The foundations of mathematics /
Stewart, Ian, 1945-
The foundations of mathematics / Ian Stewart and David Tall. - Second Edition. - xvi, 391 pages : illustrations ; 23 cm.
Includes index.
Includes bibliographical references (pages 383-385).
Part I. The intuitive background -- Mathematical thinking -- Number systems -- Part II. The beginnings of formalisation -- Sets -- Relations -- Functions -- Mathematical logic -- Mathematical proof -- Part III. The development of axiomatic systems -- Natural numbers and proof by induction -- Real numbers -- Real numbers as a complete ordered field -- Complex numbers and beyond -- Part IV. Using axiomatic systems -- Axiomatic systems, structure theorems, and flexible thinking -- Permutations and groups -- Cardinal numbers -- Infinitesimals -- Part V. Strengthening the foundations -- Axioms for set theory.
The transition from school to university mathematics is seldom straightforward. Students face a schism between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates
9780198706434 (pbk.) 019870643X (pbk.)
2014946122
Logic, Symbolic and mathematical
Lógica simbólica y matemática
QA9 / .S755 2015
511.3
The foundations of mathematics / Ian Stewart and David Tall. - Second Edition. - xvi, 391 pages : illustrations ; 23 cm.
Includes index.
Includes bibliographical references (pages 383-385).
Part I. The intuitive background -- Mathematical thinking -- Number systems -- Part II. The beginnings of formalisation -- Sets -- Relations -- Functions -- Mathematical logic -- Mathematical proof -- Part III. The development of axiomatic systems -- Natural numbers and proof by induction -- Real numbers -- Real numbers as a complete ordered field -- Complex numbers and beyond -- Part IV. Using axiomatic systems -- Axiomatic systems, structure theorems, and flexible thinking -- Permutations and groups -- Cardinal numbers -- Infinitesimals -- Part V. Strengthening the foundations -- Axioms for set theory.
The transition from school to university mathematics is seldom straightforward. Students face a schism between the algorithmic and informal attitude to mathematics at school, versus a new emphasis on proof, based on logic, and a more abstract development of general concepts, based on set theory. The authors have many years' experience of the potential difficulties involved, through teaching first-year undergraduates
9780198706434 (pbk.) 019870643X (pbk.)
2014946122
Logic, Symbolic and mathematical
Lógica simbólica y matemática
QA9 / .S755 2015
511.3