计算机代写|计算机图形学作业代写computer graphics代考|Numbers

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我们提供的计算机图形学computer graphics及其相关学科的代写,服务范围广, 其中包括但不限于:

  • Statistical Inference 统计推断
  • Statistical Computing 统计计算
  • Advanced Probability Theory 高等楖率论
  • Advanced Mathematical Statistics 高等数理统计学
  • (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|计算机图形学作业代写computer graphics代考|Numbers

计算机代写|计算机图形学作业代写computer graphics代考|Background

Over the centuries mathematicians have realised that in order to progress, they must give precise definitions to their discoveries, ideas and concepts, so that they can be built upon and referenced by new mathematical inventions. In the event of any new discovery, these rrrdefinitions have to be occasionally changed or extended. For example, once upon a time integers, rational and irrational numbers, satisfied all the needs of mathematicians, until imaginary quantities were invented. Today, complex numbers have helped shape the current number system hierarchy. Consequently, there must be clear definitions for numbers, and the operators that act upon them. Therefore, we need to identify the types of numbers that exist, what they are used for, and any problems that arise when they are stored in a computer.

计算机代写|计算机图形学作业代写computer graphics代考|Counting

Our brain’s visual cortex possesses some incredible image processing features. For example, children know instinctively when they are given less sweets than another child, and adults know instinctively when they are short-changed by a Parisian taxi driver, or driven around the Arc de Triumph several times, on the way to the airport! Intuitively, we can assess how many donkeys are in a field without counting them,

and generally, we seem to know within a second or two, whether there are just a few, dozens, or hundreds of something. But when accuracy is required, one can’t beat counting. But what is counting?

Well normally, we are taught to count by our parents by memorising first, the counting words ‘one, two, three, four, five, six, seven, eight, nine, ten, ..’ and second, associating them with our fingers, so that when asked to count the number of donkeys in a picture book, each donkey is associated with a counting word. When each donkey has been identified, the number of donkeys equals the last word mentioned. However, this still assumes that we know the meaning of ‘one, two, three, four,..’ etc. Memorising these counting words is only part of the problem-getting them in the correct sequence is the real challenge. The incorrect sequence ‘one, two, five, three, nine, four, ..’ etc., introduces an element of randomness into any calculation, but practice makes perfect, and it’s useful to master the correct sequence before going to university!

计算机代写|计算机图形学作业代写computer graphics代考|Sets of Numbers

A set is a collection of arbitrary objects called its elements or members. For example, each system of number belongs to a set with given a name, such as $\mathbb{N}$ for the natural numbers, $\mathbb{R}$ for real numbers, and $\mathbb{Q}$ for rational numbers. When we want to indicate that something is whole, real or rational, etc., we use the notation:
n \in \mathbb{N}
x \in \mathbb{R}
stands for ‘ $x$ is a real number.’
A well-ordered set possesses a unique order, such as the natural numbers $\mathbb{N}$. Therefore, if $P$ is the well-ordered set of prime numbers and $\mathbb{N}$ is the well-ordered set of natural numbers, we can write:
&P={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47, \ldots} \
&\mathbb{N}={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17, \ldots}
By pairing the prime numbers in $P$ with the numbers in $\mathbb{N}$, we have:
{{2,1},{3,2},{5,3},{7,4},{11,5},{13,6},{17,7},{19,8},{23,9}, \ldots}
and we can reason that 2 is the lst prime, and 3 is the 2 nd prime, etc. However, we still have to declare what we mean by $1,2,3,4,5, \ldots$ etc., and without getting too philosophical, I like the idea of defining them as follows. The word ‘one’, represented

by 1, stands for ‘oneness’ of anything: one finger, one house, one tree, one donkey, etc. The word ‘two’, represented by 2 , is ‘one more than one’. The word ‘three’, represented by 3 , is ‘one more than two’, and so on.

