344 Pages
by
Chapman & Hall
344 Pages
by
Chapman & Hall
344 Pages
by
Chapman & Hall
Also available as eBook on:
Beyond calculus, the world of mathematics grows increasingly abstract and places new and challenging demands on those venturing into that realm. As the focus of calculus instruction has become increasingly computational, it leaves many students ill prepared for more advanced work that requires the ability to understand and construct proofs. Introductory Concepts for Abstract Mathematics helps... Read more
LOGICAL AND PROOF
Logical and Propositional Calculus
Tautologies and Validity
Quantifiers and Predicates
Techniques of Derivation and Rules of Inference
Informal Proof and Theorem-Proving Techniques
On Theorem proving and Writing Proofs
Mathematical Induction
SETS
Sets and Set Operations
Union, Intersection, and Complement
Generalized Union and Intersection
FUNCTIONS AND RELATIONS
Cartesian Products
Relations
Partitions
Functions
Composition of Functions
Image and Preimage Functions
ALGEBRAIC AND ORDER PROPERTIES OF NUMBER SYSTEMS
Binary Operations
The Systems of Whole and Natural Numbers
The System Z of Integers
The System Q of Rational Numbers
Other Aspects of Order
The Real Number System
TRANSFINITE CARDINAL NUMBERS
Finite and Infinite Sets
Denumerable and Countable Sets
Uncountable Sets
Transfinite Cardinal Numbers
AXIOM OF CHOICE AND ORDINAL NUMBERS
Partially Ordered Sets
Least Upper Bound and Greatest Lower Bound
Axiom of Choice
Well Ordered Sets
READING LIST
HINTS AND SOLUTIONS TO SELECTED PROBLEMS
Logical and Propositional Calculus
Tautologies and Validity
Quantifiers and Predicates
Techniques of Derivation and Rules of Inference
Informal Proof and Theorem-Proving Techniques
On Theorem proving and Writing Proofs
Mathematical Induction
SETS
Sets and Set Operations
Union, Intersection, and Complement
Generalized Union and Intersection
FUNCTIONS AND RELATIONS
Cartesian Products
Relations
Partitions
Functions
Composition of Functions
Image and Preimage Functions
ALGEBRAIC AND ORDER PROPERTIES OF NUMBER SYSTEMS
Binary Operations
The Systems of Whole and Natural Numbers
The System Z of Integers
The System Q of Rational Numbers
Other Aspects of Order
The Real Number System
TRANSFINITE CARDINAL NUMBERS
Finite and Infinite Sets
Denumerable and Countable Sets
Uncountable Sets
Transfinite Cardinal Numbers
AXIOM OF CHOICE AND ORDINAL NUMBERS
Partially Ordered Sets
Least Upper Bound and Greatest Lower Bound
Axiom of Choice
Well Ordered Sets
READING LIST
HINTS AND SOLUTIONS TO SELECTED PROBLEMS
Biography
Hummel, Kenneth E.
"... very clearly written. Sophomore-level undergraduates should have no difficulty with the book."
-Zentralblatt fur Mathematik
