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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|图论作业代写Graph Theory代考|Mathematical Induction

The last proof technique we review is quite useful when studying discrete objects, especially objects that can easily be transformed into ones of smaller size. Mathematical induction relies on a two step process. In the first step (sometimes referred to as the base case or basis step) we show the statement to be proved holds for a specific value or size. In the second step (called the induction step) we assume that the statement holds for some unknown value and then show the statement also holds for the next value.

The power of induction is that we are proving a statement that holds for an infinite number of objects but only need to prove two very specific items. As we will see throughout this book, graphs naturally lend themselves to induction proofs by our ability to take a graph of a specific size (usually in terms of the number of vertices or edges) and make it smaller by removing either an edge or a vertex. This technique is shown in the result. helow about. the number of edges in a complete graph.
Proposition 1.25 The complete graph $K_{n}$ has $\frac{n(n-1)}{2}$ edges.

## 数学代写|图论作业代写Graph Theory代考|Degree Sequence

As noted above, the degree of a vertex can be seen in the adjacency matrix for a graph by summing the entries along its corresponding row or column. Here we switch gears a bit to look at what conditions must be placed on a sequence of integers so that they could be the degrees of a simple graph.
Definition 1.26 The degree sequence of a graph is a listing of the degrees of the vertices. It is customary to write these in decreasing order. If a sequence is a degree sequence of a simple graph then we call it graphical.

The example above is one instance of the general question called the graph realization problem. It is easy to confirm certain sequences are not degree sequences using graph properties (such as the Handshaking Lemma or isolated vertices), but we would like to have a procedure that will always answer this question. The theorem below, attributed to the Czech mathematician Václav Havel and the Iranian-American mathematician Seifollah Louis Hakimi, provides an iterative approach to answering the graph realization problem.

# 图论代考

## 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