## 数学代写|数学建模代写math modelling代考|MATH3102

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|Takagi Group

The Takagi group is focused on development and security evaluation of nextgeneration cryptographic systems, which will be resistant against attacks using quantum computers. In particular, the group will study algorithms for solving the mathematical problems underlying such systems, including the shortest vector problem on lattices (SVP) and solving systems of multivariate quadratic equations over a finite field (MQ problem). The group will also study the impact of attackers possessing massive computational resources by conducting corresponding cryptanalytic experiments with major mathematical problems underlying the above-mentioned cryptographic systems. Finally, the group will determine the possibility of using nextgeneration high-performance cryptographic systems in a real-world environment by building their software implementations and evaluating their performances.

Lattice-Based Cryptography: Yuan et al. presented efficient implementations of lattice-based cryptography using JavaScript, particularly, the learning with errors (LWE)-based encryptions such as Regev05 and LPR11 [19]. This paper received the Outstanding Paper in the Third International Symposium on Computing and Networking (CANDAR’15). Kudo et al. then analyzed the hardness of the LWE problem by the key recovery attack when the modulus was relatively large [20]. We also participated in the lattice challenge contest from TU Darmstadt and solved the shortest vector prublem of 625 dimensions in $2^{24.0} \mathrm{~s}$ using a single CPU core [21]. As a joint study with the Wakayama group, Okumura et al. investigated the security of lattice-based encryption proposed by Garg-Gentry-Halevi [22].

## 数学代写|数学建模代写math modelling代考|Wakayama Group

The safety of RSA encryption, which is based on the computational intractability of the prime factorization, is no longer ensured if a large-scale quantum computers become a possibility. Quantum interaction models, such as the quantum Rabi model, are used in a basic element of quantum computers. The Wakayama group will study the mathematical structure of such models. Among them, noncommutative harmonic oscillators $(\mathrm{NcHOs}[34,35])$ are thought to be universal models. The group will focus on extending the existing theory and methodology on $\mathrm{NcHOs}$ and clarifying the structure of models treated in quantum optics from various viewpoints-representation theory, number theory, functional analysis, and dynamical systems. The group will also develop an efficient method of conducting extensive numerical experiments by using systems of orthogonal functions to verify the deep Riemann hypothesis (DRH [36-38]) for various types of zeta and L-functions. Furthermore, the group will study the DRH and its relation to post-quantum cryptography along with new constructions of Ramanujan graphs through $\mathrm{L}$-functions by using probability theory and combinatorial theory.

Spectral Problem of NcHO: The Wakayama group studied NcHOs using the methodology of number theory, representation theory, analytic differential equations, and investigated the spectrum of NcHOs, the general Rabi model, and their rotation wave approximation model via representation theory. The group obtained the following results. (1) Hiroshima and Sasaki showed the simplicity of the ground state of the $\mathrm{NcHO}$ [39]. (2) Wakayama described the Heun differential equation of the spectrum problem of NcHOs for the even eigenvalue function [40]. (3) Employing the representation theoretical method developed in [41], Wakayama recently proved [42] the spectral degeneracies for the asymmetric quantum Rabi model demonstrated numerically by Li-Bachelor [43]. (4) Sugiyama obtained the meromorphic continuation of the spectral zeta functions for quantum Rabi models as the first step of the number theoretic approaches for deep understanding of the spectrum of these models [44].

## 数学代写|数学建模代写math modelling代考|Takagi Group

Takagi 小组专注于下一代密码系统的开发和安全评估，该系统将抵抗使用量子计算机的攻击。特别是，该小组将研究解决此类系统背后的数学问题的算法，包括格上的最短向量问题 (SVP) 和有限域上的多元二次方程的求解系统 (MQ 问题)。该小组还将通过对上述密码系统背后的主要数学问题进行相应的密码分析实验，研究拥有大量计算资源的攻击者的影响。最后，

## 数学代写|数学建模代写math modelling代考|Wakayama Group

NcHO的谱问题：和歌山小组使用数论、表示论、解析微分方程的方法研究了NcHO，并通过表示论研究了NcHO的谱、一般Rabi模型及其旋转波近似模型。该小组获得了以下结果。(1) Hiroshima 和 Sasaki 展示了基态的简单性ñCH○[39]。(2) Wakayama 描述了偶特征值函数的 NcHOs 谱问题的 Heun 微分方程[40]。(3) Wakayama 最近利用 [41] 中开发的表示理论方法证明了 [42] Li-Bachelor [43] 数值证明的不对称量子 Rabi 模型的光谱简并性。(4) Sugiyama 获得了量子 Rabi 模型的谱 zeta 函数的亚纯延展，这是深入理解这些模型的谱的数论方法的第一步[44]。

## 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。

## 数学代写|数学建模代写math modelling代考|MAT3104

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|Recent Developments of Mathematical Cryptography

Modern cryptography has been used for not only the narrow purposes of preventing eavesdropping over telecommunications but also wide-range security applications such as protecting intellectual property and privacy-preserving computation on encrypted data. In the 1980 s and $90 \mathrm{~s}$, public key cryptography based on the difficulty of factoring large integers started to be used for enciphering data or digital signatures. From the 1990 s to the early 2000 s, ID-based encryption based on elliptic curves and bilinear pairing has been used. Recently, the use of cryptography have been expanded to virtual currency, program obfuscation, privacy-protecting technology, etc. To construct such high-functional cryptography and analyze its security, we need novel mathematical theories such as representation theory, mathematical physics, multivariate polynomial theory, and lattice theory as well as advanced number theory. Therefore, mathematical theories required for cryptography have markedly progressed due to the expansion of cryptographic applications.

We now consider the criteria necessary for the mathematical modeling of modern cryptography by listing the historical developments of cryptanalysis (see Fig. 2).
(1) In the 1980s, the integer factorization algorithm and discrete logarithm problem were focused as mathematical problems that underpin the security of public key cryptography. As a result, the number field sieve [6], elliptic curve method [7], and lattice basis reduction algorithm [8] have been developed, and computational number theory was established as a new subject of mathematics.

