### 数学代写|组合学代写Combinatorics代考|MATH 393

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• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
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• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|组合学代写Combinatorics代考|Basic Combinatorial Structures

In our presentation, we shall use terms such as words, languages, etc., which have already a meaning in ordinary conversation. However, the meaning assigned to them here will be slightly different. Thus it is good to make this distinction precise before proceeding any further.

The basic terms are alphabet, letter, word, string, and language. They are defined as follows. First of all,
alphabet $=$ any finite collection of symbols.
Even though reordering the elements of a set does not change it, i.e.,
$${a, 5, b, x, c}={b, a, x, 5, c},$$
for instance, when we view these sets as alphabets, we assume that they are ordered from left to right in the order we put them down. Thus when we write the sentence
$$\text { Let } \mathcal{A}={a, 5, b, x, c} \text { be an alphabet, }$$
we shall mean not only that $\mathcal{A}$ consists of $a, 5, b, x$, and $c$ but also that as long as we work with $\mathcal{A}$,
\begin{aligned} &\text { a comes before } 5 \ &5 \text { comes before } b \ &b \text { comes before } x \ &x \text { comes before } c . \end{aligned}

## 数学代写|组合学代写Combinatorics代考|Concatenation

If $w_{1}$ and $w_{2}$ are $\mathcal{A}$-words by $w_{1} \cdot w_{2}$ or by simply $w_{1} w_{2}$, we mean the word of length $l\left(w_{1}\right)+l\left(w_{2}\right)$ obtained by placing $w_{1}$ and $w_{2}$ one after the other. Thus if $w_{1}=a c c d$ and $w_{2}=x x y$, then $w_{1} w_{2}$ is the 7-letter word
$$w_{1} w_{2}=\operatorname{accd} x x y .$$
It is customary to refer to this operation as concatenation. In fact, the same term is used when we juxtapose any number of words.

We should also mention that our dot notation $w_{1} \cdot w_{2}$ refers to the fact that concatenation has the mathematical character of multiplication.
Indeed, we can trivially see that for any triplet of words $w_{1}, w_{2}, w_{3}$, we have
$$\left(w_{1} \cdot w_{2}\right) \cdot w_{3}=w_{1} \cdot\left(w_{2} \cdot w_{3}\right) .$$
Clearly, it is immaterial whether we concatenate $w_{1}$ and $w_{2}$ and then concatenate the resulting word with $w_{3}$ or concatenate $w_{1}$ with the result of concatenating $w_{2}$ and $w_{3}$.
We might refer to (1.3) as associativity of word concatenation.

## 数学代写|组合学代写Combinatorics代考|Basic Combinatorial Structures

$$a, 5, b, x, c=b, a, x, 5, c$$

Let $\mathcal{A}=a, 5, b, x, c$ be an alphabet,

a comes before $5 \quad 5$ comes before $b b$ comes before $x \quad x$ comes before $c$.

## 数学代写|组合学代写Combinatorics代考|Concatenation

$$w_{1} w_{2}=\operatorname{accd} x x y .$$

$$\left(w_{1} \cdot w_{2}\right) \cdot w_{3}=w_{1} \cdot\left(w_{2} \cdot w_{3}\right) \text {. }$$

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。