雷奥那德·尤金·迪克逊
生平
迪克逊虽出生于爱荷华,但因为自幼在德州克利班成长,所以迪克逊自认自己是德州人。迪克逊的父亲同时是银行家、商人以及不动产投资者。迪克逊大学就读德州大学奥斯汀分校,受乔治·布鲁斯·赫尔斯泰德教授的鼓励下,迪克逊以数学为其专业。1893年时,迪克逊获得学士学位。1894年时,在乔治·布鲁斯·赫尔斯泰德教授的指导下,迪克逊获得硕士学位。迪克逊起先的研究方向受其导师影响,主要是在几何学方面。
芝加哥大学与哈佛大学都力争迪克逊入读其博士班。起先迪克逊决定入哈佛大学,但最终决定入芝加哥大学。1896年时,时年仅22岁的迪克逊,获得了芝加哥大学颁发的第一个数学博士学位。迪克逊的博士论文由埃利亚金·哈斯廷斯·穆尔(英语:E. H. Moore)指导,论文题目是 The Analytic Representation of Substitutions on a Power of a Prime Number of Letters with a Discussion of the Linear Group。
迪克逊在取得博士学位后,便赴德国莱比锡与法国巴黎先后访学于索菲斯·李与卡米尔·若尔当门下。返美后,迪克逊至加州大学赴任讲师。1899年,时年仅25岁的迪克逊,获德州大学之聘为该校的副教授。
工作
迪克逊对于美国数学有相当大的影响,特别是在抽象代数的研究。迪克逊在数学研究上相当多产,一生出版了18本书以及250篇以上的论文。《迪克逊全集》(Collected Mathematical Papers of Leonard Eugene Dickson)总共是六大册。
数论学家
迪克逊证明了数论中许多有趣的结果。他利用了维诺格拉朵夫的结果,在加性数论方面,解决了理想华林问题。
迪克逊所著的三巨册《数论史(英语:History of the Theory of Numbers)》(History of the Theory of Numbers)(1919–23) 至今仍是数论史研究的重要参考资料,全书内容涵盖了整除理论、质数理论、丢番图分析、二次型以及高次型式。迪克逊在《数论史》中,对于理论的介绍较为简略,亦未完整阐述理论的来龙去脉,然而此书最为精要的部分在于,此书详述了从古至1920年代一路发展过程当中每一个数论概念的想法,但对于二次互反律与高次互反律则未多加着墨。虽已预定撰写第四册的计划,但迪克逊却未完成。
亚伯拉罕·阿德利安·艾尔伯特(英语:Abraham Adrian Albert) 对此三卷书评价道:"would be a life"s work by itself for a more ordinary man."
其他
杨武之(华人物理学家杨振宁之生父)曾跟随其研究代数学和数论。
参考资料
Dickson, Leonard Eugene, Magnus, Wilhelm, 编,Linear groups: With an exposition of the Galois field theory, Dover Phoenix editions, New York: Dover Publications, 1958 [1901], ISBN 978-0-486-49548-4, MR 0104735
Dickson, Leonard Eugene,Introduction to the theory of algebraic equations, New York: John Wiley and sons, 1903 [1903]
Dickson, Leonard Eugene,Linear algebras, Reprinting of Cambridge Tracts in Mathematics and Mathematical Physics, No. 16, Naub press, 2010 [1914], ISBN 978-1-178-36805-5, MR 0118745
Dickson, Leonard Eugene,Algebraic invariants, Cornell University Library, 2010 [1914], ISBN 978-1-4297-0042-9
Dickson, Leonard Eugene,On invariants and the theory of numbers, Dover Phoenix editions, New York: Dover Publications, 2004 [1914], ISBN 978-0-486-43828-3, MR 0201389
Dickson, Leonard Eugene,Elementary theory of equations, Cornell University Library, 2009 [1914], ISBN 978-1-112-27988-1
Dickson, Leonard Eugene,History of the theory of numbers. Vol. I: Divisibility and primality., New York: Dover Publications, 2005 [1919], ISBN 978-0-486-44232-7, MR 0245499
Dickson, Leonard Eugene,History of the theory of numbers. Vol. II: Diophantine analysis, New York: Dover Publications, 2005 [1920], ISBN 978-0-486-44233-4, MR 0245500
Dickson, Leonard Eugene,History of the theory of numbers. Vol. III: Quadratic and higher forms, New York: Dover Publications, 2005 [1923], ISBN 978-0-486-44234-1, MR 0245501
Dickson, Leonard Eugene,First course in the theory of equations, University of Michigan Library, 2009 [1922]
Dickson, Leonard Eugene,Algebras and their arithmetics, New York: Dover Publications, 1960 [1923], ISBN 978-0-486-60616-3, MR 0111764
1926. Modern algebraic theories
1923, 1928. Algebraic Numbers. Report with others for U. S. National Research Council.
1929. Introduction to the Theory of Numbers
1930. Studies in the Theory of Numbers
1935. (with G. A. Bliss) "Biographical Memoir of Eliakim Hastings Moore 1862–1932."
1935. Researches on Waring"s problem
1938. (with H. F. Blichfeldt and G. A. Miller) Theory and Applications of Finite Groups
1938. Algebras And Their Arithmetics (t edn. in 1923)
1939. Modern Elementary Theory of Numbers
1939. New First Course in the Theory of Equations
Plane Trigonometry With Practical Applications
Dickson, Leonard Eugene, Albert, A. Adrian, 编,The collected mathematical papers of Leonard Eugene DicksonI–VI, New York: AMS Chelsea Publishing, 1975, ISBN 978-0-8284-0273-6, MR 0749229
参看
Cayley–Dickson sedenions或十六元数
参考文献
Fenster, D. D., 1997, "Role modeling in mathematics: the case of Leonard Eugene Dickson (1874–1954)," Historia Mathematica 24: 7–24.
Karen Parshall, 1983, "In pursuit of the finite division algebra theorem and beyond: Joseph H M Wedderburn, Leonard Dickson, and Oswald Veblen," Archives of International History of Science 33: 274–99.
--------, 1991, "A study in group theory: Leonard Eugene Dickson"s Linear groups," Mathematical Intelligencer 13: 7–11.
--------, 1999, "Leonard Eugene Dickson" in American National Biography, vol. 6. Oxford Univ. Press: 578–79.
O"Connor, John J.; Robertson, Edmund F.,Dickson,MacTutor History of Mathematics archive(英语)
Leonard Eugene Dickson在数学谱系计划的资料。
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