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Ships from the UK. Former Library book. 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. Dickson earned a B. Dickson first specialised in Halsted's own specialty, geometry.
In , 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. In 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 , and he spent the balance of his career there. At Chicago, he supervised 53 Ph.
He was a visiting professor at the University of California in , , and In , he returned to Texas to retire. Dickson was the first recipient of a prize created in by The American Association for the Advancement of Science, for his work on the arithmetics of algebras. Harvard and Princeton awarded him honorary doctorates. Dickson presided over the American Mathematical Society in — His December presidential address, titled "Mathematics in War Perspective," criticized American mathematics for falling short of those of Britain, France, and Germany:.
Up to this point, nothing has been said about inequalities in Z[i]. Thus any two expansions of x agree in the first partial quotient, and we can subtract this common part and go on to the next partial quotient, where the uniqueness argument can be repeated. Convert currency. These examples show also that the strong distinction between real and complex numbers sometimes disappears in this "modular" arithmetic, since -1 already has a square root mod 5! It can be read independently of the preceding volume, which explores divisibility and primality, and volume III, which examines quadratic and higher forms. Just as in the preceding chapter, we call the product aa the norm of a, and write N a , or simply Na. Dickson worked on finite fields and extended the theory of linear associative algebras initiated by Joseph Wedderburn and Cartan.
In , he was also the first recipient of the Cole Prize for algebra, awarded annually by the AMS, for his book Algebren und ihre Zahlentheorie. Dickson had a major impact on American mathematics, especially abstract algebra. His mathematical output consists of 18 books and more than papers.
History of the Theory of Numbers, Volume II: Diophantine Analysis (Dover Books on Mathematics) Paperback . Series: Dover Books on Mathematics (Book 2). History of the Theory of Numbers, Volume II: Diophantine Analysis (Dover Books on Mathematics) Hardcover . Series: Dover Books on Mathematics (Book 2).
In , Dickson published his first book Linear groups with an exposition of the Galois field theory , a revision and expansion of his Ph. Teubner in Leipzig published the book, as there was no well-established American scientific publisher at the time. Indexes of authors cited and subjects appear at the end of the book.
Selected pages Page 2. Title Page. Table of Contents. History of the Theory of Numbers: 3 Leonard E. Dickson No preview available -