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# 数学代写|数学建模代写Mathematical Modeling代考|MATH3290 The Conception of Modeling in Mathematics

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## 数学代写|数学建模代写Mathematical Modeling代考|The Conception of Modeling in Mathematics

Modeling may be considered the process of creating mathematical models to explain and understand phenomena and concepts outside of mathematics in mathematical terms. Quarteroni calls mathematical modeling, “The third pillar of science and engineering, achieving the fulfillment of the two more traditional disciplines, theoretical and experimental.” ( 2009 , p. 10). To generate mathematical models, the process of modeling must be engaged. The purpose of creating mathematical models is varied. As Lawson and Marion (2008) suggest, mathematical modeling may be used to create understanding of science (and mathematics), assess effects of change in systems, and facilitate decision-making. Lesh and colleagues (2000) stated that problem solvers create mathematical models to, “. . .reveal how they are interpreting mathematical situations that they encounter by disclosing how these situations are being mathematized (e.g., quantified, organized, coordinatized, dimensionalized) or interpreted (p. 593). Several points from this conception are important to note. Specifically, endemic to mathematical modeling are the processes of interpreting and mathematizing. First, to create mathematical models, some degree of interpretation must occur. That is to say, to create successfully a mathematical model, problem solvers must analyze some mathematical information (e.g., data), interpret the information, and then create a mathematical model to make sense of the information. Second, the process of mathematizing is instrumental. Mathematizing occurs when problem solvers analyze everyday information that may not ostensibly be mathematical and they make it mathematical (Presmeg 2003; Van Den HeuvelPanhuizen 2003). Treffers (1987) substantiates this point when he referred to mathematizing as, “Transferring a problem field into a mathematical problem” (p. 247). An example of mathematizing information to create a mathematical model may be defining and then quantifying factors. For instance, when most people go to a grocery store or market, an objective is to collect all desired products and then pay in as expeditious manner as possible. Though many people do not view this episode as an opportunistic one to create a mathematical model, listed below is a sample of factors that may lead to success in exiting the grocery store as quickly as possible. For instance:

1. cashier speed in scanning items and bagging them,
2. amount of customer produce in basket as produce may require a special code that needs to be entered into the register manually while products with a Universal Product Code (UPC) are quickly scanned for information,
3. consumer form of payment (e.g., electronic forms of payment are nearly always quicker than checks or cash),
4. total number of items in the basket/cart,
5. speed of consumer in delivering items to the cashier

## 数学代写|数学建模代写Mathematical Modeling代考|Affect in Mathematical Modeling

Thus far, a foundation in relation to extant literature has been provided regarding what the construct of affect is, what affect in mathematics is, and what mathematical modeling is. In this section, the three foci are combined to formulate one theory, presented in Fig. 1. In this section, the description of this theory is elucidated so that readers will have a basis on which to interpret discussion in the remaining chapters. The caveat with the theory provided is that it is simply that, theory. Theories, by definition, are unproven suppositions based roughly on previous evidence. In this case, the evidence is the empirical studies so explicated in literature.

In Fig. 1, affect and mathematical modeling are larger circles because they represent the focus of this book. Cognition is a central component that links the two constructs in the field of mathematical psychology. It is important to note that the effect of each component is postulated to be a bi-directional relationship. That is to say, at any given time, and it may be theorized that these loops are perpetual. As importantly, affect influences (and the term affect as a verb is purposefully avoided in this chapter in lieu of influence) cognition, while cognition influences affect. Similarly, cognition influences modeling in mathematics, while the process of modeling (creating models as it was described earlier) influences the process of cognition. Finally, modeling influences affect, and vice versa, though it is significant to notice that the feedback loop that represents the interaction between modeling and affect influences cognition as well. To reiterate, all influences are predicated on feedback, which may come consciously or subconsciously. In the remaining sections, individual relationships will be explained, supplemented liberally with examples to support the theory.

## 数学代写|数学建模代写Mathematical Modeling代考|The Conception of Modeling in Mathematics

1. 收银员扫描物品并将其装袋的速度，
2. 篮子中的客户产品数量，因为产品可能需要一个特殊代码，需要手动将其输入到收银机中，同时快速扫描具有通用产品代码 (UPC) 的产品以获取信息，
3. 消费者支付方式（例如，电子支付方式几乎总是比支票或现金更快），
4. 购物篮/购物车中的商品总数，
5. 消费者将物品交付给收银员的速度

## 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。