Thomas Q. Sibley is Professor of Mathematics at St. John's University in Collegeville, Minnesota.

• PART I Chapter 1: LANGUAGE, LOGIC, AND SETS1.1 Logic and Language1.2 Implication1.3 Quantifiers and Definitions1.4 Introduction to Sets1.5 Introduction to Number Theory1.6 Additional Set TheoryDefinitions from Chapter 1Algebraic and Order Properties of Number SystemsChapter 2: PROOFS2.1 Proof Format I: Direct Proofs2.2 Proof Format II: Contrapositive and Contradition2.3 Proof Format III: Existence, Uniqueness, Or2.4 Proof Format IV: Mathematical InductionThe Fundamental Theorem of Arithmetic2.5 Further Advice and Practice in ProvingProof FormatsChapter 3: FUNCTIONS3.1 Definitions3.2 Composition, One-to-One, Onto, and Inverses3.3 Images and Pre-Images of SetsDefinitions from Chapter 3Chapter 4: RELATIONS4.1 Relations4.2 Equivalence Relations4.3 Partitions and Equivalence Relations4.4 Partial OrdersDefinitions from Chapter 4PART IIChapter 5: INFINTE SETS5.1 The Sizes of Sets5.2 Countable Sets5.3 Uncountable Sets5.4 The Axiom of Choice and Its EquivalentsDefinitions from Chapter 5Chapter 6: INTRODUCTION TO DISCRETE MATHEMATICS6.1 Graph Theory6.2 Trees and Algorithms6.3 Counting Principles I6.4 Counting Principles IIDefinitions from Chapter 6Chapter 7: INTRODUCTION TO ABSTRACT ALGEBRA7.1 Operations and Properties7.2 GroupsGroups in Geometry7.3 Rings and Fields7.4 Lattices7.5 HomomorphismsDefinitions from Chapter 7Chapter 8: INTRODUCTION TO ANALYSIS8.1 Real Numbers, Approximations, and Exact ValuesZeno’s Paradoxes8.2 Limits of Functions8.3 Continuous Functions and CounterexamplesCounterexamples in Rational Analysis8.4 Sequences and Series8.5 Discrete Dynamical SystemsThe Intermediate Value TheoremDefinitions for Chapter 8Chapter 9: METAMATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS9.1 Metamathematics9.2 The Philosophy of MathematicsDefinitions for Chapter 9Appendix: THE GREEK ALPHABETAnswers: SELECTED ANSWERSIndexList of Symbols

Thomas Q. Sibley is Professor of Mathematics at St. John's University in Collegeville, Minnesota.

• PART I Chapter 1: LANGUAGE, LOGIC, AND SETS1.1 Logic and Language1.2 Implication1.3 Quantifiers and Definitions1.4 Introduction to Sets1.5 Introduction to Number Theory1.6 Additional Set TheoryDefinitions from Chapter 1Algebraic and Order Properties of Number SystemsChapter 2: PROOFS2.1 Proof Format I: Direct Proofs2.2 Proof Format II: Contrapositive and Contradition2.3 Proof Format III: Existence, Uniqueness, Or2.4 Proof Format IV: Mathematical InductionThe Fundamental Theorem of Arithmetic2.5 Further Advice and Practice in ProvingProof FormatsChapter 3: FUNCTIONS3.1 Definitions3.2 Composition, One-to-One, Onto, and Inverses3.3 Images and Pre-Images of SetsDefinitions from Chapter 3Chapter 4: RELATIONS4.1 Relations4.2 Equivalence Relations4.3 Partitions and Equivalence Relations4.4 Partial OrdersDefinitions from Chapter 4PART IIChapter 5: INFINTE SETS5.1 The Sizes of Sets5.2 Countable Sets5.3 Uncountable Sets5.4 The Axiom of Choice and Its EquivalentsDefinitions from Chapter 5Chapter 6: INTRODUCTION TO DISCRETE MATHEMATICS6.1 Graph Theory6.2 Trees and Algorithms6.3 Counting Principles I6.4 Counting Principles IIDefinitions from Chapter 6Chapter 7: INTRODUCTION TO ABSTRACT ALGEBRA7.1 Operations and Properties7.2 GroupsGroups in Geometry7.3 Rings and Fields7.4 Lattices7.5 HomomorphismsDefinitions from Chapter 7Chapter 8: INTRODUCTION TO ANALYSIS8.1 Real Numbers, Approximations, and Exact ValuesZeno’s Paradoxes8.2 Limits of Functions8.3 Continuous Functions and CounterexamplesCounterexamples in Rational Analysis8.4 Sequences and Series8.5 Discrete Dynamical SystemsThe Intermediate Value TheoremDefinitions for Chapter 8Chapter 9: METAMATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS9.1 Metamathematics9.2 The Philosophy of MathematicsDefinitions for Chapter 9Appendix: THE GREEK ALPHABETAnswers: SELECTED ANSWERSIndexList of Symbols

Thomas Q. Sibley is Professor of Mathematics at St. John's University in Collegeville, Minnesota.

• PART I Chapter 1: LANGUAGE, LOGIC, AND SETS1.1 Logic and Language1.2 Implication1.3 Quantifiers and Definitions1.4 Introduction to Sets1.5 Introduction to Number Theory1.6 Additional Set TheoryDefinitions from Chapter 1Algebraic and Order Properties of Number SystemsChapter 2: PROOFS2.1 Proof Format I: Direct Proofs2.2 Proof Format II: Contrapositive and Contradition2.3 Proof Format III: Existence, Uniqueness, Or2.4 Proof Format IV: Mathematical InductionThe Fundamental Theorem of Arithmetic2.5 Further Advice and Practice in ProvingProof FormatsChapter 3: FUNCTIONS3.1 Definitions3.2 Composition, One-to-One, Onto, and Inverses3.3 Images and Pre-Images of SetsDefinitions from Chapter 3Chapter 4: RELATIONS4.1 Relations4.2 Equivalence Relations4.3 Partitions and Equivalence Relations4.4 Partial OrdersDefinitions from Chapter 4PART IIChapter 5: INFINTE SETS5.1 The Sizes of Sets5.2 Countable Sets5.3 Uncountable Sets5.4 The Axiom of Choice and Its EquivalentsDefinitions from Chapter 5Chapter 6: INTRODUCTION TO DISCRETE MATHEMATICS6.1 Graph Theory6.2 Trees and Algorithms6.3 Counting Principles I6.4 Counting Principles IIDefinitions from Chapter 6Chapter 7: INTRODUCTION TO ABSTRACT ALGEBRA7.1 Operations and Properties7.2 GroupsGroups in Geometry7.3 Rings and Fields7.4 Lattices7.5 HomomorphismsDefinitions from Chapter 7Chapter 8: INTRODUCTION TO ANALYSIS8.1 Real Numbers, Approximations, and Exact ValuesZeno’s Paradoxes8.2 Limits of Functions8.3 Continuous Functions and CounterexamplesCounterexamples in Rational Analysis8.4 Sequences and Series8.5 Discrete Dynamical SystemsThe Intermediate Value TheoremDefinitions for Chapter 8Chapter 9: METAMATHEMATICS AND THE PHILOSOPHY OF MATHEMATICS9.1 Metamathematics9.2 The Philosophy of MathematicsDefinitions for Chapter 9Appendix: THE GREEK ALPHABETAnswers: SELECTED ANSWERSIndexList of Symbols