Introduction to Mathematical Structures and Proofs
As a student moves from basic calculus courses into upper-division courses in linear and abstract algebra, real and complex analysis, number theory, topology, and so on, a "bridge" course can help ensure a smooth transition. Introduction to Mathematical S
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Larry J. Gerstein
Introduction to Mathematical Structures and Proofs Second Edition
Undergraduate Texts in Mathematics
Undergraduate Texts in Mathematics Series Editors: Sheldon Axler San Francisco State University Kenneth Ribet University of California, Berkeley
Advisory Board: Colin C. Adams, Williams College Alejandro Adem, University of British Columbia Ruth Charney, Brandeis University Irene M. Gamba, The University of Texas at Austin Roger E. Howe, Yale University David Jerison, Massachusetts Institute of Technology Jeffrey C. Lagarias, University of Michigan Jill Pipher, Brown University Fadil Santosa, University of Minnesota Amie Wilkinson, University of Chicago
Undergraduate Texts in Mathematics are generally aimed at third- and fourthyear undergraduate mathematics students at North American universities. These texts strive to provide students and teachers with new perspectives and novel approaches. The books include motivation that guides the reader to an appreciation of interrelations among different aspects of the subject. They feature examples that illustrate key concepts as well as exercises that strengthen understanding. For further volumes: http://www.springer.com/series/666
Larry J. Gerstein
Introduction to Mathematical Structures and Proofs Second Edition
Larry J. Gerstein University of California, Santa Barbara Santa Barbara, CA USA
ISBN 978-1-4614-4264-6 ISBN 978-1-4614-4265-3 (eBook) DOI 10.1007/978-1-4614-4265-3 Springer New York Heidelberg Dordrecht London Library of Congress Control Number: 2012940655 © Springer Science+Business Media, LLC 2012 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and a
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