Description

Book Synopsis

Preface.-1 The How, When, and Why of Mathematics.- 2 Logically Speaking.- 3 Introducing the Contrapositive and Converse.- 4 Set Notation and Quantifiers.- 5 Proof Techniques.- 6 Sets.- 7 Operations on Sets.- 8 More on Operations on Sets.- 9 The Power Set and the Cartesian Product.- 10 Relations.- 11 Partitions.- 12 Order in the Reals.- 13 Consequences of the Completeness of (Bbb R).- 14 Functions, Domain, and Range.- 15 Functions, One-to-One, and Onto.- 16 Inverses.- 17 Images and Inverse Images.- 18 Mathematical Induction.- 19 Sequences.- 20 Convergence of Sequences of Real Numbers.- 21 Equivalent Sets.- 22 Finite Sets and an Infinite Set.- 23 Countable and Uncountable Sets.- 24 The Cantor-Schröder-Bernstein Theorem.- 25 Metric Spaces.- 26 Getting to Know Open and Closed Sets.- 27 Modular Arithmetic.- 28 Fermat’s Little Theorem.- 29 Projects.- Appendix.- References.- Index.

Reading Writing and Proving

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    A Hardback by Ulrich Daepp

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      Book details

      Publisher Springer Nature
      Published 10 October 2025
      ISBN-13 9781071646373
      978-1071646373
      ISBN-10 1071646370
      Also in:
      Mathematical logic

      Description

      Book Synopsis

      Preface.-1 The How, When, and Why of Mathematics.- 2 Logically Speaking.- 3 Introducing the Contrapositive and Converse.- 4 Set Notation and Quantifiers.- 5 Proof Techniques.- 6 Sets.- 7 Operations on Sets.- 8 More on Operations on Sets.- 9 The Power Set and the Cartesian Product.- 10 Relations.- 11 Partitions.- 12 Order in the Reals.- 13 Consequences of the Completeness of (Bbb R).- 14 Functions, Domain, and Range.- 15 Functions, One-to-One, and Onto.- 16 Inverses.- 17 Images and Inverse Images.- 18 Mathematical Induction.- 19 Sequences.- 20 Convergence of Sequences of Real Numbers.- 21 Equivalent Sets.- 22 Finite Sets and an Infinite Set.- 23 Countable and Uncountable Sets.- 24 The Cantor-Schröder-Bernstein Theorem.- 25 Metric Spaces.- 26 Getting to Know Open and Closed Sets.- 27 Modular Arithmetic.- 28 Fermat’s Little Theorem.- 29 Projects.- Appendix.- References.- Index.

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