Mathematical Thinking

Aims to prepare students in the logical thinking skills, necessary to understand the fundamental ideas and proofs in mathematics. This text discusses mathematical language and proof techniques, applies them to questions in elementary number theory, and then develops additional techniques of proof through discrete and continuous mathematics.

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For one/two-term courses in Transition to Advanced Mathematics or Introduction to Proofs. Also suitable for courses in Analysis or Discrete Math.

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 upperclass 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.