdom : Cambridge University Press, 2023. - xiii, 342 pages : illustrations ; 26 cm. - Cambridge mathematical textbooks. . - Cambridge mathematical textbooks. .
Title from publisher's bibliographic system (viewed on 09 Jun 2023).
Core material. Numbers, quadratics and inequalities
Sets, functions and the field axioms
Informal logic and proof strategies
Mathematical induction
Bijections and cardinality
Integers and divisibility
Relations
Additional topics. Elementarly combinatories
Preview of real analysis
limits and continuity
Complex numbers
Preview of linear algebra
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.
9781009089005 (ebook)
Proof theory
Logic, Symbolic and mathematical--Textbooks.--Textbooks.
511.36 / FUC
Introduction to proofs and proof strategies / Shay Fuchs, University of Toronto. - Cambridge, United Kingdom : Cambridge University Press, 2023. - xiii, 342 pages : illustrations ; 26 cm. - Cambridge mathematical textbooks. . - Cambridge mathematical textbooks. .
Title from publisher's bibliographic system (viewed on 09 Jun 2023).
Core material. Numbers, quadratics and inequalities
Sets, functions and the field axioms
Informal logic and proof strategies
Mathematical induction
Bijections and cardinality
Integers and divisibility
Relations
Additional topics. Elementarly combinatories
Preview of real analysis
limits and continuity
Complex numbers
Preview of linear algebra
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.
9781009089005 (ebook)
Proof theory
Logic, Symbolic and mathematical--Textbooks.--Textbooks.
511.36 / FUC