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Introduction to Proofs and Proof Strategies

Authors

Shay Fuchs
, University of Toronto
Published 2023

Description

Emphasizing the creative nature of mathematics, this conversational textbook guides students through the process of discovering a proof. The material revolves around possible strategies to approaching a problem without classifying 'types of proofs' or providing proof templates. Instead, it helps students develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow. Beginning by discussing familiar and fundamental topics from a more theoretical perspective, the book moves on to inequalities, induction, relations, cardinality,…

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Key features

  • Helps students discover possible strategies to approaching a problem and develop the thinking skills needed to tackle mathematics when there is no clear algorithm or recipe to follow
  • Focuses on 'doing mathematics', rather than on mathematical logic and proof-templates, through 200 worked examples, 100 clarifying illustrations, discussions, and over 370 problems ranging from concept checks to full proofs
  • Allows students time to adapt to the increased challenge of writing mathematical proofs and thinking mathematically before being exposed to higher level mathematical formalism
  • Aids in the transition from lower-level mathematics, focused on computations, to advanced material, focused on theory and proofs, by explaining familiar and fundamental topics from a theoretical perspective
  • Shows how readers can apply strategies they learned to more advanced topics by including supplemental chapters in elementary combinatorics, limits and continuity, complex numbers, and linear algebra

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