# 学习 Galois 理论须知的群论概念

Abelian Group. A group in which multiplication is commutative.

Alternating Group $A_n$. The subgroup of $S_n$ consisting of all the even permutations. it has order $\frac{1}{2}n!$.

Associativity. For all $x,y,z$, one has $(xy)z=x(yz)$. it follows that one does not need parentheses for any product of three or more factors.

Automorphism. An isomorphism of a group with itself.

Commutativity. For all $x,y$, one has $xy=yx$.

# 学习方法论-如何阅读数学文献

• 养成灵活的阅读习惯——对于一个主题，尽可能阅读多种不同的处理方法；
• 阅读应当是一个动态的过程——应当做一个主动的阅读者，在阅读的同时带上纸笔，以供随时检查书本上内容，验证作者所声称的命题的正确性。

# 每日一言 - 5月31日言

The theory of Fourier series and integrals has always had major difficulties and necessitated a large mathematical apparatus in dealing with questions of convergence. It engendered the development of methods of summation, although these did not lead to a completely satisfactory solution of the problem…. For the Fourier transform, the introduction of distributions (hence the space $\mathscr{S}$) is inevitable either in an explicit or hidden form…. As a result one may obtain all that is desired from the point of view of the continuity and inversion of the Fourier transform.

*L. Schwartz*, 1950