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.
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.
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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
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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.
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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.