Power, Simplicity and Beauty
I’ve just received a book named Development of Elliptic Functions According to Ramanujan by K Venkatachaliengar (deceased) , edited by: ShaunCooper , Shaun Cooper This unique book provides an innovative …
Development of Elliptic Functions According to Ramanujan Read MoreSrinivasa Ramanujan(December 22, 1887 – April 26, 1920)的贤名, 不仅仅是因为他出色的数学才能, 罕有的数学直觉, 还因为他在贫瘠的土壤挣扎, 而留下的关于社会制度与教育制度的话题. 关于 Ramanujan(拉马努金) 的生平, 最好的传记应该是 The Man Who Knew Infinity, 中文书名是知无涯者. 今年, Springer 出版了两本关于 Ramanujan 的书. 第一本是 The Mathematical Legacy of Srinivasa …
Srinivasa Ramanujan Read MoreFor which positive integers \(a, b, c, d\), any natural number \(n\) can be represented as \[n=ax^2+by^2+cz^2+dw^2,\] where \(x, y,z,w\) are integers? Lagrange’s four-square theorem states that \((a,b,c,d)=(1,1,1,1)\) works. Ramanujan …
Generalisations of Lagrange’s four-square theorem Read MoreBertrand’s postulate states that if \(x\geq4\), then there always exists at least one prime \(p\) with\(x<p<2x-2\). A weaker but more elegant formulation is: for every \(x>1\) there is always at least one prime p such that \(x<p<2x\). In …
Ramanujan’s proof of Bertrand’s postulate Read More