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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|抽象代数作业代写abstract algebra代考|Historical Note

We conclude this chapter with a bit of history concerning the noncommutativity of matrix multiplication. In 1925, quantum theory was replete with annoying and puzzling ambiguities. It was Werner Heisenberg who recognized the cause. He observed that the product of the quantum-theoretical analogs of the classical Fourier series did not necessarily commute. For all his boldness, this shook Heisenberg. As he later recalled [2, p. 94]:

In my paper the fact that $X Y$ was not equal to $Y X$ was very disagreeable to me. I felt this was the only point of difficulty in the whole scheme, otherwise I would be perfectly happy. But this difficulty had worried me and I was not able to solve it.
Heisenberg asked his teacher, Max Born, if his ideas were worth publishing. Born was fascinated and deeply impressed by Heisenberg’s new approach. Born wrote [1, p. 217]:
After having sent off Heisenberg’s paper to the Zeitschrift für Physik for publication, I began to ponder over his symbolic multiplication, and was soon so involved in it that I thought about it for the whole day and could hardly sleep at night. For I felt there was something fundamental behind it, the consummation of our endeavors of many years. And one morning, about the 10 July 1925 , I suddenly saw light: Heisenberg’s symbolic multiplication was nothing but the matrix calculus, well-known to me since my student days from Rosanes’ lectures in Breslau.

## 数学代写|抽象代数作业代写abstract algebra代考|Terminology and Notation

As we will soon discover, finite groups-that is, groups with finitely many elements – have interesting arithmetic properties. To facilitate the study of finite groups, it is convenient to introduce some terminology and notation.
Definition Order of a Group
The number of elements of a group (finite or infinite) is called its order. We will use $|G|$ to denote the order of $G$.

Thus, the group $\mathrm{Z}$ of integers under addition has infinite order, whereas the group $U(10)={1,3,7,9}$ under multiplication modulo 10 has order $4 .$
Definition Order of an Element
The order $g$ in a group $G$ is the smallest positive integer $n$ such that $g^{n}=e$. (In additive notation, this would be $n g=$
0.) If no such integer exists, we say that $g$ has infinite order. The order of an element $g$ is denoted by $|g|$.

So, to find the order of a group element $g$, you need only compute the sequence of products $g, g^{2}, g^{3}, \ldots$, until you reach the identity for the first time. The exponent of this product (or coefficient if the operation is addition) is the order of $g$. If the identity never appears in the sequence, then $g$ has infinite order.

## 数学代写|抽象代数作业代写abstract algebra代考| Terminology and Notation

0.）如果不存在这样的整数，我们说g具有无限顺序。元素的顺序g表示为|g|.

## 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
assignmentutor™您的专属作业导师