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Passage to Abstract Mathematics: International Edition

Passage to Abstract Mathematics: International Edition

          
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About the Book

Passage to Abstract Mathematics facilitates the transition from introductory mathematics courses to the more abstract work that occurs in advanced courses. This text covers logic, proofs, numbers, sets, induction, functions, and more–material which instructors of upper-level courses often presume their students have already mastered but are in fact missing from lower-level courses. Students will learn how to read and write mathematics–especially proofs–the way that mathematicians do. The text emphasizes the use of complete, correct definitions and mathematical syntax.

Table of Contents:
Preface for the Instructor vii Preface for the Student xiii   1. Logic and Proof 1.1 Proofs, what and why? 1.2 Statements and Non-statements 1.3 Logical Operations and Logical Equivalence 1.4 Conditionals, Tautologies and Contradictions 1.5 Methods of Proof 1.6 Quantifiers 1.7 Further Exercises   2. Numbers 2.1 Basic Ideas of Sets 2.2 Sets of Numbers 2.3 Some properties of N and Z 2.4 Prime Numbers 2.5 gcd’s and lcm’s 2.6 Euclid’s Algorithm 2.7 Rational Numbers and Algebraic Numbers 2.8 Further Exercises   3. Sets 3.1 Subsets 3.2 Operations with Sets 3.3 The Complement of a Set 3.4 The Cartesian Product 3.5 Families of Sets 3.6 Further Exercises   4. Induction 4.1 An Inductive Example 4.2 The Principle of Mathematical Induction 4.3 The Principle of Strong Induction 4.4 The Binomial Theorem 4.5 Further Exercises   5. Functions 5.1 Functional Notation 5.2 Operations on Functions 5.3 Induced Set Functions 5.4 Surjections, Injections, and Bijections 5.5 Identity Functions, Cancellation, Inverse Functions, and Restrictions 5.6 Further Exercises   6. Binary Relations 6.1 Partitions 6.2 Equivalence Relations 6.3 Order Relations 6.4 Bounds and Extremal Elements 6.5 Applications to Calculus 6.6 Functions Revisited 6.7 Further Exercises   7. Infinite Sets and Cardinality 7.1 Counting 7.2 Properties of Countable Sets 7.3 Counting Countable Sets 7.4 Binary Relations on Cardinal Numbers 7.5 Uncountable Sets 7.6 Further Exercises   8. Algebraic Systems 8.1 Binary Operations 8.2 Modular Arithmetic 8.3 Numbers Revisited 8.4 Complex Numbers 8.5 Further Exercises   Index of Symbols and Notation Index  


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Product Details
  • ISBN-13: 9780321766977
  • Publisher: Pearson Education (US)
  • Publisher Imprint: Pearson
  • Edition: International ed
  • Language: English
  • Returnable: Y
  • Sub Title: International Edition
  • ISBN-10: 0321766970
  • Publisher Date: 28 Feb 2011
  • Binding: Paperback
  • Height: 232 mm
  • No of Pages: 256
  • Spine Width: mm
  • Width: 178 mm


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