An Outline of Set Theory

As philosophers still debate the appropriateness of set theory in general and ZF in particular as a basis for mathematics, yet another group has begun questioning the very need for a foundation. Mathematics is not in need of definition, ...

An Outline of Set Theory

This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable to ordinary mathematics majors. I use a recent modification of R. L. Moore's famous method developed in recent years by D. W. Cohen [1]. Briefly, in this new approach, projects are assigned to groups of students each week. With all the necessary assistance from the instructor, the groups complete their projects, carefully write a short paper for their classmates, and then, in the single weekly class meeting, lecture on their results. While the em phasis is on the student, the instructor is available at every stage to assure success in the research, to explain and critique mathematical prose, and to coach the groups in clear mathematical presentation. The subject matter of set theory is peculiarly appropriate to this style of course. For much of the book the objects of study are familiar and while the theorems are significant and often deep, it is the methods and ideas that are most important. The necessity of rea soning about numbers and sets forces students to come to grips with the nature of proof, logic, and mathematics. In their research they experience the same dilemmas and uncertainties that faced the pio neers.

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An Outline of Set Theory
Language: en
Pages: 146
Authors: James M. Henle
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

This book is designed for use in a one semester problem-oriented course in undergraduate set theory. The combination of level and format is somewhat unusual and deserves an explanation. Normally, problem courses are offered to graduate students or selected undergraduates. I have found, however, that the experience is equally valuable
Sets and integration An outline of the development
Language: en
Pages: 162
Authors: D. van Dalen
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

The present text resulted from lectures given by the authors at the Rijks Universiteit at Utrecht. These lectures were part of a series on 'History of Contemporary Mathematics'. The need for such an enterprise was generally felt, since the curriculum at many universities is designed to suit an efficient treatment
An Outline of Mathematical Logic
Language: en
Pages: 596
Authors: A. Grzegorczyk
Categories: Philosophy
Type: BOOK - Published: 2013-03-07 - Publisher: Springer Science & Business Media

Recent years have seen the appearance of many English-Ianguage hand books of logie and numerous monographs on topieal discoveries in the foundations of mathematies. These publications on the foundations of mathematies as a whole are rather difficult for the beginners or refer the reader to other handbooks and various pieeemeal
An Outline of Ergodic Theory
Language: en
Pages:
Authors: Steven Kalikow, Randall McCutcheon
Categories: Mathematics
Type: BOOK - Published: 2010-03-25 - Publisher: Cambridge University Press

This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory, proofs of fundamental ergodic theorems, and material on entropy, martingales, Bernoulli processes,
Handbook of Set Theory
Language: en
Pages: 2230
Authors: Matthew Foreman, Akihiro Kanamori
Categories: Mathematics
Type: BOOK - Published: 2009-12-10 - Publisher: Springer Science & Business Media

Numbers imitate space, which is of such a di?erent nature —Blaise Pascal It is fair to date the study of the foundation of mathematics back to the ancient Greeks. The urge to understand and systematize the mathematics of the time led Euclid to postulate axioms in an early attempt to