初等数论课程笔记

这学期的“信息安全数学基础”课程利用初等数论, 引出了抽象代数中的基本概念, 让我们像是读目录一样, 粗浅地了解了抽象代数的知识体系. 已经到了学期末, 我回顾了一遍整个课程, 将笔记整理在此篇博文中.

离散数学课程笔记

后天是离散数学考试, 临时赶出一篇离散数学笔记(其实只能算是结论的堆砌), 以便自己随时查看.

初等数论习题

最近学校在教“信息安全数学基础”这门课程, 目前讲到了数论的基础知识. 我选择了 Kenneth H. Rosen 著作的《初等数论及其应用》作为辅助教材, 阅读过程中理解了一些有趣的结论, 证明和习题.

Secretary Problem

“Imagine there are eight roses in your garden; you inspect them one-by-one randomly. Take the first three roses you encounter as sample and go on. Once you encounter a rose more beautiful than any of the first three roses, you pick it up and stop. How likely is it that the one you picked up is the most beautiful one?”

Concrete Mathematics Notes

I have finished reading the first two chapters of Concrete Mathematics. Here are my notes on the book and solutions to the exercises.

Miller–Rabin 素性测试

整理了 Miller–Rabin 素性测试的原理及实现方法.