Description: This book helps the student complete the transition from purely manipulative to rigorous mathematics. The clear exposition covers many topics that are assumed by later courses but are often not covered with any depth or organization: basic set theory, induction, quantifiers, functions and relations, equivalence relations, properties of the real numbers (including consequences of the completeness axiom), fields, and basic properties of n-dimensional Euclidean spaces.

The many exercises and optional topics (isomorphism of complete ordered fields, construction of the real numbers through Dedekind cuts, introduction to normed linear spaces, etc.) allow the instructor to adapt this book to many environments and levels of students. Extensive hypertextual cross-references and hyperlinked indexes of terms and notation add truly interactive elements to the text.

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Audience: This book gives students the skills they need to succeed in the first courses in Real Analysis (it is designed specifically to prepare students for the author's award-winning Mathematical Analysis I and Mathematical Analysis II) and Abstract Algebra/Modern Algebra. Students who plan to advance to upper-level classes in computer science (discrete structures, algorithms, computability, automata theory, ...), economics, or electrical and computer engineering (signal and image processing, AI, circuit design, ...) will benefit from mastering the material in this text.

Publishing Information: Basic Concepts of Mathematics, by Elias Zakon, ISBN 978-1-931705-00-3, published by The Trillia Group, 2001. 198+x pages, 332 exercises, 23 figures, hypertextual cross-references, hyperlinked indexes of notation and terms. Download size: 1378 to 1410 KB, depending on format. Current version released May 19, 2017.

Library Catalogue Information: Librarians at the University of Windsor have prepared a catalogue entry for this book.

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Terms and Conditions: This text is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Public License. An informal description of your rights and responsibilities can be found here. Full terms can be found here. If you would like more rights to this work (e.g., commercial publication rights or including parts of this work in another work, etc.), please contact the publisher.

Errata: There is a list of errata that records changes made to the text since the version of October 29, 2001. The latest version of the book is always available at the links above.