A Taste of Pure Mathematics

FRONT MATTER

CHAPTER 1  Logic and Proofs

Section 1.1:  Sentential Logic

Section 1.2: Conditional and Biconditional Connectives

Section 1.3: Predicate Logic

Section 1.4: Mathematical Proofs

Section 1.5: Proofs in Predicate Logic

Section 1.6: Proof by Mathematical Induction

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CHAPTER 2  Sets and Counting

Section 2.1:  Basic Operations of Sets

Section 2.2: Families of Sets

Section 2.3:  Combinatorics: The Art of Enumeration

Section 2.4:  Countable Infinity

Section 2.5:  Uncountable Infinity

Section 2.6:  Larger Infinities and the ZFC Axioms

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CHAPTER 3  Relations

Section 3.1:  Relations

Section 3.2:  Order Relations

Section 3.3: Equivalence Relations

Section 3.4: The Function Relation

Section 3.5:  Image of a Set

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CHAPTER 4  The Real and Complex Number System

Section 4.1: Construction of the Real Numbers

Section 4.2: The Complete Ordered Field: The Real Numbers

Section 4.3: Complex Numbers

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CHAPTER 5  Topology

Section 5.1:  Introduction to Graph Theory

Section 5.2:  Directed Graphs

Section 5.3: Some General Ideas of Topology

Section 5.4: Point-Set Topology on the Real Line

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CHAPTER 6  Algebra

Section 6.1: Symmetries and Algebraic Systems

Section 6.2:  Introduction to the Algebraic Group

Section 6.3: Permutation Groups

Section 6.4: Subgroups Inside a Group

Section 6.5:  Rings and Fields

INDEX

 

 

 

 

 

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