## 数学代写|数学建模代写math modelling代考|Research Groups and Their Activities

There are four groups in this research project. We explain the main research activities of each group. All project members in the CREST Crypto-Math project are shown in Fig.3. The principal investigator is Tsuyoshi Takagi from the Institute of Mathematics for Industry, Kyushu University. The co-principal investigators are Masato Wakayama (Institute of Mathematics for Industry, Kyushu University), Keisuke Tanaka (Graduate School of Information Science and Engineering, Tokyo Institute of Technology), and Noboru Kunihiro (Graduate School of Frontier Sciences, University of Tokyo). In this CREST Crypto-Math project, 25 mathematicians including 4 postdocs are working on the new mathematical problems arisen from post-quantum cryptography. See the Fig. 4 for overview of research topics in each group.

## 数学代写|数学建模代写math modelling代考|Recent Developments of Mathematical Cryptography

(1) 在 1980 年代，整数分解算法和离散对数问题作为支撑公钥密码学安全性的数学问题而受到关注。于是，数域筛[6]、椭圆曲线法[7]、格基约简算法[8]相继发展起来，计算数论被确立为一门新的数学学科。

## 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。

## 数学代写|数学建模代写math modelling代考|Find2022

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|The Goal of CREST Crypto-Math Project

Classical cryptography has been used for enciphering techniques in the military and for diplomacy. However, contemporary cryptography has many applications in daily life such as for smartphones, DVDs, e-money, passports, electronic vehicles, and smart grids. Thus, cryptography is a fundamental technology in our society.

There are two cryptosystems that are currently in wide use: RSA Cryptosystem [1] and Elliptic Curve Cryptography (ECC) [2,3]. Interestingly, these cryptosystems can be constructed using number theory, which has previously been thought to have no real application. However, these cryptosystems are no longer secure in the quantum computing model because the underlying mathematical problems, i.e., the integer factorization problem and discrete logarithm problem, can be solved efficiently by using quantum computers [4]. Therefore, the cryptography research community is investigating the post-quantum cryptography, which ensures the long-term security even in the era of quantum computers. The goal of our research project “CREST: Mathematical Modelling for Next-Generation Cryptography” supported by Japanese Science and Technology Agency is to eventually construct mathematical modeling of next-generation cryptography using wide-range mathematical theories and mathematical analysis of various quantum interaction models which are considered as a theoretical foundation of quantum technology including quantum information theory (Fig. 1).

Recent advances in cryptanalysis, due in particular to quantum computation and physical attacks on cryptographic devices (such as side channel attacks or power analysis), introduced increasing security risks regarding state-of-the-art cryptographic schemes. This project will focus on developing foundations for the mathematical modeling of next-generation cryptographic systems; therefore, addressing the above-mentioned risks.

To achieve this goal, a new mathematical approach will be used that will draw ideas from beyond number theory and theory of computation, which have historically proven to provide a good interchange with cryptography. Specifically, the focus will be in areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics. Specifically, this project will create a platform for involving mathematicians in research focused on the promotion of a safe society, while at the same time stimulating the development of the respective branches of mathematics.

## 数学代写|数学建模代写math modelling代考|Our Research Events in 2015 and 2016

The CREST Crypto-Math Project started in November 2014, and it is a $5.5$-year research project. On January 19-20, 2015, we held the first kick-off meeting, where all project members presented their expertise. To promote interaction among the project members of mathematics and cryptography, we also held 12 tutorial talks in three workshops on mathematical cryptography such as provably security techniques in cryptography, basic mathematics in quantum computing, and Ramanujan graphs. In 2015 and 2016, we organized one-day CREST workshops on the main research topics in the CREST Crypto-Math project: “Ramanujan Graphs and Cryptography”, “Geometry and Cryptography”, “L-functions and Cryptography”, “Photons and Lattices”, and “Computational Number Theory and Cryptography”.

A turning point in mathematical cryptography is that the National Security Agency (NSA) announcing a preliminary plan for transitioning to quantum-resistant algorithms in August 2015. On February 24-26, 2016, we organized the 7th International Conference on Post-Quantum Cryptography (PQCrypto 2016) [5] at Kyushu University co-organized by CREST, JST. At PQCrypto 2016, Dustin Moody gave at talk on “Post-Quantum Cryptography: NIST’s Plan for the Future”, and we intensively discussed the security analysis and efficiency estimation of post-quantum cryptography. Moreover, the National Institute of Standards and Technology (NIST) started a standardization process of post-quantum cryptography in 2016 (see their homepage at http: //www.nist.gov/pqcrypto).

## 数学代写|数学建模代写math modelling代考|Our Research Events in 2015 and 2016

CREST Crypto-Math 项目于 2014 年 11 月开始，它是一个5.5- 年的研究项目。2015 年 1 月 19-20 日，我们召开了第一次启动会议，所有项目成员都展示了他们的专业知识。为了促进数学和密码学项目成员之间的互动，我们还在密码学中的可证明安全技术、量子计算中的基础数学和拉马努金图等三个数学密码学研讨会中举办了 12 场辅导讲座。在 2015 年和 2016 年，我们针对 CREST Crypto-Math 项目中的主要研究课题组织了为期一天的 CREST 研讨会：“Ramanujan Graphs and Cryptography”、“Geometry and Cryptography”、“L-functions and Cryptography”、“Photons and Lattices” ”和“计算数论与密码学”。

## 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。

## 数学代写|数学建模代写math modelling代考|SOLVING ADDITIVE COMPARE PROBLEMS

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|COMPS PROGRAM

Teacher: Correct! It is a comparison problem that describes one quantity as more than the other quantity.
(Teacher point to the AC Word Problem [WP] Story Grammar Poster, which is posted on the board or classroom wall throughout the lesson)

As it is a comparison problem that involves “more than” or “less than” relationships between the two quantities, we will use the AC WP story grammar poster to guide our problem representation.

So the first step is to find out the comparison sentence. Can you tell which sentence is the comparison sentence?
Students: Patrick has 72 more sports cards.
Teacher: That is correct. This comparison sentence tells us that the number of sports cards Patrick has is MORE ( 72 more) than the number of sports cards Joy has.
Let’s underline this comparison sentence (Teachers does that on the board, and the students do the same in their worksheet)

What is the difference between the number of cards Patrick has and the number of cards that Joy has?
Students: Patrick has more than Joy, and the difference between the two is ” 72 .”
Teacher: Let’s write the difference amount in the PPW diagram (teacher presents the PPW diagram on board, and asks a student volunteer to write the difference amount [i.e.,” “72”] in the 2 nd small box labeled “difference”).

