A Transition to Advanced Mathematics 8th edition

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• Chapter 1: Logic and Proofs
  • 1.1: Propositions and Connectives
  • 1.2: Conditionals and Biconditionals
  • 1.3: Quantified Statements
  • 1.4: Basic Proof Methods I
  • 1.5: Basic Proof Methods II
  • 1.6: Proofs Involving Quantifiers
  • 1.7: Strategies for Constructing Proofs
  • 1.8: Proofs from Number Theory
  
  
• Chapter 2: Sets and Induction
  • 2.1: Basic Concepts of Set Theory
  • 2.2: Set Operations
  • 2.3: Indexed Families of Sets
  • 2.4: Mathematical Induction
  • 2.5: Equivalent Forms of Induction
  • 2.6: Principles of Counting
  
  
• Chapter 3: Relations and Partitions
  • 3.1: Relations
  • 3.2: Equivalence Relations
  • 3.3: Partitions
  • 3.4: Modular Arithmetic
  • 3.5: Ordering Relations
  
  
• Chapter 4: Functions
  • 4.1: Functions as Relations
  • 4.2: Constructions of Functions
  • 4.3: Functions That Are Onto; One-to-One Functions
  • 4.4: Inverse Functions
  • 4.5: Set Images
  • 4.6: Sequences
  • 4.7: Limits and Continuity of Real Functions
  
  
• Chapter 5: Cardinality
  • 5.1: Equivalent Sets; Finite Sets
  • 5.2: Infinite Sets
  • 5.3: Countable Sets
  • 5.4: The Ordering of Cardinal Numbers
  • 5.5: Comparability and the Axiom of Choice
  
  
• Chapter 6: Concepts of Algebra
  • 6.1: Algebraic Structures
  • 6.2: Groups
  • 6.3: Subgroups
  • 6.4: Operation Preserving Maps
  • 6.5: Rings and Fields
  
  
• Chapter 7: Concepts of Analysis
  • 7.1: The Completeness Property
  • 7.2: The Heine—Borel Theorem
  • 7.3: The Bolzano—Weierstrass Theorem
  • 7.4: The Bounded Monotone Sequence Theorem
  • 7.5: Equivalents of Completeness
  
  
• Chapter A: Appendix: Sets, Number Systems, and Functions
  • A.1: Sets
  • A.2: Number Systems
  • A.3: Functions