Overview
- Gives a broad view of the field of mathematics without the artificial division of subjects???
- Provides students with a broad exposure to mathematics by including an unusually diverse array of topics
- Discusses important milestones in the history of mathematics and features some of the most interesting recent accomplishments in the field
- Goes beyond the typical elementary text by providing a more thorough and deeper treatment whenever feasible
- The text can be studied at various levels and depths, with, hopefully, plenty of fun for students and instructors alike
- Request lecturer material: sn.pub/lecturer-material
Part of the book series: Undergraduate Texts in Mathematics (UTM)
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Table of contents (24 chapters)
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Front Matter
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What’s Mathematics?
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Front Matter
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Advanced Math for Beginners
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Front Matter
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Keywords
About this book
This undergraduate textbook is intended primarily for a transition course into higher mathematics, although it is written with a broader audience in mind. The heart and soul of this book is problem solving, where each problem is carefully chosen to clarify a concept, demonstrate a technique, or to enthuse. The exercises require relatively extensive arguments, creative approaches, or both, thus providing motivation for the reader. With a unified approach to a diverse collection of topics, this text points out connections, similarities, and differences among subjects whenever possible. This book shows students that mathematics is a vibrant and dynamic human enterprise by including historical perspectives and notes on the giants of mathematics, by mentioning current activity in the mathematical community, and by discussing many famous and less well-known questions that remain open for future mathematicians.
Ideally, this text should be used for a two semester course, where the first course has no prerequisites and the second is a more challenging course for math majors; yet, the flexible structure of the book allows it to be used in a variety of settings, including as a source of various independent-study and research projects.
Reviews
From the reviews:
“Bajnok’s new book truly invites students to enjoy the beauty, power, and challenge of abstract mathematics. … Bajnok’s book can most certainly be used as a text for a traditional transition course designed for mathematics majors. He wrote the book with a broader audience in mind, and personally uses it at Gettysburg College for anyone interested in deepening his or her mathematical knowledge … .” (Jill Dietz, MAA Reviews, May, 2014)
“This book can be added to the growing population of ‘transition’ books--texts aimed at bridging the leap from the traditional calculus sequence to upper-division coursework in mathematics. The topics typically associated with such a text are all present: basic logic, predicates and quantifiers, induction, relations, and functions. … any reader able to complete this work and its problems will be suitably prepared for further studies in mathematics. Summing Up: Recommended. Lower- and upper-division undergraduates.” (D. S. Larson, Choice, Vol. 51 (5), January, 2014)
“This textbook aims for the spot in many departments’ curriculum where students are introduced to advanced mathematics. … the author introduces the game in an applied setting that the reader will likely find both compelling and intriguing: a set of options for two corporations in competition. … This text definitely focuses on mathematics. The material covers a wide range of material, probably more than most instructors will cover in one semester … .” (John Perry, zbMATH, Vol. 1274, 2013)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: An Invitation to Abstract Mathematics
Authors: Béla Bajnok
Series Title: Undergraduate Texts in Mathematics
DOI: https://doi.org/10.1007/978-1-4614-6636-9
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Béla Bajnok 2013
Hardcover ISBN: 978-1-4614-6635-2Published: 10 May 2013
eBook ISBN: 978-1-4614-6636-9Published: 13 May 2013
Series ISSN: 0172-6056
Series E-ISSN: 2197-5604
Edition Number: 1
Number of Pages: XIV, 406
Topics: Mathematics, general, History of Mathematical Sciences, Mathematical Logic and Foundations