Teacher: According to the comparison sentence: “Patrick has 72 more sports cards than Joy,” let’s name the bigger box and the smaller box either Joy or Patrick. Everyone, “who has more and who has less?”
Students: Patrick has more and Joy has less.
Teacher: Super! I will ask a volunteer to name the smaller box and bigger box on the PPW diagram.
(Teacher asks a volunteer to name the bigger box [i.e., Patrick] and the smaller box [i.e., Joy] on the board in the PPW diagram. See Slide 4-6-3-a)

Teacher: We have done the first step in the AC Word Problem (WP) Story Grammar poster. I will check off the first box. The rest of the steps are very straight forward. Once you have defined the bigger and smaller quantity based on “the more or less” relationship, all you need to do is to find the bigger quantity and the smaller quantity and write them in corresponding boxes in the diagram.

## 数学代写|数学建模代写math modelling代考|DIRECTIONS FOR TRY-IT-OUT AND INDEPENDENT

In worksheets below, you will use the PPW diagram equation to represent and solve the problems. The AC Problem Story Grammar prompt card (see Figure $3-5$ in Unit 3 , page 67 ) can be used to guide your problem solving process.

After you read and understand the story, if it is an additive comparison (AC) problem (see definition of AC problem in Figure 3-5 in page 67), you will find the comparison sentence that tells who has more (or less) and how many more (or less). Underline the comparison sentence as the comparison sentence is where you will decide who has more (or the bigger quantity) and who has less (or the smaller quantity). It will be helpful if you name the bigger box and smaller box in the diagram so that you make sure the bigger quantity goes into the big box on one side of the equation, and

the smaller quantity goes into the smaller box on the other side of the equation next to the difference quantity box.

You will use the letter ” $a$ ” to represent the unknown quantity (in fact, you can choose to use any letter to represent the unknown quantity). In the last step, you will solve for the unknown quantity and check for the accuracy of your answer. You can do this by checking whether the sum on the left side of the equation equals the value on the right side of the equation.
Unit 4: Try it out Worksheet -AC Problem Solving 5 \& 6
(Note: Suggested diagram equation representation is presented in the parentheses following each of the problems)

1. Phillip has 64 worms. Phillip has 34 more worms than Harley. How many worms does Harley have? $(a+34=64)$
2. Lucas has 30 stamps. He has 44 fewer stamps than Ben. How many stamps does Ben have? $(30+44=a)$
Unit 4: Independent Worksheet -AC Problem Solving 7, 8 \& 9
3. Adriana has 70 cows. Michelle has 75 more cows than Adriana. How many cows does Michelle have $(70+75=$ a)
4. Rodolfo has 79 glue sticks. Felipe has 38 glue sticks. How many more glue sticks does Rodolfo have than Felipe? $(38+a=79)$
5. Marlene has 49 fewer shirts than Jack. Jack has 96 shirts. How many shirts does Marlene have? $(a+49=96)$

## 数学代写|数学建模代写math modelling代考|SOLVING MIXED PPW AND AC PROBLEMS

$\begin{array}{ll}\text { Learning outcome: } & \begin{array}{l}\text { Be able to solve mixed PPW and AC word problems with } \ \text { the diagram equations }\end{array} \ \begin{array}{ll}\text { Materials Needed: }\end{array} & \begin{array}{l}\text { Part-Part-Whole (PPW) Diagram Equation } \ \text { Diagrams }\end{array} \ \text { Posters } & \text { PPW and AC WP Story Grammar Posters } \ \text { Overhead Modeling } & \text { Modeling PPW and AC Problem Solving 1, 2,3, and } 4 \ \text { Student Worksheets } & \text { Modeling PPW and AC Problem Solving 1,2,3, and } 4 \ & \text { Try-It-Out-mixed PPW and AC problem solving } \ & 5 \text { \& } 6 \ \text { Independent worksheet- mixed PPW and AC problem } \ \text { solving } 7,8,9, \& 10 \ \text { Reference Guide -mixed PPW and AC problem solving } \ \text { Reference Guide } & \begin{array}{l}1-10 .\end{array}\end{array}$
Teacher: In units 1, 2 and 3, we learned how to represent and solve Part-PartWhole (PPW) problems. We discovered that the bar model and the PPW diagram equation are telling the same stories. That is, Part and Part makes up the Whole or total (teacher can use both the bar model and the PPW diagram equation to explain).

Given the PPW problem structure, some types of problems will ask us to solve for the total, while others will ask us to solve for one of the parts (that make up the whole). Table 5-7-a presents variations of PPW problem construction (with the same story context) and its corresponding diagram representation, where letter ” $a$ ” represents the unknown quantity.

In Units 3 and 4 , we learned how to represent and solve comparison problems that involve “more than’ or “less than” relations. The two parts in the part-partwhole diagram are the Smaller quantity and the Difference quantity (between the two quantities being compared). The smaller quantity and the difference quantity together make up the bigger quantity (the whole).

## 数学代写|数学建模代写math modelling代考|COMPS PROGRAM

（教师指向 AC Word Problem [WP] Story Grammar Poster，该海报在整个课程中都张贴在黑板上或教室墙上）

（教师让志愿者说出 PPW 图中黑板上较大的方框 [即 Patrick] 和较小的方框 [即 Joy]。见幻灯片 4-6-3-a）

## 数学代写|数学建模代写math modelling代考|DIRECTIONS FOR TRY-IT-OUT AND INDEPENDENT

（注意：建议的图表方程表示在每个问题后面的括号中）

1. 菲利普有 64 条蠕虫。菲利普的蠕虫比哈雷多 34 条。哈雷有多少条虫子？(一种+34=64)
2. 卢卡斯有 30 枚邮票。他的邮票比本少 44 枚。本有多少张邮票？(30+44=一种)
单元 4：独立工作表 -AC 问题解决 7、8 \& 9
3. 阿德里安娜有 70 头奶牛。米歇尔的奶牛比阿德里安娜多 75 头。米歇尔有多少头奶牛(70+75=一种）
4. Rodolfo 有 79 根胶棒。费利佩有 38 根胶棒。Rodolfo 的胶棒比 Felipe 多多少？(38+一种=79)
5. 马琳的衬衫比杰克少 49 件。杰克有 96 件衬衫。马琳有几件衬衫？(一种+49=96)

## 数学代写|数学建模代写math modelling代考|SOLVING MIXED PPW AND AC PROBLEMS

学习成果：  能够解决混合的 PPW 和 AC 单词问题   图方程   所需材料：  部分-部分-整体 (PPW) 图方程   图表   海报  PPW 和 AC WP 故事语法海报   架空建模  建模 PPW 和 AC 问题解决 1、2、3 和 4  学生工作表  建模 PPW 和 AC 问题解决 1、2、3 和 4  Try-It-Out-mixed PPW 和 AC 问题解决方案  5 \& 6  独立工作表 – 混合 PPW 和 AC 问题   解决 7,8,9,&10  参考指南 – 混合 PPW 和 AC 问题解决   参考指南 1−10.

