Mathematical thinking : problem-solving and proofs
著者
書誌事項
Mathematical thinking : problem-solving and proofs
Prentice Hall, c1997
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注記
Includes bibliographical references (p. 355-356) and index
内容説明・目次
内容説明
Developing logical thinking and fundamental mathematical ideas, and using problems that pique students' mathematical curiosity, this work aims to prepare readers for all upper-division mathematics courses and improve their skills in presenting coherent arguments.
目次
- Part 1 Elementary concepts: sets and numbers
- language and proofs
- functions
- induction. Part 2 Properties of numbers: cardinality and counting
- divisibility
- modular arithmetic
- the rational numbers. Part 3 Discrete mathematics: combinatorial reasoning
- two principles of counting
- graph theory
- recurrence relations. Part 4 Continuous mathematics: the real numbers
- sequences and series
- continuity
- differentiation
- integration
- the complex numbers
- hints to selected exercises.
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