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# 数学代写|抽象代数代写Abstract Algebra代考|Math417 What is abstract about Abstract Algebra?

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## 数学代写|抽象代数代写Abstract Algebra代考|What is abstract about Abstract Algebra?

Abstract Algebra is abstract in the same sense in which other Auman thinking is abstract: its concepts can be instantiated in ple ways. For instance, you recognize things like trees and You can do that because you understand the abstract ideas ‘tree’ ‘window’, and you can match them to objects in the world. You do not need to look at one tree to identify another; you do it by reference to the abstract idea.

Now, trees and windows are physical objects-you can walk up and touch them, and identify them by sight. But you can think about concepts that are more abstract, too. For instance, you can identify an aunt. You do that by reference to a criterion: is this a female person with a sibling who has children? If yes, it’s an aunt. If no, it’s not. Moreover, you can think about abstract concepts that are not single objects, like family. A family includes multiple people-perhaps many-who are related to one another-genetically or by marriage or by other caring relationships. Families vary a lot, and you couldn’t necessarily recognize a family by sight or by checking simple criteria. But you nevertheless understand the idea.

Abstract Algebra is about concepts that are somewhat like each of these more abstract ideas. They are like aunts in that they are defined by criteria. Abstract Algebra is stricter, though. Everyday human concepts, even defined ones like ‘aunt’, tend to be used flexibly. Is your mum’s brother’s female partner your aunt? Maybe, maybe not. And where I grew up, adult female neighbours and friends were commonly referred to as ‘Auntie’, even where there were no family relationships. Such flexibility doesn’t happen in Abstract Algebra, because mathematical concepts are specified by precise definitions about which all mathematicians agree. ${ }^1$

## 数学代写|抽象代数代写Abstract Algebra代考|What is algebraic about Abstract Algebra?

To understand what is algebraic about Abstract Algebra, it is probably useful to consider what is algebraic about earlier algebra. Many students think of algebra as something you do, where doing algebra means manipulating an expression or equation in valid ways to arrive at another. This is often in service of a goal: solving a mechanics problem, say. And thinking of algebra in this way is not wrong-certainly it captures most students’ experience prior to undergraduate mathematics. But it is not enough to grasp the aims of Abstract Algebra.

Abstract Algebra focuses not on performing algebraic manipulations but on understanding the mathematical structures that make those manipulations valid. To see what I mean, consider this algebraic argument (the arrow ‘ $\Rightarrow$ ‘ means ‘implies’).
\begin{aligned} & x(x+y)=y x \ & \Rightarrow x^2+x y-y x=0 \ & \Rightarrow \quad x^2=0 \ & \Rightarrow \quad x=0 \text {. } \ & \end{aligned}

## 数学代写|抽象代数代写Abstract Algebra代考|What is algebraic about Abstract Algebra?

$$x(x+y)=y x \quad \Rightarrow x^2+x y-y x=0 \Rightarrow \quad x^2=0 \quad \Rightarrow \quad x=0$$

## 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。