## 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。

## 数学代写|数学建模代写math modelling代考|DIRECTIONS FOR THE INDEPENDENT WORKSHEET

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|SUMMARY

In this unit, we have used PPW diagram equation to represent the AC problems. Figure 3-5 present a story grammar prompt card (Xin et al., 2008) that students can use to facilitate meaningful representation of AC problems. As presented in Figure 3-5, word problem (WP) story grammar questions and prompts were generated in accordance with the key elements in the AC stories (or problems) to help students understand the problem structure and correctly map information from the problem to the PPW diagram equation. As shown in Figure 2-3, the diagram equation emphasizes algebraic expression of mathematical relations among key elements of the problem structure. Specifically, an additive compare $(\mathrm{AC})$ problem describes one quantity as “more than” the other quantity (i.e., the $A C$-more type) or “less than” the other quantity (i.e., the AC-less type). Please refer to Table C2-1 in Chapter 2 (page 15 ) for three variations of $\mathrm{AC}$-more problem structure and three variations of $\mathrm{AC}$-less problem structure.

## 数学代写|数学建模代写math modelling代考|Independent Work–AC Problem Representation

In the worksheets below, you will use the PPW diagram equation (see Figure 3-5) to represent the story. After you read and understand the story, if it is an additive comparison (AC) problem (see definition of AC problem in Figure 3-5: AC problem story grammar prompt card), you will find the comparison sentence that tells who has “more” “or “less” (or which quantity is the bigger one and which quantity is the smaller one) and how many more (or less). Underline that sentence as the comparison sentence is where you will decide who has the bigger quantity and who has the smaller quantity.

It will be helpful if you name the bigger box and smaller box in the diagram so that you make sure the bigger quantity goes into the “bigger” box on one side of the equation, and the smaller quantity goes to the “smaller” box on the other side of the equation. But please note that: When there is an unknown in the problem, the unknown quantity may be the bigger or smaller quantity. Therefore, you do not judge the “big” or “small” by looking at the size of the numbers given in the problem; you need to read the comparison sentience, which tells you who has more, or which quality is the bigger one. Remember, the unknown quantity you are asked to solve for, might be the bigger quantity! In the next Unit, you will learn how to use the diagram equation to solve real AC problems when there is an unknown.

The comparison sentence also tells how many more or how many less, which is the difference quantity that goes into the 2 nd small box in the PPW diagram labelled “difference”. The smaller quantity and the difference amount should make up, or equal, the bigger quantity on the other side of the equation.

If you are ever confused about the story situation, draw the bar model to help you understand the story, or specifically, the two parts that make up the whole, or total (which is the bigger quantity in comparison stories).

## 数学代写|数学建模代写math modelling代考|SOLVING MIXED AC PROBLEMS

$\begin{array}{ll}\text { Learning Outcome: } & \begin{array}{l}\text { Be able to solve mixed AC word problems with the PPW } \ \text { diagram equation }\end{array} \ \begin{array}{ll}\text { Materials Needed: }\end{array} & \text { Part-Part-Whole (PPW) Diagram Equation Model } \ \text { Posters } & \text { AC Word Problem }(\text { WP) Story Grammar Poster } \ \text { Overhead Modeling } & \text { Modeling AC Problem Solving 1, 2, 3, and } 4 \ \text { Student Worksheets } & \text { Modeling AC Problem Solving 1, 2, 3, and } 4 \ & \text { Try-It-Out Worksheet-AC problem solving } 5 \text { and } 6 \ \text { Independent worksheet-AC problem solving } 7,8, \text { and } 9 \ \text { Reference Guide } & \text { Reference Guide-AC problem solving } 1-9\end{array}$
Teacher: In the last Unit, we learned how to represent $A C$ stories (including $\mathrm{AC}-\mathrm{more}$ and $\mathrm{AC}$-less) using the bar model and the PPW diagram equation. As all three quantities are given (the bigger quantity, the smaller quality, and the difference quantity) in the story, we are able to see whether the PPW diagram equation can still be used to represent the mathematical relations in the AC stories. We discovered that in the case of $\mathrm{AC}$ stories the bigger quantity is made up of the smaller quantity AND the difference between the bigger and smaller quantities. As presented in the PPW diagram equation, the bigger quantity represents the whole, and the smaller quantity and the difference between the two quantities are the two parts. Further, the bigger quantity is the sum of the smaller quantity and the difference between the two quantities.

During this lesson, we will discover that the Part-Part-Whole diagram equation will help us solve the $A C$ problems when one quantity (the smaller quantity, the bigger quantity, or the difference amount) is the unknown.

We will use the Word Problem Story Grammar Prompt Cards (see Figure 2-3 in page 47 and Figure $3-5$ in page 67 ) to help us represent the problem in the diagram equation, and then we will solve for the unknown quantity in the equation.

## 数学代写|数学建模代写math modelling代考|SOLVING MIXED AC PROBLEMS

学习成果：  能够使用 PPW 解决混合 AC 单词问题   图方程   所需材料：  部分-部分-整体 (PPW) 图方程模型   海报  交流单词问题 ( WP) 故事语法海报   架空建模  建模交流问题解决 1、2、3 和 4  学生工作表  建模交流问题解决 1、2、3 和 4  Try-It-Out Worksheet-AC 问题解决 5 和 6  独立工作表-AC问题解决 7,8, 和 9  参考指南  参考指南-AC问题解决 1−9

## 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。

## 数学代写|数学建模代写math modelling代考|REPRESENTING AC-LESS PROBLEMS

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|REPRESENTING AC-LESS PROBLEMS

Learning Outcome: $\quad$ Be able to represent $\mathrm{AC}$ word problem stories with the bar model and the PPW diagram equation

Teacher: During the last lesson, we learned how to use the Bar model and Diagram Equation to represent a type of comparison problem. Today we will learn how to represent more comparison problem situations.
Problem #3-5-10
Cristal has 29 pens, and she has 71 fewer pens than a boy named Warren. Warren has 100 pens.
Teacher: What is this story all about?
Students: This story compares the number of pens Cristal has to the number of pens that Warren has.

