Application of Mathematical Models and Techniques in the field of Statistics.

Pawan Kumar Ray
Assistant Professor
Harkamaya College of Education
6thMile Tadong Gangtok
Email-ccc4job@gmail.com
9832359082/7908401075

Abstract

Mathematics is the science of measurement, quantity and magnitude. Developing children's abilities for mathematics is the main goal of mathematics education. Its knowledge is exact, systematic, logical and clear. Mathematics involves the process for intellectual development of mental faculties. Besides the mental ability, mathematics develops some quality like concentration, truthfulness, seriousness and reasoning. Thus, in the words of Locke it is rightly said that, “Mathematics is a way to settle in the mind the habit of reasoning”. Statistics plays a vital role in every fields of human activity. It has important role in determining the existing position of per capita income, unemployment, population growth rate, housing, schooling medical facilities etc in a country. Modeling and Statistics are two branches of applied mathematics. Modeling involves fitting equations to data, usually just approximately. Statistics is the science of uncertainty. Mathematics is the most closely related subject “Statistics” in our daily life. This paper deals with the concept of the Mathematical techniques, Modeling .The Importance & Uses of Mathematical techniques and Modeling in the field of Statistics. It discusses the different Mathematical techniques and Modeling in respect to statistics. The paper also discusses “How to make statistics easy for learner by using Mathematical techniques and Modeling?”
Key words: Mathematical Modeling, Mathematical Techniques, Statistics, Population.

This 14-minute video lesson for high school educators introduces working with Common Core Standards. How will teaching to the Common Core affect teaching practice in the classroom? How can teachers help students learn to apply math and think about problem solving outside the math classroom? What does an emphasis on “depth” look like in practice? How can teachers make adapting to the Common Core a reflection point in their own practice? Teachers and principals discuss the opportunities Common Core offers for their students and for their own focus and teaching practice.

In this activity, students simulate the interaction of variables, including carbon dioxide, in a radiation balance exercise using a spreadsheet-based radiation balance model. Through a series of experiments, students attempt to mimic the surface temperatures of Earth, Mercury, Venus and Mars, and account for the influence of greenhouse gases in atmospheric temperatures. The activity supports inquiry into the real-world problem of contemporary climate change. Student-collected data is needed from activity A in the same module, "How do atmospheres interact with solar energy?" to complete this activity. Included in the resource are several student data sheets and a teacher's guide. This activity is part of module 4, "How do Atmospheres Affect Planetary Temperatures?" in Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

This resource is a video abstract of a research paper created by Research Square on behalf of its authors. It provides a synopsis that's easy to understand, and can be used to introduce the topics it covers to students, researchers, and the general public. The video's transcript is also provided in full, with a portion provided below for preview:

"Adoptive cell therapy is a powerful anticancer strategy in which patients are administered extra immune cells. Often, the cells are engineered to express chimeric antigen receptors (CARs) that recognize specific cancer cell proteins (antigens), enabling cancer targeting. The strength of the anticancer effect depends on structures within the CARs called costimulatory domains. One such domain, 4-1BB, activates the NFκB signaling pathway, but the relationship between the amount of antigen present and the strength of the elicited response isn’t well described. To help, researchers recently developed a mathematical model of NFκB signaling induced by a 4-1BB-containing CAR. Simulations revealed that the degree of NFκB pathway activation differed in response to different antigen concentrations, but the timing was consistent. The model performed well even when the input parameters were changed, suggesting its reliability under different conditions..."

The rest of the transcript, along with a link to the research itself, is available on the resource itself.

This is an introductory course on computational thinking. We use the Julia programming language to approach real-world problems in varied areas, applying data analysis and computational and mathematical modeling. In this class you will learn computer science, software, algorithms, applications, and mathematics as an integrated whole. Topics include image analysis, particle dynamics and ray tracing, epidemic propagation, and climate modeling.

This half-semester course introduces computational thinking through applications of data science, artificial intelligence, and mathematical models using the Julia programming language. This Spring 2020 version is a fast-tracked curriculum adaptation to focus on applications to COVID-19 responses.
See the MIT News article Computational Thinking Class Enables Students to Engage in Covid-19 Response

How do populations grow? How do viruses spread? What is the trajectory of a glider?

Many real-life problems can be described and solved by mathematical models. In this course, you will form a team with another student and work in a project to solve a real-life problem.

You will learn to analyze your chosen problem, formulate it as a mathematical model (containing ordinary differential equations), solve the equations in the model, and validate your results. You will learn how to implement Euler’s method in a Python program.

If needed, you can refine or improve your model, based on your first results. Finally, you will learn how to report your findings in a scientific way.

This course is mainly aimed at Bachelor students from Mathematics, Engineering and Science disciplines. However it will suit anyone who would like to learn how mathematical modeling can solve real-world problems.

In this activity, student teams design small-scale physical models of hot and cold planets, (Venus and Mars), and learn that small scale models allow researchers to determine how much larger systems function. There is both a team challenge and competition built into this activity. Experimental findings are then used to support a discussion of human outposts on Mars. The resource includes an experimental design guide for students as well as a handout outlining a method for the design of controlled experiments, and student data sheets. Student questions and an essay assignment are provided as classroom assessments. This is Activity A in the second module, titled "Modeling hot and cold planets," of the resource, "Earth Climate Course: What Determines a Planet's Climate?" The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

This course introduces the basic ideas for understanding the dynamics of continuum systems, by studying specific examples from a range of different fields. Our goal will be to explain the general principles, and also to illustrate them via important physical effects. A parallel goal of this course is to give you an introduction to mathematical modeling.

The Oregon Math Project Practice Briefs provide a summary of research and practice related to critical topics in mathematics education. They were developed as a collaborative effort between Oregon State University and the Oregon Department of Education.

In this activity, student teams learn about research design and design a controlled experiment exploring the relationship between a hypothetical planet, an energy source, and distance. They analyze the data and derive an equation to describe the observations. Includes student data sheets, a teacher's guide, and a tutorial on how to use the spreadsheet program Excel. This is Activity A in module 3, titled "Using Mathematic Models to Investigate Planetary Habitability," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

In this activity, students build a simple computer model to determine the black body surface temperature of planets in our solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune and Pluto. Experiments altering the luminosity and distance to the light source will allow students to determine the energy reaching the object and its black body temperature. The activity builds on student outcomes from activity A, "Finding a Mathematical Description of a Physical Relationship." It also supports inquiry into a real-world problem, the effect of urban heat islands and deforestation on climate. Includes a teacher's guide, student worksheets, and an Excel tutorial. This is Activity B of module 3, titled "Using Mathematic Models to Investigate Planetary Habitability," of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.

Students explore how mathematical descriptions of the physical environment can be fine-tuned through testing using data. In this activity, student teams obtain satellite data measuring the Earth's albedo, and then input this data into a spreadsheet-based radiation balance model, GEEBITT. They validate their results against published the published albedo value of the Earth, and conduct similar comparisons Mercury, Venus and Mars. The resource includes an Excel spreadsheet tutorial, an investigation, student data sheets and a teacher's guide. Students apply their understanding to the real life problem of urban heat islands and deforestation. The activity links builds on student outcomes from activities A and B: "Finding a Mathematical Description of a Physical Relationship," and "Making a Simple Mathematical Model." This is Activity C in module 3, Using Mathematical Models to Investigate Planetary Habitability, of the resource, Earth Climate Course: What Determines a Planet's Climate? The course aims to help students to develop an understanding of our environment as a system of human and natural processes that result in changes that occur over various space and time scales.