Bridge to abstract mathematics

Bridge to abstract mathematics / Ralph W. Oberste-Vorth, Aristides Mouzakitis, Bonita A. Lawrence.

Of the Properties of the Nonnegative IntegersThe Integers -- Introduction: Integers as Equivalence Classes -- A Total Ordering of the Integers -- Addition of Integers -- Multiplication of Integers -- Embedding the Natural Numbers in the Integers -- Supplemental Exercises -- Summary of the Properties...

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Bibliographic Details
Main Author: Oberste-Vorth, Ralph W., 1959-
Other Authors: Mouzakitis, Aristides, Lawrence, Bonita A., 1957-
Format: eBook
Language:English
Published: [Washington, DC] : Mathematical Association of America, ©2012.
Series:MAA textbooks.
Subjects:
Logic, Symbolic and mathematical > Textbooks.
Mathematics > Textbooks.
MATHEMATICS > Infinity.
MATHEMATICS > Logic.
Logic, Symbolic and mathematical
Mathematics
Beweis
Mathematik
Textbooks
Online Access:Click for online access
Table of Contents:
  • Front cover
  • copyright page
  • title page
  • Contents
  • Some Notes on Notation
  • To the Students
  • To Those Beginning the Journey into Proof Writing
  • How to Use This Text
  • Do the Exercises!
  • Acknowledgments
  • For the Professors
  • To Those Leading the Development of Proof Writing for Students in a Broad Range of Disciplines
  • I THE AXIOMATIC METHOD
  • Introduction
  • The History of Numbers
  • The Algebra of Numbers
  • The Axiomatic Method
  • Parallel Mathematical Universes
  • Statements in Mathematics
  • Mathematical Statements
  • Mathematical ConnectivesSymbolic Logic
  • Compound Statements in English
  • Predicates and Quantifiers
  • Supplemental Exercises
  • Proofs in Mathematics
  • What is Mathematics?
  • Direct Proof
  • Contraposition and Proof by Contradiction
  • Proof by Induction
  • Proof by Complete Induction
  • Examples and Counterexamples
  • Supplemental Exercises
  • How to THINK about mathematics: A Summary
  • How to COMMUNICATE mathematics: A Summary
  • How to DO mathematics: A Summary
  • II SET THEORY
  • Basic Set Operations
  • Introduction
  • Subsets
  • Intersections and UnionsIntersections and Unions of Arbitrary Collections
  • Differences and Complements
  • Power Sets
  • Russell's Paradox
  • Supplemental Exercises
  • Functions
  • Functions as Rules
  • Cartesian Products, Relations, and Functions
  • Injective, Surjective, and Bijective Functions
  • Compositions of Functions
  • Inverse Functions and Inverse Images of Functions
  • Another Approach to Compositions
  • Supplemental Exercises
  • Relations on a Set
  • Properties of Relations
  • Order Relations
  • Equivalence Relations
  • Supplemental ExercisesCardinality
  • Cardinality of Sets: Introduction
  • Finite Sets
  • Infinite Sets
  • Countable Sets
  • Uncountable Sets
  • Supplemental Exercises
  • III NUMBER SYSTEMS
  • Algebra of Number Systems
  • Introduction: A Road Map
  • Primary Properties of Number Systems
  • Secondary Properties
  • Isomorphisms and Embeddings
  • Archimedean Ordered Fields
  • Supplemental Exercises
  • The Natural Numbers
  • Introduction
  • Zero, the Natural Numbers, and Addition
  • Multiplication
  • Supplemental Exercises
  • Summary of the Properties of the Nonnegative IntegersThe Integers
  • Introduction: Integers as Equivalence Classes
  • A Total Ordering of the Integers
  • Addition of Integers
  • Multiplication of Integers
  • Embedding the Natural Numbers in the Integers
  • Supplemental Exercises
  • Summary of the Properties of the Integers
  • The Rational Numbers
  • Introduction: Rationals as Equivalence Classes
  • A Total Ordering of the Rationals
  • Addition of Rationals
  • Multiplication of Rationals
  • An Ordered Field Containing the Integers
  • Supplemental Exercises

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