Teacher: Correct! It is a comparison story that involves a statement of “more” or “less.” Mathematically, we name this type of story Additive Compare (AC).
Teachers: Do you know who has more pens?
Students: “Cristal has 71 fewer pens than Warren,” and so Warren has more.
Teacher: That is right! Warren has more. I will underline the comparison sentence on board, and you will do the same on your worksheet.
Let’s first represent the story using the bar model. (Teacher calls on student volunteers and student(s) come to board and make the segment of bars that represent the number of pens Cristal has, and the number of pens Warren has. In addition, student volunteers indicate on the bar graph the difference between the bar for Cristal and the bar for Warren). See Slide 3-5-10-a.

## 数学代写|数学建模代写math modelling代考|represents the number of pens

In Slide 3-5-10-a, the 2 nd bar represents the number of pens Warren has, a total of 100 . As indicated in the bar model, it is 71 longer than Cristal’s bar, or in other words, as stated in the story, Cristal has 71 fewer pens than Warren. In short, the difference between the number of pens Cristal has and the number of pens Warren has is 71 , which is indicated by the clear part of the longer bar (Teacher points to the segment of the bar that is not shaded in the longer bar)

Teacher: If we look at the longer bar (Warren’s bar), it is actually made up of two parts: (a) the first part (shaded bar), which is the same as Cristal (29); and (b) the second part (clear bar), which is the additional pens that Warren has. These two parts (a and b) make up the total number of pens that Warren has.
So now we are ready to represent the same story in the PPW diagram equation.
(Teacher presents the PPW diagram equation)
Who can tell us the two parts (that make up the bigger quantity) that we should enter into the two small boxes on the left side of the PPW diagram equation?
Students: 29 and $71 .$
Teacher: That is correct. I will write 29 in the first small box that is labeled “smaller.” I will write 71 in the 2nd small box that is labeled “difference.”

What should I write in the big box for the “larger” quantity on the other side of the equation?
Students: 100 .
Teacher: That is correct. The big box is for the total number of pens Warren has. I will write 100 in the big box that is labeled “bigger” or “whole.” You will do the same in your worksheet. See Slide 3-5-10-b for a completed bar model and PPW diagram equation.

## 数学代写|数学建模代写math modelling代考|the difference amount

Teacher: As shown in the above PPW diagram equation (the lower panel of Slide 3-5-10-b), when representing the comparison story onto the PPW diagram equation, the smaller quantity (Cristal in this case) of the two being compared (Cristal and Warren) AND the difference amount between the bigger and the smaller quantities, or between Cristal and Warren’s pens (as indicated by “71 fewer … than” in this story) will make up the “whole” or the Bigger quantity (Warren in this case), as shown exactly in the bar model.

Lets’ check to see whether the sum of the two quantities on the left side (LS) of the equal sign is the same as (or equal to) the quantity on the right side (RS) of the equal sign.
LS: $29+71=100$
RS: 100
Does the LS equal the RS of the equation and why?
Students: Yes, they are the same, because “100” from the LS is the same as or equals ” 100 ” from the RS of the equation.

Teacher: That means, “part” and “part” from the left side (LS) of the diagram equation did make up the “whole” in the right side (RS) of the equation. Both the bar model and the PPW diagram equation model tell exactly the same story (teacher points to the Bar model and the PPW diagram equation in Slide 3-5-10-b during the explanation).
Let’s try to do two more similar comparison problems. Instead of using both the bar model and the PPW diagram equation, we will simply use the PPW diagram equation (but if you feel you need the bar model to help you, please feel free to use both).

## 数学代写|数学建模代写math modelling代考|REPRESENTING AC-LESS PROBLEMS

Cristal 有 29 支钢笔，她的钢笔比一个名叫 Warren 的男孩少 71 支。沃伦有 100 支笔。
（学生一起读故事。）

（教师展示 PPW 图方程）

## 数学代写|数学建模代写math modelling代考|the difference amount

LS：29+71=100
RS：100
LS 是否等于方程的 RS，为什么？

## 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。

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|REPRESENTING AC-MORE PROBLEMS

Learning Outcome: $\quad$ Be able to represent $\mathrm{AC}$ word problem stories with the bar model and the PPW diagram equation

Teacher: In the last Unit, we learned how to use a bar model and diagram equation to represent and solve PPW problems. In this unit, we will use the bar model and the diagram equation to represent Additive Compare (AC) problems, or the comparison problems that involve addition and subtraction.
Problem #3-4-1
Christine has 43 toy cars. Bob has 66 more toy cars than Christine. Bob has 109 toy cars.
Teacher: What is this story all about?
Students: This story is about Christine and Bob, and the toy cars they have.
Teacher: Yes, you are right. Specifically, this story compares the number of the toy cars Christine has to the number of toy cars that Bob has. After reading the problem, do you know who has more?
Students: Bob has 66 more than Christine.

## 数学代写|数学建模代写math modelling代考|comparison sentence

Teacher: Let’s underline this comparison sentence. From this sentence, we know Bob has more and Christine has less, and the difference between the two is 66 . Let’s use the bar model to represent the given information in the problem.
I am going to ask a volunteer to make the first bar to represent the number of toy cars that Christine has.
(Teacher calls on a volunteer. Student volunteer makes the first bar to represent the number of toy cars Christine has). See Slide 3-4-1-a.

Teacher: Above bar represents the number of toy cars Christine has (i.e., 43).
From reading the story, we know that Bob has 66 more than Christine. I will make another bar for Bob. How will the bar for Bob be different from the bar for Christine?
Students: Bob has 66 more.
Teacher: Yes. So I will make a new bar for Bob immediately below the one for Christine. The new bar for Bob should be ” 66 ” longer than the bar for Christine as the story says that “Bob has 66 more.” I will also indicate that the total number of toy cars Bob has is 109 as provided in the story.
(Teacher makes the bar for Bob below the one for Christine. See Slide 3-4-1-b.)

