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Basic Concepts of Mathematics, by Elias Zakon
Basic Concepts of Mathematics
by Elias Zakon

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.

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.

This text is appropriate for courses that might otherwise use the books (we give US list prices for current hardcover editions at Amazon on July 10, 2006): A Transition to Advanced Mathematics by D. Smith, M. Eggen, and R. St. Andre ($117.95); Transition to Higher Mathematics: Structure and Proof by B. Dumas and J. McCarthy ($106.88); An Introduction to Abstract Mathematics by R. Bond and W. Keane ($132.95); Foundations of Higher Mathematics by P. Fletcher and C. W. Patty ($149.95); Mathematical Reasoning: Writing and Proof by T. Sundstrom ($103.00); Foundations of Mathematical Thinking: Problem-Solving and Proofs by J. D'Angelo and D. West ($111.00); etc.

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 February 3, 2014.

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

Excerpts from the Text: The Terms and Conditions, the Preface, the Table of Contents, and the Index.

Reviews and Recognition: Reviews and recognition for Basic Concepts of Mathematics are noted here. You can review this book at The Assayer.

Terms and Conditions: All uses of this text are subject to the Terms and Conditions contained in this text. As part of these terms, we license this text free of charge to students using it for self-study, and to lecturers evaluating it as a required or recommended text for a course. All other uses of this text are subject to a charge of $10US for individual use and $300US for use by all individuals at a single site of a college or university.

Site Licenses: Site licenses for this text have been purchased by Lehman College, Bronx NY, USA; Marianopolis College, Montreal QC, Canada; Purdue University, West Lafayette IN campus, USA; Swarthmore College, Swarthmore PA, USA; and the University of Windsor, Windsor ON, Canada. Check our list of site licenses to see whether you are a member of a group that has purchased a site license for any of our other products.

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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.

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