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Proofs and Fundamentals: A First Course in Abstract Mathematics

Ethan D. Bloch
Publisher: 
Springer
Publication Date: 
2011
Number of Pages: 
359
Format: 
Hardcover
Edition: 
2
Series: 
Undergraduate Texts in Mathematics
Price: 
74.95
ISBN: 
9781441971265
Category: 
Textbook
[Reviewed by
Fernando Q. Gouvêa
, on
03/3/2011
]

See David P. Roberts' review of the first edition (2000). Besides the move from Birkhäuser to Springer's Undergraduate Texts in Mathematics series, the main change for this edition is that the original chapter 8, which started from the Peano axioms and included constructions of the integers and the rationals, has been removed. The author says that this "was always somewhat out of place given the level and scope of this text." This material has moved to Bloch's (forthcoming?) The Real Numbers and Real Analysis (Springer 2011).

Several other changes have been made:

  • A survey section on the Zermelo-Fraenkel axioms for set theory has been added.
  • The chapter about cardinality has been rearranged and expanded.
  • The treatment of families of sets has been modified to remove the assumption that families are indexed.
  • The standard notations for direct and inverse image of a set under a function have been adopted (despite the loss of clarity this implies).
  • A new section on sequences and convergence has been added.
  • A new section called "You Are the Professor" has been added. This includes sample "proofs" collected from actual homework assignments, giving the reader the opportunity to read and critique them.

 

Preface to the Second Edition Preface to the First Edition To the Student To the Instructor Part I. Proofs 1. Informal Logic 2. Strategies for Proofs Part II. Fundamentals 3. Sets 4. Functions 5. Relations 6. Finite and Infinite Sets Part III. Extras 7. Selected Topics 8. Explorations Appendix: Properties of Numbers Bibliography Index

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