Pure Math Soln

Solutions: A Taste of Pure Mathematics

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

Chapter 2   Sets and Combinatorics

Section 2.1; Basic Operations of Sets

Section 2.2; Families of Sets 

Section 2.3; Counting: The Art of Enumeration 

Section 2.4; Countable Infinity 

Section 2.5; Uncountable Sets

Section 2.6; Larger Infinities and the ZFC Axioms

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 and Inverse Image of a Set

Chapter 4: Real and Complex Number Systems

Section 4.1; Construction of the Real Numbers

Section 4.2; The Complete Ordered Field: The Real Numbers

Section 4.3; Complex Numbers

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 

Chapter 6  Algebra

Section 6.1; Symmetries and Algebraic Systems

Section 6.2; Introduction to the Algebraic Group

Section 6.3; Groups of Permutations: The Symmetric Group

Section 6.4; Subgroups : Groups Inside a Group

Section 6.5; Rings and Fields

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