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Exploring Mathematics An Engaging Introduction to Proof

Authors

John Meier
, Lafayette College, Pennsylvania,
Derek Smith
, Lafayette College, Pennsylvania
Published 2017

Description

Exploring Mathematics gives students experience with doing mathematics - interrogating mathematical claims, exploring definitions, forming conjectures, attempting proofs, and presenting results - and engages them with examples, exercises, and projects that pique their interest. Written with a minimal number of pre-requisites, this text can be used by college students in their first and second years of study, and by independent readers who want an accessible introduction to theoretical mathematics. Core topics include proof techniques, sets, functions, relations, and cardinality, with…

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Key features

  • Mixes the creativity and rigor that is essential to conducting mathematical enquiry and includes model proofs as well as a range of accessible topics, such as Fibonacci numbers and games, to encourage students to explore and to build intuition and background
  • Engages the reader thanks to in-text exercises with complete solutions and robust hints included in an appendix and helps students develop the skill of frequently interrogating the definitions, examples, and arguments presented
  • Offers students the opportunity to practice their mathematical writing skills in response to sometimes challenging questions, and with less emphasis on formal logic and rote proof-writing exercises

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