Introductory Concepts for Abstract Mathematics
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A01=Kenneth E. Hummel
Abstract Mathematics
Assumed Properties
AUB
Author_Kenneth E. Hummel
Cardinal Numbers
Category=PB
Category=PBCH
eq_isMigrated=1
eq_nobargain
equivalence
Finite Cardinal Numbers
Follow
Indirect Proofs
Infinite Sets
Lattice Diagram
natural
Natural Numbers
Nonempty Set
Nonempty Subset
number
Number System
order
partial
Partial Order Relation
Positive Rational Numbers
Prove Theorem
prover
rational
Real Numbers
relation
Set A
Set Builder Notation
theorem
Transfinite Cardinal Numbers
Triangle ABC
trichotomy
Trichotomy Law
Upper Bound
Wo
Product details
- ISBN 9780367398835
- Weight: 453g
- Dimensions: 156 x 234mm
- Publication Date: 05 Sep 2019
- Publisher: Taylor & Francis Ltd
- Publication City/Country: GB
- Product Form: Paperback
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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 readers bridge that gap. It teaches them to work with abstract ideas and develop a facility with definitions, theorems, and proofs. They learn logical principles, and to justify arguments not by what seems right, but by strict adherence to principles of logic and proven mathematical assertions - and they learn to write clearly in the language of mathematics
The author achieves these goals through a methodical treatment of set theory, relations and functions, and number systems, from the natural to the real. He introduces topics not usually addressed at this level, including the remarkable concepts of infinite sets and transfinite cardinal numbers
Introductory Concepts for Abstract Mathematics takes readers into the world beyond calculus and ensures their voyage to that world is successful. It imparts a feeling for the beauty of mathematics and its internal harmony, and inspires an eagerness and increased enthusiasm for moving forward in the study of mathematics.
Hummel, Kenneth E.
