• 记录一些数学世界留下璀璨般印记的大数学家。

    Hi, welcome to Mathematics world!

     

    让我们踏上历史小火车, 回到那个纯粹的年代, 回顾那一颗颗人类史上的璀璨明星。

  • Georg Cantor

    March 3.1845 - January 6. 1918

    German mathematician

    He created set theory, which has become a fundamental theory in mathematics. Cantor established the importance of one-to-one correspondence between the members of two sets, defined infinite and well-ordered sets, and proved that the real numbers are more numerous than the natural numbers.

     

    Cantor's work between 1874 and 1884 is the origin of set theory. No one had realized that set theory had any nontrivial content before Cantor.

     

    Cantor retired in 1913, living in poverty and suffering from malnourishment during World War I. Georg Cantor had a fatal heart attack on January 6, 1918, in the sanatorium where he had spent the last year of his life.

     

     

    于集合论来说, 我个人喜欢这句话。

     

    在集合论的基础上,现代数学有两大家族:分析(Analysis)和代数(Algebra)。

    John von Neumann

    Dec.28 1903 - Feb.8 1957

     

    "

    It seems fair to say that if the influence of scientist is interpreted broadly enough to include impact on fields beyond science proper, then John von Neumann was probably the most influential mathematician.

    "

     

    His mathematical legacy is deeply profound that I wish you go to his page:

     

    https://en.wikipedia.org/wiki/John_von_Neumann#Mathematical_legacy

     

    In 1955, von Neumann was diagnosed with what was either bone or pancreatic cancer. He died at age 53 on February 8, 1957.

     

     

     

    1940年后, 人类进入计算时代。

     

    von Neumann 则是帮人们推开门的那个人。

  • 数学分析与实变函数

    实数完备性、函数、极限、连续性

    微积分(黎曼积分、勒贝格积分、多元积分)

     

  • 线性代数

    线性空间, 内积, 范数(L1,L2),正交性... ...

    特征值与特征向量、矩阵对角化

     

     

    施密特正交化(Gram-Schimidt orthogonalization)

     

     

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