## 数学代写|数学建模代写math modelling代考|the smaller quantity

Teacher: Now let’s look at Slide 3-4-1-b. The first bar (the short one) represents the number of toy cars Christine has; the second bar (the longer one) represents the number of toy cars Bob has, which is 66 more than the first bar for Christine. In other words, the difference between the bar for Christine (the shorter one) and the bar for Bob (the longer one) is ” 66 ,” which is indicated by the clear part of the longer bar. (Teacher points to the segment of the bar that is not shaded in the longer bar)

Teacher: If we look at the longer bar (Bob), it is actually made up of two parts: (a) the first part (shaded bar), which is the same as Christine (43); and (b) the second part (clear bar), which is the additional toy cars that Bob has. These two parts (a and b) make up the total number of toy cars that Bob has.
So now we are ready to represent the same story in the PPW diagram equation.
(Teacher presents the PPW diagram equation)
Who can tell us the quantities of the two parts (that make up the bigger quantity) that we should write in the two small boxes labeled “part” on the left side of the PPW diagram equation?
Students: 43 and $66 .$
Teacher: Great! I will write 43 in one of the small boxes that represent the small quantity. I will write 66 in the other small box that is labeled as “difference” in the PPW diagram.
What number will we write in the big box that represents the bigger quantity in this comparison story?
Students: $109 .$
Teacher: That is correct. The big box is for the total number of toy cars Bob has. I will write 109 in the big box that is labeled “whole” in the PPW diagram equation. You will do the same in your worksheet. See Slide 3-4-1-c for a completed bar model and the PPW diagram equation.

Teacher: As shown above, when representing the comparison story onto the PPW diagram equation, the smaller quantity (Christine in this case) of the two being compared (Christine and Bob) AND the difference amount (between the bigger and the smaller quantities; or between Bob and Christine’s toy cars, as indicated by ” 66 more… than” in this story) will make up the “whole,” or the bigger quantity (Bob in this case), as shown exactly in the bar model.

Lets’ check to see whether the sum of the two quantities on the left side (LS) of the equal sign is the same as (or equal to) the quantity on the right side (RS) of the equal sign.

## 数学代写|数学建模代写math modelling代考|REPRESENTING AC-MORE PROBLEMS

Christine 有 43 辆玩具车。鲍勃的玩具车比克里斯汀多 66 辆。鲍勃有 109 辆玩具车。
（学生一起读故事。）

## 数学代写|数学建模代写math modelling代考|comparison sentence

（老师请来一名志愿者。学生志愿者制作第一个条形图来表示 Christine 拥有的玩具车的数量）。参见幻灯片 3-4-1-a。

（教师将 Bob 的横杆置于 Christine 的横杆下方。参见幻灯片 3-4-1-b。）

（教师展示 PPW 图方程）

## 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。

## 数学代写|数学建模代写math modelling代考|Diagram equation

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|Diagram equation

Let’s look at the lower panel, or the diagram equation:
The first box in the diagram equation represents the boxes of cookies sold, the second box represents the leftover unsold boxes of cookies, and the big box on the other side of the equation represents the total number of boxes of cookies for sale. Adding the two parts (boxes sold and the boxes unsold) together should make up, or equal, the whole.
In summary, the bar model and the diagram equation representations tell the same story in the problem.

To find out the answer to “How many boxes of cookies will the Girl Scouts have to take back home?” we can generate a math sentence based on the bar model. That is, in order to find the difference between the long bar and the short bar we subtract. The math sentence would read:
$$?=93-47$$
Therefore, ? $=46$.
Now we know that the 2 nd short, clear bar is 46 , meaning there are 46 boxes of cookies that were not sold, or 46 boxes that the girl scouts have to take back home.
However, if we use the PPW diagram equation, the math sentence for solving the problem is given by the diagram equation. That is, if we “peel off” the boxes from the diagram equation, we get
$$47+?=93$$
Because the number we are adding is unknown, we have to “undo” the addition to find out the unknown addend. That is, we subtract the given part from the whole (or total) for solving for the unknown part. The math sentence would read:
$$\begin{gathered} ?=93-47 \ ?=46 \end{gathered}$$
[Note: For higher level students, the teacher can simply use basic algebra properties for the instruction on how to find out the unknown in the equation. That is-
Given: $47+?=93$,
To solve for the unknown (i.e., the question mark, ?), we need to isolate the unknown ? by subtracting 47 from both sides of the equation:
$$\text { 47-47 + ? =93-47 }$$
We get: ? $=93-47$, or ? $=46$
In fact, we can verify the algebraic way of solving for the unknown from the bar model presented in the upper panel of slide $2-3-2-\mathrm{d}$. That is, to find out the difference between the whole and one part, we subtract. In other words, ? $=93-47=46$.]

## 数学代写|数学建模代写math modelling代考|What is a complete answer to this problem

What is a complete answer to this problem?
Students: The answer is: The Girl Scouts will have to take 46 boxes of cookies back home.
Teacher: Very good!
We have gone through several problems using both the bar model and the PPW diagram equation, and learned that the PPW diagram equation tells the same story (that is, “Part and Part make up the Whole”) as the bar model. Because the PPW diagram equation directly provides us with the math sentence, or equation for solving the problem, we may not need to draw the bar model for future PPW problems. Instead we can directly use the PPW diagram equation to set up the math equation for accurate problem solving. Let’s try it out with the next problem. That is, we will only use the PPW diagram equation to solve the PPW problems.
Problem #2-3-3
Travis ordered 68 baseball cards from a magazine. Then he ordered some more for his brother. In all, he ordered 129 baseball cards. How many did he order for his brother?
Teacher: What is this problem all about?
Teacher: How many baseball cards did he order the first time?
Students: 68 baseball cards.
Teacher: How many more did he order for his brother?
Students: He ordered some more… we do not know how many he ordered for his brother.
Teacher: Correct. That is, in fact, the question we are asked to solve for. Let’s underline the question in the problem. (Teacher does so on the board; students do so in their worksheet).
Teacher: What else do we know?
Students: He ordered a total of 129 baseball cards.
Teacher: Great! So Travis ordered 68 baseball cards. Then he ordered some more, but we do not know that number. We do know that, at the end, he ordered a total of 129 baseball cards in all. Is this still the part-part-whole (PPW) type of problem?
Students: Yes.

