数学代写|现代代数代写Modern Algebra代考|MATH 612

Doug I. Jones

Lorem ipsum dolor sit amet, cons the all tetur adiscing elit

couryes-lab™ 为您的留学生涯保驾护航 在代写现代代数Modern Algebra方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写现代代数Modern Algebra代写方面经验极为丰富，各种代写现代代数Modern Algebra相关的作业也就用不着说。

• 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
couryes™为您提供可以保分的包课服务

数学代写|现代代数代写Modern Algebra代考|Topological Groups, Lie Groups and Hopf Groups

An abstract group endowed with an additional structure having its group operations (multiplication and inversion) compatible with the additional structure, invites further attraction. Some of such groups are studied in this section. For example, we study topological groups, Lie groups and Hopf groups which are very important in topology, geometry, and physics. Topological groups were first considered by S. Lie (1842-1899). A topological group is a topological space whose elements form an abstract group such that the group operations are continuous with respect to the topology of the space. A Lie group is a topological group having the structure of a smooth manifold for which the group operations are smooth functions. On the other hand, a Hopf group (H-group) is a pointed topological space with a continuous multiplication such that it satisfies all the axioms of a group up to homotopy. The concept of an $H$-group is a generalization of the concept of topological groups. Lie groups are an important branch of group theory. The importance of Lie groups lies in the fact that Lie groups include almost all important groups of geometry and analysis. The theory of Lie groups stands at the crossing point of the theories of differential manifolds, topological groups, and Lie algebras.

数学代写|现代代数代写Modern Algebra代考|Topological Groups

Definition 2.9.1 A topological group $G$ is a non-empty set with a group structure and a topology on $G$ such that the function $f: G \times G \rightarrow G,(x, y) \mapsto x y^{-1}$ is continuous.
The above condition of continuity is equivalent to the statement:
The functions $G \times G \rightarrow G,(x, y) \mapsto x y$ and $G \rightarrow G, x \mapsto x^{-1}$ are both continuous.
Some important examples of topoological groups.
Example $2.9 .1$ (i) $(\mathbf{R},+)$, under usual addition of real numbers and with the topology induced by the Euclidean metric $d(x, y)=|x-y|$.
(ii) The circle group $\left(S^{1}, \cdot\right)$ in $\mathbf{C}$, topologized by considering it as a subset of $\mathbf{R}^{2}$.
(iii) $\left(\mathbf{R}^{n},+\right)$, under usual coordinatewise addition and with product topology.
(iv) $(G L(n, \mathbf{R}), \cdot)$, undêr usual multiplication of reeal matricês ând with thè Euclidean subspace topology of $\mathbf{R}^{n^{2}}(n>1)$.
(v) The orthogonal group $(O(n),-)$ of real matrices with the Euclidean subspace topology $(n>1)$. It is a subgroup of $G L(n, \mathbf{R})$.

(vi) The general linear group $(G L(n, \mathbf{C}), \cdot)$ over $\mathbf{C}$ topologized by considering it as a subspace of $\mathbf{R}^{2 n^{2}}$.
(vii) $(U(n), \cdot)$ of all $n \times n$ complex matrices $A$ such that $A \bar{A}^{T}=I$. It is a subgroup of $G L(n, \mathbf{C})$.

现代代数代考

数学代写|现代代数代写Modern Algebra代考|Topological Groups

$f: G \times G \rightarrow G,(x, y) \mapsto x y^{-1}$ 是连续的。

(ii) 圏子组 $\left(S^{1}, \cdot\right)$ 在 $\mathbf{C}$, 通过将其视为的子集进行拓扑 $\mathbf{R}^{2}$.
$(\xi)\left(\mathbf{R}^{n},+\right)$ ，在通常的坐标加法和乘积拓扑下。
(四) $(G L(n, \mathbf{R}), \cdot)$, 在实矩阵的通常乘法下 ând 与欧几里得子空间拓扑 $\mathbf{R}^{n^{2}}(n>1)$.
(v) 正交组 $(O(n),-)$ 欧几里得子空间拓扑的实矩阵 $(n>1)$. 它是一个子群 $G L(n, \mathbf{R})$
(vi) 一般线性群 $(G L(n, \mathbf{C}), \cdot)$ 超过 $\mathbf{C}$ 通过将其视为的子空间进行拓扑 $\mathbf{R}^{2 n^{2}}$. (七) $(U(n), \cdot)$ 其中 $n \times n$ 复杂矩阵 $A$ 这样 $A \bar{A}^{T}=I$. 它是一个子群 $G L(n, \mathbf{C})$

有限元方法代写

tatistics-lab作为专业的留学生服务机构，多年来已为美国、英国、加拿大、澳洲等留学热门地的学生提供专业的学术服务，包括但不限于Essay代写，Assignment代写，Dissertation代写，Report代写，小组作业代写，Proposal代写，Paper代写，Presentation代写，计算机作业代写，论文修改和润色，网课代做，exam代考等等。写作范围涵盖高中，本科，研究生等海外留学全阶段，辐射金融，经济学，会计学，审计学，管理学等全球99%专业科目。写作团队既有专业英语母语作者，也有海外名校硕博留学生，每位写作老师都拥有过硬的语言能力，专业的学科背景和学术写作经验。我们承诺100%原创，100%专业，100%准时，100%满意。

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。

Days
Hours
Minutes
Seconds

15% OFF

On All Tickets

Don’t hesitate and buy tickets today – All tickets are at a special price until 15.08.2021. Hope to see you there :)