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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 Mathematical Analysis I) 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 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 January 5, 2007.
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 Mathematical Analysis I) 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 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 January 5, 2007.