## 数学代写|数学建模代写math modelling代考|the PPW problem structure

Teacher: You are right. It is still the PPW problem structure. So let’s use the PPW diagram to represent the information from the problem.

Teacher: I will make the PPW diagram on the board. I will ask for your help to fill the numbers into the PPW model equation.
(Teacher presents the PPW diagram equation without filling any numbers in the boxes)
Teacher: What is the total number of baseball cards Travis ended up with after ordering some for himself and for his brother?
Students: 129 baseball cards.
Teachers: So 129 is the total, or the whole amount.
Where do I write ” 129 “, the total number of baseball cards in the diagram equation?
Students: In the big box.
Teacher: That is right. We always input the total, or the whole, into the big box on one side of the equation by itself. (Teacher enters ” 129 ” in the big box. Students do the same in their worksheets.)

Teacher: do we know any information about the two parts, or the two orders Travis made that makes up the total?
Students: We know he ordered 68 baseball cards for himself the first time.
Teacher: OK. That is one part. Let’s write ” 68 in the first box in the diagram. Do we know the other part?
Students: We do not know.
Teacher: You are right. We do not know how many he ordered for his brother. We are asked to solve for this part.
I will write a ” ?” in the second small box in the PPW diagram. Instead of using a question mark, we can also use a letter to represent the unknown quantity. (Teacher writes a letter “a” in the 2nd box that is labeled “Part”). In your worksheet, please write the letter ” $a$ ” in the 2 nd box for the part that is not known.
Now let’s look at the completed diagram (Slide 2-3-3)

## 数学代写|数学建模代写math modelling代考|Diagram equation

?=93−47

47+?=93

?=93−47 ?=46
[注：对于较高水平的学生，教师可以简单地使用基本代数性质来指导如何找出方程中的未知数。那是-

47-47 + ? =93-47

（学生一起读故事）

## 数学代写|数学建模代写math modelling代考|the PPW problem structure

（老师展示了PPW图方程，没有在方框中填写任何数字）

## 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。

## 数学代写|数学建模代写math modelling代考|DIRECTIONS FOR TRY-IT-OUT AND INDEPENDENT WORKSHEET

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|Try it Out–PPW Story Representation 4, 5, and 6

In the below worksheets, first, you will use the bar model to represent the story. Then you will map the information into the PPW diagram equation. After you map the information into the diagram, you will check whether the sum of the two quantities from the left side of the equation IS THE SAME AS, or EQUAL to, the quantity from the right side of the equation. If NOT, you need to check the accuracy of your mapping against the story provided. Make sure you have, both, correctly entered the two parts into the two smaller boxes labelled part, and that you have correctly entered the total in the bigger box labelled whole on the other side of the equation. After correcting the mapping in the diagram, you will check again whether the sum of the two parts from the left side of the equation IS THE SAME AS, or EQUAL to, the quantity from the right side of the equation.

1. The pound had 67 dogs in cages waiting to be adopted. One week, 24 of the dogs were adopted. There were still 43 left at the pound.
2. A basketball player named Sarah scored 43 points in the first half of a game. Then she scored 12 more points in the second half. By the end of the game, she had scored 55 points.
3. Alex had 164 colored pencils. 57 of them were different shades of blue. There were 107 colored pencils which were not blue.One teacher had 23 flashcards for his students. Another teacher had 89 flashcards. In total, the two teachers had 112 flashcards.
4. One student’s mom baked 56 cookies for the class party. Her son and his friends ate 32 of the cookies before she woke up. There were only 24 cookies left for the party.
5. A cat caught 23 mice in the spring and summer. In the fall and winter, the same cat caught 53 mice. The cat caught a total of 76 mice that year.

## 数学代写|数学建模代写math modelling代考|SOLVING PPW PROBLEMS

Teacher: In the last Unit, we learned how to use the bar model and diagram equation to represent PPW problems. In this unit, we will use the bar model and the diagram equation to help us solve real world problems.
Problem $# 2-3-1$
Christie read two books over the summer. One book was 193 pages and the other book was 267 pages. How many pages did Christie read over the summer?
Teacher: what is this problem all about?
Students: The problem is about the two books Christie read over the summer.
Teacher: That’s right. What else does it tell us?
Students: One book is 193 pages, and the other book is 267 pages.
Teacher: Good. What are we asked to solve for?
Students: How many pages did Christie read over the summer?
Teacher: Great. Let’s underline the question in your worksheet. (Students underline the question in their worksheet; teacher does so on the board.)

## 数学代写|数学建模代写math modelling代考|COMPS PROGRAM

Teacher: Slide 2-3-1-a represents the story of problem 1. Slide 2-3-1-b represents the mathematical relation in the problem. To find out the answer to “How many pages did Christie read over the summer.” we can generate a math sentence based on the bar model. That is,
Total # of pages = the first short bar $+$ the 2 nd short bar, or
Total # of pages $=193+267=460$.
However, if we use the PPW diagram equation, the math sentence (or equation) for solving the problem is given by the diagram equation. That is, if we peel off the boxes from the diagram equation, we get
$$\begin{gathered} 193+267=? \ \text { Or ? }=193+267=460 \end{gathered}$$
What is a complete answer to this problem?
Students: The answer is: Christie read a total of 460 pages over the summer.
Teacher: Super!
The reason we use both the bar model and the diagram equation is that the bar model helps us to understand the meaning of the problem, as well as the meaning of the diagram. Later in the program, we will not have to draw the bar models. Instead, we can directly use the PPW diagram equation to represent and solve problems, as the diagram equation provides us with a defined math sentence, or equation, for our solution.

Let’s look at one more problem and represent it with both a bar model and the diagram equation. After that, we will only use the PPW diagram equation to represent and solve the problem.
Problem #2-3-2
The Girl Scouts were selling cookies at the mall. They brought 93 boxes of cookies with them, and they sold 47 boxes that day. How many boxes of cookies will the Girl Scouts have to take back home?
Teacher: What is this problem all about?
Students: The problem is about the Girl Scouts selling cookies. They have a total of 93 boxes of cookies, they sold 47 boxes.

