Studying Mathematics The Beauty, the Toil and the Method /

This book is dedicated to preparing prospective college students for the study of mathematics. It can be used at the end of high school or during the first year of college, for personal study or for introductory courses. It aims to set a meeting between two relatives who rarely speak to each other:...

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Hlavní autor: Bramanti, Marco (Autor)
Médium: Elektronický zdroj E-kniha
Jazyk:angličtina
Vydáno: Cham : Springer International Publishing, 2018.
Vydání:1st ed. 2018.
Témata:
Mathematics-Study and teaching .
Learning.
Instruction.
ISBN:9783319913551
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Obsah:
  • Part 1. The Language of Mathematics
  • A Few Ambiguities of Everyday Language
  • To represent by Sets
  • Propositions and Properties
  • Proofs, Implications and Counterexamples
  • Negations and Indirect Proofs
  • Formulae and Indices
  • Saturation of Indices and Syntactic Consistency of a Formula
  • Induction and Natural Numbers
  • Part 2. The Study of a Mathematical Book
  • To Read a Definition
  • To Understand, i.e. to Know How to Reuse
  • To Learn How to Correct
  • To Sift the Ideas
  • To Understand, i.e. to Know How to Explain
  • Part 3. Pages and Ideas
  • Majorizations
  • Uniqueness Proofs (Level B)
  • Functions and Set Theoretic Arguments
  • Tiles, Polyhedra, Characterizations
  • Index. .

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