An Invitation to Abstract Mathematics (2nd Edition) (Undergraduate Texts in Mathematics)

December 8, 2020
An Invitation to Abstract Mathematics (2nd Edition) (Undergraduate Texts in Mathematics)

Motivates readers to understand the connections betweendifferent concepts when transitioning to higher mathematicsEncourages creative and analytical approaches to solvingnumerous, carefully chosen problemsIllustrates the many ways in which mathematics is a vibranthuman enterprise by exploring historical perspectives, currenttrends, and open questions——————————This undergraduate textbook promotes an active transition tohigher mathematics. Problem solving is the heart and soul of thisbook: each problem is carefully chosen to demonstrate, elucidate,or extend a concept. More than 300 exercises engage the reader inextensive arguments and creative approaches, while exploringconnections between fundamental mathematical topics.Divided into four parts, this book begins with a playfulexploration of the building blocks of mathematics, such asdefinitions, axioms, and proofs. A study of the fundamentalconcepts of logic, sets, and functions follows, before focus turnsto methods of proof. Having covered the core of a transitioncourse, the author goes on to present a selection of advancedtopics that offer opportunities for extension or further study.Throughout, appendices touch on historical perspectives, currenttrends, and open questions, showing mathematics as a vibrant anddynamic human enterprise.This second edition has been reorganized to better reflect thelayout and curriculum of standard transition courses. It alsofeatures recent developments and improved appendices. AnInvitation to Abstract Mathematics is ideal for those seekinga challenging and engaging transition to advanced mathematics, andwill appeal to both undergraduates majoring in mathematics, as wellas non-math majors interested in exploring higher-levelconcepts.From reviews of the first edition:Bajnok’s new book truly invites students to enjoy the beauty,power, and challenge of abstract mathematics. … The book can beused as a text for traditional transition or structure courses …but since Bajnok invites all students, not just mathematics majors,to enjoy the subject, he assumes very little backgroundknowledge. Jill Dietz, MAA ReviewsThe style of writing is careful, but joyously enthusiastic….The author’s clear attitude is that mathematics consists of problemsolving, and that writing a proof falls into this category.Students of mathematics are, therefore, engaged in problem solving,and should be given problems to solve, rather than problems toimitate. The author attributes this approach to his Hungarianbackground … and encourages students to embrace the challenge inthe same way an athlete engages in vigorous practice.John Perry, zbMATH