Logic
Statements, Negation, and Compound Statements
Truth Tables and Logical Equivalences
Conditional and Biconditional Statements
Logical Arguments
Open Statements and Quantifiers
Chapter Review
Deductive Mathematical Systems and Proofs
Deductive Mathematical Systems
Mathematical Proofs
Chapter Review
Set Theory
Sets and Subsets
Set Operations
Additional Set Operations
Generalized Set Union and Intersection
Chapter Review
Relations
Relations
The Order Relations <, , >,
Reflexive, Symmetric, Transitive, and Equivalence Relations
Equivalence Relations, Equivalence Classes, and Partitions
Chapter Review
Functions
Functions
Onto Functions, One-to-One Functions and One-to-One Correspondences
Inverse of a Function
Images and Inverse Images of Sets
Chapter Review
Mathematical Induction
Mathematical Induction
The Well-Ordering Principle and the Fundamental Theorem of Arithmetic
Cardinalities of Sets
Finite Sets
Denumerable and Countable Sets
Uncountable Sets
Proofs from Real Analysis
Sequences
Limit Theorems for Sequences
Monotone Sequences and Subsequences
Cauchy Sequences
Proofs from Group Theory
Binary Operations and Algebraic Structures
Groups
Subgroups and Cyclic Groups
Appendix Reading and Writing Mathematical Proofs
Answers to Selected Exercises
References
Index
Biography
Charles Roberts, PhD, professor, Department of Math and Computer Science, Indiana State University, Terre Haute, USA
