Mathematical Thinking: Problem-Solving and Proofs (2nd Edition)

D'Angelo, John P.,West, Douglas B.

ISBN 10: 0130144126 / ISBN 13: 9780130144126

Editore: Pearson, 1999

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Riassunto:

This survey of both discrete and continuous mathematics focuses on the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics, rather than on rote symbolic manipulation. Coverage begins with the fundamentals of mathematical language and proof techniques (such as induction); then applies them to easily-understood questions in elementary number theory and counting; then develops additional techniques of proofs via fundamental topics in discrete and continuous mathematics. Topics are addressed in the context of familiar objects; easily-understood, engaging examples; and over 700 stimulating exercises and problems, ranging from simple applications to subtle problems requiring ingenuity. ELEMENTARY CONCEPTS. Numbers, Sets and Functions. Language and Proofs. Properties of Functions. Induction. PROPERTIES OF NUMBERS. Counting and Cardinality. Divisibility. Modular Arithmetic. The Rational Numbers. DISCRETE MATHEMATICS. Combinatorial Reasoning. Two Principles of Counting. Graph Theory. Recurrence Relations. CONTINUOUS MATHEMATICS. The Real Numbers. Sequences and Series. Continuity. Differentiation. Integration. The Complex Numbers. For anyone interested in learning how to understand and write mathematical proofs, or a reference for college professors and high school teachers of mathematics.

Product Description: For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Maths. This text is designed to prepare students thoroughly in the logical thinking skills necessary to understand and communicate fundamental ideas and proofs in mathematics skills vital for success throughout the upper-level mathematics curriculum. The text offers both discrete and continuous mathematics, allowing instructors to emphasize one or to present the fundamentals of both. It begins by discussing mathematical language and proof techniques (including induction), applies them to easily-understood questions in elementary number theory and counting, and then develops additional techniques of proof via important topics in discrete and continuous mathematics. The stimulating exercises are acclaimed for their exceptional quality. *A clearly outlined transition course. *Now contains an excellent course in analysis. *Offers over 850 exercises ranging from relatively straightforward applications of ideas in the text to subtle problems requiring some ingenuity. *Distinguishes easier exercises by (-), harder by (+), and particularly valuable or instructive exercises by (!)

Dati bibliografici

Titolo: Mathematical Thinking: Problem-Solving and ...
Casa editrice: Pearson
Data di pubblicazione: 1999
Legatura: hardcover
Condizione: Acceptable
Edizione: seconda edizione