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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
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 数学代写|离散数学作业代写discrete mathematics代考|CLASSES AND SETS. AXIOMS AND THEOREMS

So far, we have discussed propositions, denoted by $p, q$, etc. However, many symbols or combinations of symbols are not propositions. For instance, the expression $3+3=3$ is a proposition, but $x+3=3$ is not, since we cannot determine whether it is True or False, its truth value depends upon the numerical value of $x$, and it becomes a proposition if we specify the value of $x$; say, if $x=3$, we get $3+3=3$, which is a false proposition, etc. In formal theories, this distinction is important, and we call strings like $x+3=3$ propositional forms. Propositions can be represented not only by logical operations but also by other symbols; for example, $\lim _{x \rightarrow \pi / 2} \frac{\sin x}{x}=1$ is a (false) proposition. Propositions and propositional forms are together called formulas.

Similarly, symbol 3 is a name of a number, while the symbol $n$ is a name form. The names and name forms together are called terms. Formulas and terms make a frame of any formal theory. We do not study here axiomatic theories, leaving that for the formal mathematical logic. Instead, in the next lecture, we study the informal set theory. But first, we want to say a few more words about the language of formal theories.

Any collection of things, objects, possessing specified properties is called a class.

## 数学代写|离散数学作业代写discrete mathematics代考|Classical Set Theory

First of all, we describe the ways to represent the sets, to write them down on paper, or on the blackboard, or in computer memory. In the example above, we just gave a description of a class in words (All people who ever lived on the Earth). This way may be vague, and the other methods of presenting classes were developed as well. The simplest way is to write down all the elements of a set $A$, if we are able to do this. This way is called list or roster notation. For instance,
$$\begin{gathered} S_{1}={1,2,3} \ S_{2}={A, B, C, \ldots, X, Y, Z} \ \mathcal{N}={0,1,2,3, \ldots} . \end{gathered}$$
Set $S_{1}$ contains three natural numbers, set $S_{2}$ contains 26 capital letters of the English alphabet; such sets are called finite, because they contain only finite number of elements. “Finite” means that we can count all the elements of such a set using the natural (or counting) numbers, starting from 1 or from 0 and reaching but not exceeding some natural number $n$. This $n$ is called the number of elements or cardinality of the class.

For instance, in the first example, 1 is an element of the set $S_{1}, 2$ is another element, and 3 is also an element of the set $S_{1}$; what is more, $S_{1}$ contains no other element. In the second example, $A$ is the lst element of the set $S_{2}, B$ is the 2 nd element, $C$ is the 3rd element, etc., $Y$ is the 25 th element, and $Z$ is the 26 th element. We used the writing $1^{\text {st }}$ element, etc., only for convenience – an order of listing of the elements of a set does not matter. We can write the same set as $S_{2}={B, A, C, \ldots, X, Y, Z}$ or in many other ways; we shall soon discuss this issue in more detail. Because it turns out sufficient to use only the first 26 counting numbers, $S_{2}$ is a finite set containing 26 elements. The ellipsis, …, in this example shows that we just saved some space and did not write all the 26 elements of $S_{2}$ explicitly, even though in this example, we can do that.

## 数学代写|离散数学作业代写discrete mathematics代考| Classical Set Theory

$$S_{1}=1,2,3 S_{2}=A, B, C, \ldots, X, Y, Z \mathcal{N}=0,1,2,3, \ldots$$

## 有限元方法代写

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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。

assignmentutor™您的专属作业导师
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