We are now in a position to associate some mathematical notation with our numbers by introducing the $+$ and $=$ signs. We know that $+$ means add, but it also can stand for ‘more’. We also know that = means equal, and it can also stand for ‘is the same as’. Thus the statement:
is read as ‘two is the same as one more than one.’
We can also write:
which is read as ‘three is the same as one more than two.’ But as we already have a definition for 2 , we can write
3 &=1+2 \
Developing this idea, and including some extra combinations, we have:
&2=1+1 \
&3=1+2 \
&4=1+3=2+2 \
&5=1+4=2+3 \
&6=1+5=2+4=3+3 \
and can be continued without limit. These numbers, $1,2,3,4,5,6$, etc., are called natural numbers, and are the set $\mathbb{N}$.

计算机代写|计算机图形学作业代写computer graphics代考|Numbers


计算机代写|计算机图形学作业代写computer graphics代考|Background

几个世纪以来,数学家们已经意识到,为了取得进步,他们必须对他们的发现、想法和概念给出精确的定义,这样他们才能被新的数学发明所建立和引用。如果有任何新发现,则必须偶尔更改或扩展这些 rrr 定义。例如,曾几何时,整数、有理数和无理数满足了数学家的所有需求,直到虚数被发明出来。今天,复数帮助塑造了当前的数字系统层次结构。因此,必须有明确的数字定义,以及作用于它们的运算符。因此,我们需要识别存在的数字类型、它们的用途以及它们存储在计算机中时出现的任何问题。

计算机代写|计算机图形学作业代写computer graphics代考|Counting




计算机代写|计算机图形学作业代写computer graphics代考|Sets of Numbers

代表 ‘X是一个实数。
良序集具有唯一的顺序,例如自然数ñ. 因此,如果磷是素数的良序集,并且ñ是有序的自然数集,我们可以写成:
磷=2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,… ñ=1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,…
通过将素数配对磷与数字ñ, 我们有:
我们可以推断出 2 是第一个素数,3 是第二个素数,等等。但是,我们仍然必须声明我们的意思1,2,3,4,5,…等等,而且不用太哲学化,我喜欢将它们定义如下的想法。“一”字,代表

用 1 表示任何事物的“一体性”:一根手指、一栋房子、一棵树、一头驴等。由 2 表示的“二”一词是“多于一”。用 3 表示的单词“三”是“一多二”,依此类推。

读作“三等于一多二”。但是因为我们已经有了 2 的定义,所以我们可以写
3=1+2 =1+1+1
2=1+1 3=1+2 4=1+3=2+2 5=1+4=2+3 6=1+5=2+4=3+3 7=1+6=2+5=3+4

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术语 广义线性模型(GLM)通常是指给定连续和/或分类预测因素的连续响应变量的常规线性回归模型。它包括多元线性回归,以及方差分析和方差分析(仅含固定效应)。



有限元是一种通用的数值方法,用于解决两个或三个空间变量的偏微分方程(即一些边界值问题)。为了解决一个问题,有限元将一个大系统细分为更小、更简单的部分,称为有限元。这是通过在空间维度上的特定空间离散化来实现的,它是通过构建对象的网格来实现的:用于求解的数值域,它有有限数量的点。边界值问题的有限元方法表述最终导致一个代数方程组。该方法在域上对未知函数进行逼近。[1] 然后将模拟这些有限元的简单方程组合成一个更大的方程系统,以模拟整个问题。然后,有限元通过变化微积分使相关的误差函数最小化来逼近一个解决方案。





随机过程,是依赖于参数的一组随机变量的全体,参数通常是时间。 随机变量是随机现象的数量表现,其时间序列是一组按照时间发生先后顺序进行排列的数据点序列。通常一组时间序列的时间间隔为一恒定值(如1秒,5分钟,12小时,7天,1年),因此时间序列可以作为离散时间数据进行分析处理。研究时间序列数据的意义在于现实中,往往需要研究某个事物其随时间发展变化的规律。这就需要通过研究该事物过去发展的历史记录,以得到其自身发展的规律。


多元回归分析渐进(Multiple Regression Analysis Asymptotics)属于计量经济学领域,主要是一种数学上的统计分析方法,可以分析复杂情况下各影响因素的数学关系,在自然科学、社会和经济学等多个领域内应用广泛。


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。



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