Discrete Mathematics

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SI120 Discrete Mathematics. This course will focus on the basic notions, theories, methods and applications of discrete structures. It will cover four important topics in discrete mathematics: mathematical logic, elementary number theory, Combinatorial counting techniques, and graph theory. This course will provide solid mathematical foundations for many future courses. Logic plays an important role in programming, artificial intelligence, database theory, theory of computation and compiler design. Number theory and related algorithms are central to modern cryptography. The techniques of combinatorial counting are useful for obtaining formulas and estimates in algorithm analysis. Graphs and trees are fundamental tools in software engineering.

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Discrete Mathematics

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L02 – Equivalence, Congruence, and Residue Class

L02 – Equivalence, Congruence, and Residue Class

本文主要介绍了离散数学中的等价关系、同余及剩余类概念。文章阐述了等价关系的性质与划分，定义了模n同余及其运算规则，并探讨了剩余类环Zn和可逆元群Zn*的结构与性质。

Discrete Mathematics # 数学基础 # 数论基础 # 模运算

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L01 – Fundamental theorem of arithmetic, the well-ordering property, division algorithm, ideal,greatest common divisor, and Bézout’s theorem

L01 – Fundamental theorem of arithmetic, the well-ordering property, division algorithm, ideal,greatest common divisor, and Bézout’s theorem

本文主要阐述了初等数论的基础内容，包括整除性、素数与合数、算术基本定理及其证明、带余除法、理想的概念与性质，以及最大公约数和 Bézout 定理等核心概念和重要定理。

Discrete Mathematics # 密码学基础 # 数学基础 # 数据分析

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