Bela Bajnok
Invitation to Abstract Mathematics
Invitation to Abstract Mathematics
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An Invitation to Abstract Mathematics is a textbook for undergraduates that promotes an active transition to higher mathematics through problem-solving. It covers the core concepts of logic, sets, and functions, as well as advanced topics, and is organized into four parts. The second edition has been reorganized to better reflect the layout and curriculum of standard transition courses and features recent developments and improved appendices. The book is ideal for students seeking a challenging and engaging transition to advanced mathematics, and will appeal to both undergraduates majoring in mathematics and non-math majors interested in exploring higher-level concepts.
\n Format: Hardback
\n Length: 442 pages
\n Publication date: 28 October 2020
\n Publisher: Springer Nature Switzerland AG
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This comprehensive undergraduate textbook aims to facilitate a seamless transition into higher mathematics. At its core, problem-solving takes center stage, with each problem carefully selected to showcase, elucidate, or extend a mathematical concept. Over 300 engaging exercises encourage readers to engage in extensive discussions and innovative approaches, while exploring the interconnectedness between fundamental mathematical topics.
Divided into four parts, the book begins with a playful exploration of the foundational elements of mathematics, including definitions, axioms, and proofs. The subsequent section delves into the fundamental concepts of logic, sets, and functions, laying the groundwork for subsequent chapters. Once the core of a transition course is covered, the author presents a selection of advanced topics that offer opportunities for extension or further study. Throughout, appendices provide historical perspectives, current trends, and open questions, showcasing mathematics as a vibrant and dynamic human enterprise.
In this second edition, the book has been reorganized to align more closely with the structure and curriculum of standard transition courses. Additionally, recent developments and enhanced appendices have been included to provide readers with the most up-to-date information.
An Invitation to Abstract Mathematics is particularly well-suited for individuals seeking a rigorous and engaging journey into advanced mathematics, whether they are undergraduates majoring in mathematics or non-math majors with an interest in exploring higher-level concepts.
From reviews of the first edition:
Bajnok's new book truly invites students to embrace 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 Reviews
\n Weight: 826g\n
Dimension: 162 x 241 x 35 (mm)\n
ISBN-13: 9783030561734\n
Edition number: 2nd ed. 2020\n
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