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    Read more about Proofs and Concepts: The Fundamentals of Abstract Mathematics

    Proofs and Concepts: The Fundamentals of Abstract Mathematics

    (6 reviews)

    Dave Witte Morris, University of Lethbridge

    Joy Morris, University of Lethbridge

    Copyright Year:

    Publisher: Dave Witte Morris, Joy Morris

    Language: English

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    Reviewed by Swati Kelkar, Professor, Bunker Hill Community College on 3/25/23

    This textbook covers a comprehensive list of topics in a typical undergraduate advanced mathematics curriculum. Topics include logic, set theory, functions, relations, and mathematical induction. Proof techniques form a foundation for... read more

    Reviewed by Davide Fusi, Assistant Professor, USC-Beaufort on 8/11/20

    The book covers all the topics included in an undergraduate course that aims to be students' first exposure to mathematical proofs: propositional logic, induction, sets, and functions. The book has plenty of good examples and exercises appropriate... read more

    Reviewed by Adriana Salerno, Associate Professor, Bates College on 5/25/20

    I may even cover too much logic before getting into the more mathematical applications and proof writing. read more

    Reviewed by Chris Hiatt, Associate Professor, University of Texas of the Permian Basin on 6/19/18

    This book is a very comprehensive look at proof methods. It appropriately covers the subject starting at logic and moving to various topics. One difference from other books of its type is that the text on proof y induction is not with the other... read more

    Reviewed by Jonathan Poritz, Associate Professor, Colorado State University - Pueblo on 2/1/18

    The book gives a beautiful, complete, and careful exposition of its central material -- logic and proofs -- and of several beautiful and powerful applications in different areas of mathematics. The methods of logic taught here are so central to... read more

    Reviewed by Nic Gilbertson, Assistant Professor, Winona State University on 2/1/18

    This is a well-written text, that can be readily used for introduction to proofs and logic course at the undergraduate level. The text covers topics one would expect to see in first course on logic and proofs, including proofs by contradiction and... read more

    Table of Contents

    Part I. Introduction to Logic and Proofs

    • 1. What is Logic?
    • 2. Propositional Logic
    • 3. Two-Column Proofs

    Part II. Sets and First-Order Logic

    • 4. Sets, Subsets, and Predicates
    • 5. Operations on Sets
    • 6. First-Order Logic
    • 7. Quantifier Proofs
    • 8. Divisibility and Congruence

    Part III. Other Fundamental Concepts

    • 9. Functions
    • 10. Cardinality
    • 11. Proof by Induction
    • 12. Equivalence Relations

    Ancillary Material

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    About the Book

    This free undergraduate textbook provides an introduction to proofs, logic, sets, functions, and other fundamental topics of abstract mathematics. It is designed to be the textbook for a bridge course that introduces undergraduates to abstract mathematics, but it is also suitable for independent study by undergraduates (or mathematically mature high-school students), or for use as a very inexpensive supplement to undergraduate courses in any field of abstract mathematics.

    About the Contributors


    Dave Witte Morris is professor of mathematics at the University of Lethbridge. 

    Joy Morris is associate professor of mathematics at the University of Lethbridge. 

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