## 数学代写|数学建模代写math modelling代考|Try it Out–PPW Story Representation 4, 5, and 6

1. 英镑有 67 只狗在笼子里等待收养。一周，24只狗被收养。英镑还剩下43个。
2. 一位名叫莎拉的篮球运动员在上半场比赛中得到 43 分。然后她在下半场又得到12分。到比赛结束时，她已经得到55分。
3. 亚历克斯有 164 支彩色铅笔。其中 57 种是不同深浅的蓝色。有 107 支不是蓝色的彩色铅笔。一位老师为他的学生准备了 23 张抽认卡。另一位老师有 89 张抽认卡。两位老师总共有 112 张抽认卡。
4. 一位学生的妈妈为班级聚会烤了 56 块饼干。她的儿子和他的朋友在她醒来之前吃了 32 块饼干。派对只剩下 24 块饼干了。
5. 一只猫在春夏两季抓到了23只老鼠。秋天和冬天，同一只猫抓到了53只老鼠。那一年，这只猫一共抓了76只老鼠。

（学生一起读故事。）

## 数学代写|数学建模代写math modelling代考|COMPS PROGRAM

193+267=?  或者 ？ =193+267=460

（学生一起读故事）

## 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。

## 数学代写|数学建模代写math modelling代考|REPRESENTING PART-PART-WHOLE

statistics-lab™ 为您的留学生涯保驾护航 在代写数学建模math modelling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。我们的专家在代写数学建模math modelling代写方面经验极为丰富，各种代写数学建模math modelling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

## 数学代写|数学建模代写math modelling代考|Learning Outcome

Teacher: (Display Slide 1-1-1) How many circles are there in the first row? (Point to the first row and ask one student to answer.)
Students: 4 circles.
(If the student cannot answer, let him/her count);
Teacher: How many circles are there in the second row?
Students: Seven,
Teacher: How many circles are there in all?
Students: Eleven.
Teacher: Good. There are eleven circles altogether. If we want to express it in math language, we say: Four plus seven is eleven (” $4+7=11$ “), where 11 is the sum of 4 and $7 .$Teacher: (Give out cubes in two different colors ) First, please pick out 8 white color cubes and form a bar; Next, please pick out 5 gray color cubes and form another bar. (Monitor students’ actions; Display Slide 1-1-2.)How many cubes are there in all? We can stack the two bars together (see Slide 1-1-2-a) and find out the answer by counting them all or by using the strategy of “counting on” $(8$, then $9,10,11,12,13)$.Or we can find out the answer by using the Part-Part-Whole (PPW) Diagram Equation that we are going to learn today.

Teacher: (Display Slide 1-1-3) Let’s read it together three times: “part and part make up the whole.”
Let’s map information from the bar model to the PPW diagram equation and see how the bar model is represented by the PPW diagram equation.

## 数学代写|数学建模代写math modelling代考|Teacher points to the bar model in Slide

As 8 is one part (the white bar made of 8 cubes) and 5 is the other part (the gray bar made of 5 cubes), putting the two bars together makes up the “whole” (the long bar). The “whole” equals the sum of 5 and 8 .
(Teacher now points to the PPW diagram, the lower panel of Slide 1-1-4) Let’s fill the first box with 8 and the second box with 5 for the two parts (or two short bars), and 13 in the bigger box on the other side of the equal sign to represent the long bar, which is the whole, or sum of the two parts.

In summary, the bar model tells us that the white bar and the gray bar (two short bars) make up the long bar. The PPW diagram equation tells the same story: One part (8) and the other part (5), which represent the two short bars, make up the whole (13), which represents the long bar. In other words, $8+5=13$.

Now lets’ check to see whether the sum of the two quantities on the left side of the equal sign is the same as (or equals to) the quantity at the right side (of the equal sign).
Left side of the equation (LS): $8+5=13$,
Right side of the equation (RS): 13 .
Teacher: Does 13 “equal” or “the same as” 13 ?
Students: Yes, $13=13$.
Teacher: That means the PPW diagram equation or the statement “Part and Part make up the Whole” makes sense, and the PPW diagram equation is consistent with the bar model.
Teacher: Let’s look at Slide 1-1-5.
(Display Slide 1-1-5) There is one white bar, and one gray bar. Each represents a number. If the two numbers are 7 and 4 , which bar represents 7 ? Which bar represents 4?

## 数学代写|数学建模代写math modelling代考|Learning Outcome

Learning Outcome: & Be able to represent PPW word problem stories with the bar model and the PPW diagram equation \
Materials Needed: & Part-Part-Whole (PPW) Diagram Equation \
Dverhead Modeling & Modeling PPW story representation 1, 2, and 3 \
Student Worksheets & Modeling PPW story representation 1, 2, and 3 \
& Try It Out-PPW story representation 4,5, and 6 Independent Worksheet-PPW story representation 7,8, and 9 Reference Guide (PPW story representation 1-9) \
Reference Guide & \
\hline
\end{tabular}
Teacher: In the last lesson, we learned that the bar model and the PPW diagram equation are telling the same story: Part and Part make up the Whole. Today we will use the bar model, and the PPW diagram equation, to represent word problems. This will help us understand more about the mathematical relation presented in word problems.

## 数学代写|数学建模代写math modelling代考|Learning Outcome

（如果学生不能回答，让他/她数数）；

## 数学代写|数学建模代写math modelling代考|Teacher points to the bar model in Slide

（教师现在指着 PPW 图，幻灯片 1-1-4 的下面板）让我们在第一个方框中填入 8，在第二个方框中填入 5 代表两个部分（或两个短条），在较大的方框中填入 13在等号的另一边代表长条，它是整体，或两部分的总和。

（显示幻灯片 1-1-5） 有一个白色条和一个灰色条。每个代表一个数字。如果这两个数字是 7 和 4 ，哪个条形图代表 7 ？哪个条形代表 4？

## 数学代写|数学建模代写math modelling代考|Learning Outcome

Dverhead Modeling & Modeling PPW 故事表示 1、2 和 3 \

& Try It Out-PPW 故事表示 4,5 和 6 独立工作表-PPW 故事表示 7,8 和 9 参考指南（PPW 故事表示 1-9 ) \

\hline
\end{tabular}

## 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。