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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|Application of Vector Spaces to Coding Theory

The representation of codewords in coding theory (which is discussed in Chap. 11) is by $n$-dimensional vectors over the finite field $F_q$. A codeword vector $v$ is represented as the $n$-tuple:
$$v=\left(a_0, a_1, \ldots a_{n-1}\right)$$
where each $a_i \in F_q$. The set of all $n$-dimensional vectors is the $n$-dimensional vector space $\mathbf{F}^n{ }q$ with $q^n$ elements. The addition of two vectors $v$ and $w$, where $v=\left(a_0, a_1, \ldots a{n-1}\right)$ and $w=\left(b_0, b_1, \ldots b_{n-1}\right)$, is given by
$$v+w=\left(a_0+b_0, a_1+b_1, \ldots a_{n-1}+b_{n-1}\right) .$$
The scalar multiplication of a vector $v=\left(a_0, a_1, \ldots a_{n-1}\right) \in \mathrm{F}q^n$ by a scalar $\beta \in$ $F_q$ is given by $$\beta v=\left(\beta a_0, \beta a_1, \ldots \beta a{n-1}\right) .$$
The set $\mathbf{F}^n{ }_q$ is called the vector space over the finite field $\mathrm{F}_q$ if the vector space properties above hold. A finite set of vectors $v_1, v_2, \ldots v_k$ is said to be linearly independent if
$$\beta_1 v_1+\beta_2 v_2+\cdots+\beta_k v_k=0 \quad \Rightarrow \quad \beta_1=\beta_2=\cdots \beta_k=0 .$$
Otherwise, the set of vectors $v_1, v_2, \ldots v_k$ is said to be linearly dependent.
A non-empty subset $W$ of a vector space $V(W \subseteq V)$ is said to be a subspace of $\mathrm{V}$, if $W$ forms a vector space over $F$ under the operations of $V$. This is equivalent to $W$ being closed under vector addition and scalar multiplication: i.e. $w_1, w_2 \in$ $W, \alpha, \beta \in F$ then $\alpha w_1+\beta w_2 \in W$.

The dimension $(\operatorname{dim} W)$ of a subspace $W \subseteq V$ is $k$ if there are $k$ linearly independent vectors in $W$ but every $k+1$ vectors are linearly dependent. A subset of a vector space is a basis for $V$ if it consists of linearly independent vectors, and its linear span is $V$ (i.e. the basis generates $V$ ). We shall employ the basis of the vector space of codewords (see Chap. 11) to create the generator matrix to simplify the encoding of the information words. The linear span of a set of vectors $v_1, v_2, \ldots, v_k$ is defined as $\beta_1 v_1+\beta_2 v_2+\cdots+\beta_k v_k$.

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

Automata Theory is the branch of computer science that is concerned with the study of abstract machines and automata. These include finite-state machines, pushdown automata and Turing machines. Finite-state machines are abstract machines that may be in one of a finite number of states. These machines are in only one state at a time (current state), and the input symbol causes a transition from the current state to the next state. Finite-state machines have limited computational power due to memory and state constraints, but they have been applied to a number of fields including communication protocols, neurological systems and linguistics.

Pushdown automata have greater computational power than finite-state machines, and they contain extra memory in the form of a stack from which symbols may be pushed or popped. The state transition is determined from the current state of the machine, the input symbol and the element on the top of the stack. The action may be to change the state and/or push/pop an element from the stack.

The Turing machine is the most powerful model for computation, and this theoretical machine is equivalent to an actual computer in the sense that it can compute exactly the same set of functions. The memory of the Turing machine is a tape that consists of a potentially infinite number of one-dimensional cells. The Turing machine provides a mathematical abstraction of computer execution and storage, as well as providing a mathematical definition of an algorithm. However, Turing machines are not suitable for programming, and therefore they do not provide a good basis for studying programming and programming languages.

# 离散数学代写

## 数学代写|离散数学作业代写离散数学代考|向量空间在编码理论中的应用

.

$$v=\left(a_0, a_1, \ldots a_{n-1}\right)$$
where each $a_i \in F_q$。所有的集合 $n$-维向量是 $n$-维向量空间 $\mathbf{F}^n{ }q$ 用 $q^n$ 元素。两个向量的加法 $v$ 和 $w$，其中 $v=\left(a_0, a_1, \ldots a{n-1}\right)$ 和 $w=\left(b_0, b_1, \ldots b_{n-1}\right)$，由

$$\beta_1 v_1+\beta_2 v_2+\cdots+\beta_k v_k=0 \quad \Rightarrow \quad \beta_1=\beta_2=\cdots \beta_k=0 .$$

## 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