### 计算机代写|计算机图形学代写computer graphics代考|CS559

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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

## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System

Over recent millennia, mankind has invented and discarded many systems for representing number. People have counted on their fingers and toes, used pictures (hieroglyphics), cut marks on clay tablets (cuneiform symbols), employed Greek symbols (Ionic system) and struggled with, and abandoned Roman numerals (I, V, X, L, C, D, M, etc.), until we reach today’s decimal place system, which has Hindu-Arabic and Chinese origins. And since the invention of computers we have witnessed the emergence of binary, octal and hexadecimal number systems, where 2, 8 and 16 respectively, replace the 10 in our decimal system.

The decimal number 23 stands for ‘two tens and three units’, and in English is written ‘twenty-three’, in French ‘vingt-trois’ (twenty-three), and in German ‘dreiundzwanzig’ (three and twenty). Let’s investigate the algebra behind the decimal system and see how it can be used to represent numbers to any base. The expression:
$$a \times 1000+b \times 100+c \times 10+d \times 1$$
where $a, b, c, d$ take on any value between 0 and 9 , describes any whole number between 0 and 9999 . By including
$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$
where $e, f, g, h$ take on any value hetween 0 and 9 , any decimal number hetween 0 and $9999.9999$ can be represented.
Indices bring the notation alive and reveal the true underlying pattern:
$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots$$
Remember that any number raised to the power 0 equals 1 . By adding extra terms both left and right, any number can be accommodated.

In this example, 10 is the base, which means that the values of $a$ to $h$ range between 0 and 9,1 less than the base. Therefore, by substituting $B$ for the base we have
$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$
where the values of $a$ to $h$ range between 0 and $B-1$.

## 计算机代写|计算机图形学代写computer graphics代考|Binary Numbers

The binary number system has $B=2$, and $a$ to $h$ are 0 or 1 :
$$\ldots a 2^3+b 2^2+c 2^1+d 2^0+e 2^{-1}+f 2^{-2}+g 2^{-3}+h 2^{-4} \ldots$$
and the first 13 binary numbers are:
$$1_2, 10_2, 11_2, 100_2, 101_2, 110_2, 111_2, 1000_2, 1001_2, 1010_2, 1011_2, 1100_2, 1101_2 \text {. }$$
Thus $11011.11_2$ is converted to decimal as follows:
$$\begin{gathered} \left(1 \times 2^4\right)+\left(1 \times 2^3\right)+\left(0 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right)+\left(1 \times 2^{-1}\right)+\left(1 \times 2^{-2}\right) \ (1 \times 16)+(1 \times 8)+(0 \times 4)+(1 \times 2)+(1 \times 0.5)+(1 \times 0.25) \ (16+8+2)+(0.5+0.25) \ 26.75 \end{gathered}$$
The reason why computers work with binary numbers-rather than decimal-is due to the difficulty of designing electrical circuits that can store decimal numbers in a stable fashion. A switch, where the open state represents 0, and the closed state represents 1, is the simplest electrical component to emulate. No matter how often it is used, or how old it becomes, it will always behave like a switch. The main advantage of electrical circuits is that they can be switched on and off trillions of times a second, and the only disadvantage is that the encoded binary numbers and characters contain a large number of bits, and humans are not familiar with binary.

## 计算机代写|计算机图形学代写computer graphics代考|The Base of a Number System

$$a \times 1000+b \times 100+c \times 10+d \times 1$$

$$e \times 0.1+f \times 0.01+g \times 0.001+h \times 0.0001$$

$$\ldots a 10^3+b 10^2+c 10^1+d 10^0+e 10^{-1}+f 10^{-2}+g 10^{-3}+h 10^{-4} \ldots$$

$$\ldots a B^3+b B^2+c B^1+d B^0+e B^{-1}+f B^{-2}+g B^{-3}+h B^{-4} \ldots$$

## 计算机代写|计算机图形学代写computer graphics代考|Binary Numbers

$$\ldots a 2^3+b 2^2+c 2^1+d 2^0+e 2^{-1}+f 2^{-2}+g 2^{-3}+h 2^{-4} \ldots$$

$$1_2, 10_2, 11_2, 100_2, 101_2, 110_2, 111_2, 1000_2, 1001_2, 1010_2, 1011_2, 1100_2, 1101_2 .$$

$$\left(1 \times 2^4\right)+\left(1 \times 2^3\right)+\left(0 \times 2^2\right)+\left(1 \times 2^1\right)+\left(1 \times 2^0\right)+\left(1 \times 2^{-1}\right)+\left(1 \times 2^{-2}\right)(1 \times 16)$$

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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。