翻訳言語

Statistics of a Distribution on Unitary Matrices

MathOverflow上で、ユニタリ行列上の特定の確率分布（Haar測度に関連する分布など）の統計的性質について議論された質問。回答では、行列の固有値分布、トレースのモーメント、あるいはランダム行列理論における大偏差原理などが話題となっている可能性がある。

Three examples suffice
1.0
A blog post discusses a mathematical identity where pentagonal numbers can be expressed in terms of triangular numbers. It highlights that while examples don't typically prove theorems, in this case the identity Pn = T(2n−1) − T(n−1) holds, showing that three examples can suffice for proving certain relationships.
Pulling on a thread
0.5
John D. Cook describes how a sequence of his blog posts often follows a hidden thread, beginning with a post about the mathematical approximation exp(−x²) ≈ (1 + cos(sin(x) + x))/2, which some commenters incorrectly attributed solely to a first-order Taylor expansion.
Testing pentagonal numbers
0.5
The nth pentagonal number Pn follows the formula Pn = (3n² − n)/2 for positive integer n. For non-positive integer n, the same formula defines a generalized pentagonal number.
Partial fraction decomposition
0.3
Partial fraction decomposition is commonly introduced in calculus as a technique for integrating rational functions by breaking P(x)/Q(x) into simpler terms. However, the post suggests that this method has applications beyond integration that are often overlooked in a typical calculus class.

翻訳言語

Three examples suffice
1.0
A blog post discusses a mathematical identity where pentagonal numbers can be expressed in terms of triangular numbers. It highlights that while examples don't typically prove theorems, in this case the identity Pn = T(2n−1) − T(n−1) holds, showing that three examples can suffice for proving certain relationships.
Pulling on a thread
0.5
John D. Cook describes how a sequence of his blog posts often follows a hidden thread, beginning with a post about the mathematical approximation exp(−x²) ≈ (1 + cos(sin(x) + x))/2, which some commenters incorrectly attributed solely to a first-order Taylor expansion.
Testing pentagonal numbers
0.5
The nth pentagonal number Pn follows the formula Pn = (3n² − n)/2 for positive integer n. For non-positive integer n, the same formula defines a generalized pentagonal number.
Partial fraction decomposition
0.3
Partial fraction decomposition is commonly introduced in calculus as a technique for integrating rational functions by breaking P(x)/Q(x) into simpler terms. However, the post suggests that this method has applications beyond integration that are often overlooked in a typical calculus class.

関連記事