Alfred Tarski: Early Work in Poland--Geometry and Teaching

ISBN-13: 9781493914739 / Angielski / Twarda / 2014 / 499 str.

Andrew McFarland; Joanna McFarland; James Smith

Opis

Alfred Tarski (1901-1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic and universal algebra. Throughout his career, he taught mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now.This self-contained book focuses on Tarski's early contributions to geometry and mathematics education, including the famous Banach-Tarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy. These themes are significant since Tarski's later research on geometry and its foundations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations and much newly uncovered social background of these works written during Tarski's years in Poland.Alfred Tarski: Early Work in Poland serves the mathematical, educational, philosophical and historical communities by publishing Tarski's early writings in a broadly accessible form, providing background from archival work in Poland and updating Tarski's bibliography.

Recenzje

"The volume is richly illustrated with photographs, reproductions of artwork, copies of documents, and mathematical drawings. ... the book will be warmly welcomed by readers interested in the history and philosophy of logic. Moreover, its many fascinating and informative commentaries on the publications it contains, on the people connected with the publications, and on the relevant social and political events in Poland during the pre-war period serve to make the volume of potential appeal to a wide spectrum of readers." (Steven R. Givant, Mathematical Reviews, ams.org, January, 2016)

"This work sheds new light on mathematicians' understanding of Tarski and his work. As a scholarly contribution, it provides translations of many of Tarski's publications, especially those dealing with geometry and teaching. ... Throughout the text, the editors serve as guides who provide relevant fascinating historical details, biographical asides for many logicians and mathematicians and thorough documentation, commentary, and references as necessary. This work is a gem. ... Summing Up: Highly recommended. Upper-division undergraduates through researchers/faculty." (J. Johnson, Choice, Vol. 52 (7), March, 2015)

"With its focal point being the life and work of Alfred Tarski, this big book provides an almost an encyclopaedic account of mathematical life in Poland in the period 1920 to 1945 ... . one's motivation to proceed through the extensive amount of material is enhanced by the liveliness of its presentation. In short, it should appeal to many readers and could form a reference work for those interested in the history of early 20th century mathematics." (P. N. Ruane, MAA Reviews, January, 2015)

Spis treści

Foreword, by Ivor Grattan-Guinness.- Preface.- Illustrations.- Maps of Central Europe.- Part One: Debut.- 1 School, University, Strife.- 2 A Contribution to the Axiomatics of Well-Ordered Sets (1921).- 3 Doctoral Research.- Part Two: Geometry.- 4 Area, Volume, Measure.- 5 On the Equivalence of Polygons (1924).- 6 On Decomposition of Point Sets into Respectively Congruent Parts (1924).- 7 Degree of Equivalence of Polygons.- 8 Research Threads.- Part Three: Teaching.- 9 Career and Family.- 10 Congress of Mathematicians of Slavic Countries (1929).- 11 Circumference of a Circle (1932).- 12 Exercises Posed by Tarski.- 13 Geometry for the Third Gimnazjum Class (1935).- 14 Teaching and Logic—to the New World.- Part Four: Supplement.- 15 Assorted Contributions.- 16 Posthumous Publications.- 17 Biographical Studies.- 18 Research Surveys.- Bibliography.- Permissions.- Index of Persons.- Index of Subjects.

O autorze

James Smith, Professor für Afrika- und Entwicklungsstudien, ist Direktor des ESRC Innogen Research Centre in Edinburgh und bekleidet eine Ehrenprofessur an der Universität von Johannesburg. Er hat mit zahlreichen internationalen Organisationen zusammengearbeitet, unter anderem mit Oxfam.

Blurb

Alfred Tarski (1901–1983) was a renowned Polish/American mathematician, a giant of the twentieth century, who helped establish the foundations of geometry, set theory, model theory, algebraic logic, and universal algebra. Throughout his career, he taught mathematics and logic at universities and sometimes in secondary schools. Many of his writings before 1939 were in Polish and remained inaccessible to most mathematicians and historians until now.

This self-contained book focuses on Tarski’s early contributions to geometry and mathematics education, including the famous Banach–Tarski paradoxical decomposition of a sphere as well as high-school mathematical topics and pedagogy. These themes are significant since Tarski’s later research on geometry and its foundations stemmed in part from his early employment as a high-school mathematics teacher and teacher-trainer. The book contains careful translations and much newly uncovered social background of these works written during Tarski’s years in Poland.

Alfred Tarski: Early Work in Poland—Geometry and Teaching serves the mathematical, educational, philosophical, and historical communities by publishing Tarski’s early writings in a broadly accessible form, providing background from archival work in Poland, and updating Tarski’s bibliography.