History of Modern Mathematics

by David Eugene Smith

Overview

Introduction Theory of Numbers Irrational and Transcendent Numbers Complex Numbers Quaternions and Ausdehnungslehre Theory of Equations Substitutions and Groups Determinants Quantics Calculus Differential Equations Infinite Series Theory of Functions Probabilities and Least Squares Analytic Geometry Modern Geometry Elementary Geometry Non-Euclidean Geometry Bibliography General Tendencies

Product Details

ISBN-13:	9788180940491
Publisher:	Mjp Publishers
Publication date:	10/10/2008
Series:	History of Modern Mathematics , #4
Pages:	126
Product dimensions:	5.50(w) x 8.50(h) x 0.30(d)

About the Author

David Eugene Smith (1860 - 1944) was an American mathematician, educator, and editor.

David Eugene Smith is considered one of the founders of the field of mathematics education. Smith was born in Cortland, New York, to Abram P. Smith, attorney and surrogate judge, and Mary Elizabeth Bronson, who taught her young son Latin and Greek.

He attended Syracuse University, graduating in 1881 (Ph. D., 1887; LL.D., 1905). He studied to be a lawyer concentrating in arts and humanities, but accepted an instructorship in mathematics at the Cortland Normal School in 1884 where he attended as a young man. While at the Cortland Normal School Smith became a member of the Young Men's Debating Club (today the Delphic Fraternity.)

He became a professor at the Michigan State Normal College in 1891 (later Eastern Michigan University), the principal at the State Normal School in Brockport, New York (1898), and a professor of mathematics at Teachers College, Columbia University (1901) where he remained until his retirement in 1926.

Smith became president of the Mathematical Association of America in 1920 and served as the president of the History of Science Society in 1927. He also wrote a large number of publications of various types. He was editor of the Bulletin of the American Mathematical Society; contributed to other mathematical journals; published a series of textbooks; translated Felix Klein's Famous Problems of Geometry, Fink's History of Mathematics, and the Treviso Arithmetic. He edited Augustus De Morgan's A Budget of Paradoxes (1915) and wrote many books on Mathematics.

Read an Excerpt

IRRATIONAL AND TRANSCENDENT NUMBERS. 13 To Gauss is also due the representation of numbers by binary quadratic forms. Cauchy, Poinsot (1845), Lebesque (1859, 1868), and notably Hermite have added to the subject. In the theory of ternary forms Eisenstein has. been a leader, and to him and H. J. S. Smith is also due a noteworthy advance in the theory of forms in general. Smith gave a com- plete classification of ternary quadratic forms, and extended Gauss's researches concerning real quadratic forms to complex forms. The investigations concerning the representation of numbers by the sum of 4, 5, 6, 7, 8 squares were advanced by Eisenstein and the theory was completed by Smith. In Germany, Dirichlet was one of the most zealous workers in the theory of numbers, and was the first to lecture upon the subject in a German university. Among his contributions is the extension of Fermat's theorem on xn -f-y = z", which Euler and Legendre had proved for = 3, 4, Dirichlet showing that xb--y az. Among the later French writers are Borel; Poincare, whose memoirs are numerous and valuable; Tannery, and Stieltjes. Among the leading contributors in Germany are Kronecker, Kummer, Schering, Bachmann, and Dedekind. In Austria Stolz's Vorlesungen iiber allgemeine Arithmetik (1885-86)," and in England Mathews' Theory of Numbers (Part I, 1892) are among the most scholarly of general works. Genocchi, Sylvester, and J. W. L. Glaisher have also added to the theory. Art. .3. Irrational And Transcendent Numbers. The sixteenth century saw the final acceptance of negative numbers, integral and fractional. The seventeenth century saw decimal fractions with the modern notation quite generally used bymathematicians. The next hundred years saw the imaginary become a powerful tool in the hands of De Mo...