Posted on Categories:Modern Algebra, 数学代写, 现代代数

# 数学代写|现代代数代考Modern Algebra代写|GEOMETRIC CONSTRUCTIONS

## avatest™帮您通过考试

avatest™的各个学科专家已帮了学生顺利通过达上千场考试。我们保证您快速准时完成各时长和类型的考试，包括in class、take home、online、proctor。写手整理各样的资源来或按照您学校的资料教您，创造模拟试题，提供所有的问题例子，以保证您在真实考试中取得的通过率是85%以上。如果您有即将到来的每周、季考、期中或期末考试，我们都能帮助您！

•最快12小时交付

•200+ 英语母语导师

•70分以下全额退款

## 数学代写|现代代数代考Modern Algebra代写|GEOMETRIC CONSTRUCTIONS

Among the geometric construction problems left unsolved by the ancient Greeks, three became especially famous. Each involved the construction of one geometrical segment from another, using only unmarked straightedge and compass (Figure 5):
I. Construct the edge of a cube having twice the volume of a given cube.
II. Show that every angle can be trisected.
III. Construct the side of a square having the same area as a circle of given radius.
These problems remained unsolved for more than 2000 years. Then, in the nineteenth century, it was proved that the constructions are impossible. What makes this interesting for us is that although the constructions were to be geometric, the proofs of their impossibility involve algebra. And the key algebraic concepts needed are the same as those used to analyze solvability by radicals; these include facts about fields that go far beyond what is necessary to characterize the familiar number systems.

## 数学代写|现代代数代考Modern Algebra代写|NUMBER THEORY

The motivation for studying some of the deeper properties of rings came from a source totally different from the applications already mentioned. Pythagorean triples are triples $(x, y, z)$ of positive integers such that $x^2+y^2=z^2$. That is, they are the triples of integers that can occur as lengths of sides of right triangles (relative to an appropriate unit of length). Examples are $(3,4,5),(5,12,13),(8,15,17)$, and (199, 19800, 19801). The Greek mathematician Diophantus derived a method for determining all such triples around A.D. 250. (The Babylonians had determined many Pythagorean triples by much the same method around 1500 B.C.) In reading about this problem in Diophantus’s book Arithmetica, the French mathematician Pierre de Fermat (1601-1665) was led to introduce one of the most famous problems in mathematics: Are there nonzero integers $x, y, z$ such that
$$x^n+y^n=z^n$$
for any integer $n>2$ ? Actually, Fermat claimed that there are no such integers, and this claim eventually came to be known as Fermat’s Last Theorem. But Fermat did not give a proof of his claim, and the problem of constructing a proof defied some of the world’s best mathematicians for over 350 years.

Fermat’s Last Theorem was finally proved in 1994 by Andrew Wiles of Princeton University. The proof by Wiles, who was born in Cambridge, England, and educated at Cambridge University, is extremely complicated and draws on ideas developed by other mathematicians over many years. Nothing in the statement of the theorem suggests the depth of the ideas required for its proof. For a hint at these ideas, see Section 41. For an interesting history of Fermat’s Theorem and the work of Wiles, as well as an insight into mathematics as a creative process, see the book Fermat’s Enigma, by Simon Singh, which is listed at the end of this Introduction.

In the book by Singh, Wiles is quoted as saying that “the definition of a good mathematical problem is the mathematics it generates rather then the problem itself.” This brings out an important lesson from the history of mathematics, namely that attempts to solve problems, both successful and unsuccessful, have been responsible for the development of the subject. In particular, attempts to solve Fermat’s Last Theorem have had a profound effect on number theory and algebra.

# 现代代数代写

## 数学代写|现代代数代考Modern Algebra代写|GEOMETRIC CONSTRUCTIONS

2证明每个角都可以被三等分。
3构造一个面积与给定半径的圆相同的正方形的边。
2000多年来，这些问题一直没有得到解决。然后，在19世纪，人们证明这种结构是不可能的。让我们感兴趣的是，尽管这些构造是几何的，但证明它们的不可能涉及到代数。所需要的关键代数概念与用来分析根式可解性的代数概念是相同的;这些包括关于字段的事实，这些事实远远超出了描述熟悉的数字系统所必需的。

## 数学代写|现代代数代考Modern Algebra代写|NUMBER THEORY

$$x^n+y^n=z^n$$

1994年，普林斯顿大学的安德鲁·怀尔斯终于证明了费马大定理。怀尔斯出生在英国剑桥，并在剑桥大学接受教育，他的证明极其复杂，并借鉴了其他数学家多年来发展起来的思想。在这个定理的陈述中，没有任何东西表明证明它所需要的思想的深度。有关这些思想的提示，请参见第41节。关于费马定理和怀尔斯工作的有趣历史，以及对数学作为一个创造性过程的见解，请参阅西蒙·辛格(Simon Singh)所著的《费马谜》(Fermat’s Enigma)一书，该书列在本介绍的末尾。

avatest.org 为您提供可靠及专业的论文代写服务以便帮助您完成您学术上的需求，让您重新掌握您的人生。我们将尽力给您提供完美的论文，并且保证质量以及准时交稿。除了承诺的奉献精神，我们的专业写手、研究人员和校对员都经过非常严格的招聘流程。所有写手都必须证明自己的分析和沟通能力以及英文水平，并通过由我们的资深研究人员和校对员组织的面试。

## 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。