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Introductory Concepts for Abstract Mathematics /

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"Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires...

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Bibliographic Details
Main Author: Hummel, Kenneth E. (Author)
Corporate Author: Taylor & Francis
Format: eBook
Language:English
Published: Boca Raton, FL : CRC Press, 2000.
Edition:First edition.
Subjects:
Mathematics.
Statistics.
Set theory.
Mathematics
Mathématiques.
Théorie des ensembles.
Statistique.
applied mathematics.
mathematics.
statistics.
Set theory
Statistics
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Cover; Half Title; Title Page; Copyright Page; Table of Contents; PREFACE; SECTION I: LOGIC AND PROOF; Chapter 1: Logic and Propositional Calculus; Chapter 2: Tautologies and Validity Chapter; Chapter 3: Quantifiers and Predicates Chapter; Chapter 4: Techniques of Derivation and Rules of Inference; Chapter 5: Informal Proof and Theorem-Proving Techniques; Chapter 6: On Theorem Proving and Writing Proofs; Chapter 7: Mathematical Induction; SECTION II: SETS; Chapter 8: Sets and Set Operations; Chapter 9: Set Union, Intersection, and Complement; Chapter 10: Generalized Union and Intersection
  • SECTION III: FUNCTIONS AND RELATIONSChapter 11: Cartesian Products; Chapter 12: Relations; Chapter 13: Partitions; Chapter 14: Functions; Chapter 15: Composition of Functions; Chapter 16: Image and Preimage Functions; SECTION IV: ALGEBRAIC AND ORDER PROPERTIES OF NUMBER SYSTEMS; Chapter 17: Binary Operations; Chapter 18: The Systems of Whole and Natural Numbers; Chapter 19: The System Z of Integers; Chapter 20: The System Q of Rational Numbers; Chapter 21: Other Aspects of Order; Chapter 22: The Real Number System; SECTION V: TRANSFINITE CARDINAL NUMBERS; Chapter 23: Finite and Infinite Sets
  • Chapter 24: Denumerable and Countable SetsChapter 25: Uncountable Sets; Chapter 26: Transfinite Cardinal Numbers; SECTION VI: AXIOM OF CHOICE AND ORDINAL NUMBERS; Chapter 27: Partially Ordered Sets; Chapter 28: Least Upper Bound and Greatest Lower Bound; Chapter 29: Axiom of Choice; Chapter 30: Well Ordered Sets; READING LIST; HINTS AND SOLUTIONS TO SELECTED EXERCISES; INDEX