An Introduction To Abstract Mathematics
by Robert J. Bond /
2007 / English / PDF
14.3 MB Download
Bond and Keane explicate the elements of logical, mathematical
argument to elucidate the meaning and importance of mathematical
rigor. With definitions of concepts at their disposal, students
learn the rules of logical inference, read and understand proofs of
theorems, and write their own proofs--all while becoming familiar
with the grammar of mathematics and its style. In addition, they
will develop an appreciation of the different methods of proof
(contradiction, induction), the value of a proof, and the beauty of
an elegant argument. The authors emphasize that mathematics is an
ongoing, vibrant discipline--its long, fascinating history
continually intersects with territory still uncharted and questions
still in need of answers. The authors' extensive background in
teaching mathematics shines through in this balanced, explicit, and
engaging text, designed as a primer for higher-level mathematics
courses. They elegantly demonstrate process and application and
recognize the byproducts of both the achievements and the missteps
of past thinkers. Chapters 1-5 introduce the fundamentals of
abstract mathematics and chapters 6-8 apply the ideas and
techniques, placing the earlier material in a real context.
Readers' interest is continually piqued by the use of clear
explanations, practical examples, discussion and discovery
exercises, and historical comments.
Bond and Keane explicate the elements of logical, mathematical
argument to elucidate the meaning and importance of mathematical
rigor. With definitions of concepts at their disposal, students
learn the rules of logical inference, read and understand proofs of
theorems, and write their own proofs--all while becoming familiar
with the grammar of mathematics and its style. In addition, they
will develop an appreciation of the different methods of proof
(contradiction, induction), the value of a proof, and the beauty of
an elegant argument. The authors emphasize that mathematics is an
ongoing, vibrant discipline--its long, fascinating history
continually intersects with territory still uncharted and questions
still in need of answers. The authors' extensive background in
teaching mathematics shines through in this balanced, explicit, and
engaging text, designed as a primer for higher-level mathematics
courses. They elegantly demonstrate process and application and
recognize the byproducts of both the achievements and the missteps
of past thinkers. Chapters 1-5 introduce the fundamentals of
abstract mathematics and chapters 6-8 apply the ideas and
techniques, placing the earlier material in a real context.
Readers' interest is continually piqued by the use of clear
explanations, practical examples, discussion and discovery
exercises, and historical comments.
