This is an elementary text, aimed at first-year undergraduates, which has
been designed to bridge the gap between school and university mathematics
and to emphasise the importance of proofs - both how to follow a proof and
how to construct a proof. The book lays the foundation for most of the key
subjects studied in an undergraduate degree program, and provides numerous
exercises and a bibliography with suggestions for further and background
reading.
Rezensionen / Stimmen
From the reviews:
"It took me a while to appreciate the need for a course intended to introduce mathematics undergraduates to advanced mathematics after they finish the calculus sequence. . This was the first book I found that seems really close to the core. It is well-written and very well suited to such a course." (James M. Cargal, UMAP Journal, Vol. 31 (1), 2010)
Reihe
Auflage
1st ed. 1998. Corr. 2nd printing 1998
Sprache
Verlagsort
Verlagsgruppe
Zielgruppe
Für höhere Schule und Studium
Lower undergraduate
Illustrationen
Maße
Höhe: 235 mm
Breite: 178 mm
Dicke: 11 mm
Gewicht
ISBN-13
978-3-540-76123-5 (9783540761235)
DOI
10.1007/978-1-4471-0603-6
Schweitzer Klassifikation
1. Numbers.- 1.1 Arithmetic Progressions.- 1.2 Proof by Contradiction.- 1.3 Proof by Contraposition.- 1.4 Proof by Induction.- 1.5 Inductive Definition.- 1.6 The Well-ordering Principle.- 2. Logic.- 2.1 Propositions.- 2.2 Truth Tables.- 2.3 Syllogisms.- 2.4 Quantifiers.- 3. Sets.- 3.1 Introduction.- 3.2 Operations.- 3.3 Laws.- 3.4 The Power Set.- 4. Relations.- 4.1 Equivalence Relations.- 4.2 Congruences.- 4.3 Number Systems.- 4.4 Orderings.- 5. Maps.- 5.1 Terminology and Notation.- 5.2 Examples.- 5.3 Injections, Surjections and Bijections.- 5.4 Peano's Axioms.- 6. Cardinal Numbers.- 6.1 Cardinal Arithmetic.- 6.2 The Cantor-Schroeder-Bernstein theorem.- 6.3 Countable Sets.- 6.4 Uncountable Sets.- Solutions to Exercises.- Guide to the Literature.- Dramatis Personae.
