This undergraduate textbook promotes an active transition to higher
mathematics. Problem solving is the heart and soul of this book:
each problem is carefully chosen to demonstrate, elucidate, or
extend a concept. More than 300 exercises engage the reader in
extensive arguments and creative approaches, while exploring
connections between fundamental mathematical topics. Divided into
four parts, this book begins with a playful exploration of the
building blocks of mathematics, such as definitions, axioms, and
proofs. A study of the fundamental concepts of logic, sets, and
functions follows, before focus turns to methods of proof. Having
covered the core of a transition course, the author goes on to
present a selection of advanced topics that offer opportunities for
extension or further study. Throughout, appendices touch on
historical perspectives, current trends, and open questions,
showing mathematics as a vibrant and dynamic human enterprise. This
second edition has been reorganized to better reflect the layout
and curriculum of standard transition courses. It also features
recent developments and improved appendices. An Invitation to
Abstract Mathematics is ideal for those seeking a challenging and
engaging transition to advanced mathematics, and will appeal to
both undergraduates majoring in mathematics, as well as non-math
majors interested in exploring higher-level concepts. 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 be used 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 background knowledge. Jill Dietz, MAA ReviewsThe style of
writing is careful, but joyously enthusiastic.... The author's
clear attitude is that mathematics consists of problem solving, 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 to imitate. The
author attributes this approach to his Hungarian background ... and
encourages students to embrace the challenge in the same way an
athlete engages in vigorous practice. John Perry, zbMATH
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