McFarland, Andrew, McFarland, Joanna, Smith, James (Eds.)
2014, XXIII, 499 p. 126 illus., 10 illus. in color.
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Unique compilation of papers from Alfred Tarki's early years as a mathematician and logician
Contains material which has previously been inaccessible to mathematicians and historians of mathematics
Evaluates and reflects upon Alfred Taski's early writings
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.
Content Level »Professional/practitioner
Keywords »Alfred Tarski - analytic geometry - degree of equivalence of polygons - high school geometry - symbolic logic - theory of deduction - well-ordered sets
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.