First Course in the Theory of Equations (Classic Reprint) - Softcover

Campbell, Rev. Eugene

Softcover

ISBN 10: 1451001460 ISBN 13: 9781451001464

Publisher: Forgotten Books, 2012

Synopsis

The theonof equations is not only a necessity in the subsequent mathematical courses and their apphcations, but furnishes an illuminating sequel to geometry-, algebra and analytic geometn .M oreover, it develops anew and in greater detail various fundamental ideas of calculus for the simple, but important, case of poh-nomials. The theon, of equations therefore affords a useful supplement to differential calculus whether taken subsequentlj or simultaneoush .I twas to meet the numerous needs of the student in regard to his earU er and future mathematical courses that the present book was planned with great care and after wide consultation. It differs essentially from the authors Elementary Theory of Equations, both in regard to omissions and additions, and since it is addressed to younger students and Tna.y be used parallel with a course in differential calculus. Simpler and more detailed proofs are now emplo ed. The exercises are simpler, more numerous, of greater variety, and involve more practical apphcations. This book throws important Ught on various elementarjtopics. For example, an alert student of geometrj who has learned how to bisect any angle is apt to ask if everjangle can be trisected with ruler and compasses and if not, whj not. After learning how to construct regular polygons of 3, 4, 5, 6, 8and 10 sides, he wiU be inquisitive about the missing ones of 7and 9sides. The teacher will be in a comfortable position if he knows the facts and what is involved in the simplest discussion to date of these questions, as given inC hapter III. Other chapters throw needed hght on various topics of algebra. In particular, the theory of graphs is presented inC hapter Vin a more scientific and practical manner than was possible in algebra and anah tic geometry. There is developed a method of computing a real root of an equation with minimum labor and with certai
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About this title

About the Author

Leonard Eugene Dickson (1874 – 1954) was an American mathematician. He was one of the first American researchers in abstract algebra, in particular the theory of finite fields and classical groups, and is also remembered for a three-volume history of number theory, History of the Theory of Numbers. Dickson considered himself a Texan by virtue of having grown up in Cleburne, where his father was a banker, merchant, and real estate investor. He attended the University of Texas at Austin, where George Bruce Halsted encouraged his study of mathematics. Dickson earned a B.S. in 1893 and an M.S. in 1894, under Halsted's supervision. Dickson first specialised in Halsted's own specialty, geometry. Both the University of Chicago and Harvard University welcomed Dickson as a Ph.D. student, and Dickson initially accepted Harvard's offer, but chose to attend Chicago instead. In 1896, when he was only 22 years of age, he was awarded Chicago's first doctorate in mathematics, for a dissertation titled The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group, supervised by E. H. Moore. Dickson then went to Leipzig and Paris to study under Sophus Lie and Camille Jordan, respectively. On returning to the USA, he became an instructor at the University of California. In 1899 and at the extraordinarily young age of 25, Dickson was appointed associate professor at the University of Texas. Chicago countered by offering him a position in 1900, and he spent the balance of his career there. At Chicago, he supervised 53 Ph.D. theses; his most accomplished student was probably A. A. Albert. He was a visiting professor at the University of California in 1914, 1918, and 1922. In 1939, he returned to Texas to retire. Dickson was elected to the National Academy of Sciences in 1913, and was also a member of the American Philosophical Society, the American Academy of Arts and Sciences, the London Mathematical Society, the French Academy of Sciences and the Union of Czech Mathematicians and Physicists. Dickson was the first recipient of a prize created in 1924 by The American Association for the Advancement of Science, for his work on the arithmetics of algebras. Harvard (1936) and Princeton (1941) awarded him honorary doctorates.

Edition details

• Publisher: Forgotten Books
• Publication date: 2012
• Language: English
• ISBN 10: 1451001460
• ISBN 13: 9781451001464
• Binding: Paperback
• Number of pages: 176