| Description |
1 online resource : text file, PDF |
| 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 |
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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 |
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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 |
| Summary |
"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 the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematicsThe author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbersIntroductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics."--Provided by publisher |
| Bibliography |
Includes bibliographical references and index |
| Subject |
Mathematics.
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Statistics.
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Set theory.
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applied mathematics.
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mathematics.
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statistics.
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Mathematics
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Set theory
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Statistics
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| Form |
Electronic book
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| ISBN |
9781482285642 |
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1482285649 |
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9781315273761 |
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1315273764 |
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9781351993135 |
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1351993135 |
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