CLASS PROJECT/SIGNATURE ASSIGNMENT INSTRUCTIONS
An understanding of applied math integrates concepts. This signature assignment extends your learning beyond your ability to solve problems. Mastering the concepts in Applied Mathematics builds critical thinking skills, develops a breadth of knowledge in multiple areas of mathematics, and teaches you new ways to solve everyday problems at work, home, family, and social organizations. This Final Class Project/Signature Assignment is a synthesis of the knowledge obtained throughout the class. You will submit a paper that pulls together the applied mathematics you have learned and applies these concepts to a final project.
PROJECT:
Upon successful completion of this course, you decide to analyze one of four topics as a consultant. You are told that the project will give you full credit and a promotion if you have a thorough analysis.
Your objective is to provide a written report that explains the context of the case, an analysis of the problem, graphs that represent the information provided, an explanation of the calculations used, and a presentation of your results. As the consultant, you will provide a cover page, report, conclusion, recommendations, references, and an appendix with data or supporting information.
Your goal, and the purpose of this assignment, is to compile all pertinent information into one report. We will use George Polya’s Four-Step Method for Problem Solving (Chapter 1):
1. Understand the Problem
2. Devise a Plan
3. Carry Out the Plan
4. Look Back and Check
In order to organize this, an outline is provided. The assignment is broken down into four parts: Situation Analysis, Compilation of Research, Data, or Other Pertinent Information, Problem Solving Related to this Situation, and Conclusion/Recommendations.
While, in actuality, this may be a final project for this class, these projects can pay thousands and even hundreds of thousands of dollars. Why? We present analyses order to improve businesses, medicine, business, crime rates, or society. You will explain your calculations and symbolic operations in order to interpret social and economic trends for this project.
Part 1: Situation Analysis:
1. Before you can examine the problem, you must figure out what/who is the focus of your analysis. What are you studying, what research must you collect? You must design your research by gathering enough information to uncover and understand the problem. You will describe the problem in your first two to three paragraphs. The first couple of paragraphs should include the following:
a. The basic question you, as the researcher, want to address.
b. Describe the historical and practical context, variables, units, and application.
c. The problems you might encounter with missing variables or information.
d. Describe the big picture of this study.
e. Why is it important to readers?
f. Describe the information you must collect and how it relates to the big picture of social and economic trends.
Part 2: Compilation of Research, Data, or Other Pertinent Information
2. Your next step is to collect and organize information. The research you collect will be included in part 2. Since each study is different, you will compile whatever you need to analyze your situation. You will describe and accurately compute symbolic operations. This part of the study will include:
a. Data, calculations, and other information.
b. Graphs and charts should be presented to explain your situation.
c. Additional elements of the big picture, like social and economic factors.
Part 3: Problem Solving Related to this Situation
3. Assuming that all assumptions have been met, it is now time for you to conduct some analysis. You might want to add some statistical data like measures of the center, distribution, skewness, correlation, probability, or hypotheses.
a. What assumptions did you make?
b. Does your data support the research you have done?
c. How do the parts of your research connect?
d. Going back to the problem, what is your analysis?
Part 4: Conclusion and Recommendations
4. Use your research to interpret and explain the information you collected. Consider your project in terms of social and economic factors.
a. What can you infer?
b. What information might lead you to a different conclusion?
c. What variables are missing?
d. What additional information would be valuable to help draw a more certain conclusion?
e. What are your recommendations?
f. What follow up study might be helpful?
Hint: This is your conclusion, but it is also a window to further research and analysis.
Final Comments Before you Begin
Computers and calculators are good at yielding results, but such results typically require the careful interpretation that breathes life into an otherwise meaningless set of information and outcomes. We should recognize that a result is not automatically valid simply because it was computer-generated. Computers do not think, even though they crunch out results.
The key in this study is to have this research project make sense in the context of the real world. So be sure to criticize, analyze, and connect the information to the question to be answered in a clear way.
FORMAT: Word document.
Length:
Title page: You should have a cover page. The cover page should have the title of your study, your name, Brandman University, MATU 103, term, and year. You might find it helpful to include an image of something representative of the study on the cover. This is not necessary, but may provide a visual context for your report.
Write Up/Body: The body should not exceed 6 pages with the graphs, images, screen shots, data output, and text.
References: Please include all articles, books, websites, publications, or other information that helped you reach your conclusion. The references come before the appendix.
Appendices: You should have appendices; this might be an additional 1-2 pages. In the appendix, include data and additional information. You may also want to include computations, but this is not necessary. It may be helpful when you refer to this later or if the reader wants to review your computations.
The four topics are:
1. Gambling
Gambling occurs in many forms. Although we typically think of gambling in terms of casinos, playing the stock market, playing the lottery, and investment decisions are gambling too. All of this relies on probabilities and the odds of winning. Your great aunt passed away and left you with $250,000. You decide not to spend the money, but to invest it in one of four options you envision so that your money grows to $1,000,000 when you retire in 20 years. You will write up a report/analysis of your various choices for investments/gambling. Your will present research that shows what the chances of each outcome coming to fruition. Briefly explain the social and economic consequences of gambling.
2. Home Buying Decisions
Peter wants to buy a house, but the ads say that he can get a subprime rate, ARM, extended loan, and other buying options. You are asked to come in and analyze this for Peter, but you need to get your arms around this situation. Before you start your study, you decide to research what happened in the housing market in 2008. Why did it happen? What are the trend data for home purchases over the past decade? What is projected in the future? Peter has $100,000 to put down on the home that he collected for awhile and he earns $80,000 per year. What locations are good? What is a good investment? Although his job is in Irvine, California and he would like to live in Orange County, California, he does not think that is possible. Give Peter four options for where he can live, what he can do, and explain why. Briefly explain the social and economic trends in home buying.
3. Fractals
Fractals were developed by Benoit Mandelbrot. Although they are beautiful creations and they have been replicated in an infinite number of ways, many practical applications of fractals exist as well. If you go to Epcot Center in Disney World you will see in the Imagination Center numerous fractals and you can make new ones too. After Mandelbrot explored fractals, many mathematicians started using them in their research. This exploded and geographers, cartographers, filmmakers, and biologists began to see how they could use fractals. You have a job with a production company, Steelberg Films. The head of Steelberg films, Mike Steelberg, has approached you about using fractals in his filmmaking so that realistic landscapes and ocean formations could be digitally created. He wants you to create a presentation on fractals, including the history, geometry, and uses. He also wants to know what other films have used fractals, the basics of how to create them, some examples, and what you recommend for the spaceship scenes he wants to make for his new movie, Mars Landing. Briefly explain the social and economic opportunities of fractal geometry.
4. Cryptanalysis/Code Breaking
Although cryptanalysis and code making/breaking sounds like undercover work of spies, it is part of your everyday life whether you know it or not. Your personal information is out there in digital form. Most of this is encrypted, but some is vulnerable to attack and people’s identity (social security numbers, names, images, etc.) are taken each year. Your company, Music and Film Innovators (MFI), has discovered that some of the music and music videos it creates have been stolen and used by other music/film creators. You have been asked to write up a report on the prevalence of intellectual property, identity theft, and copyright and various ways to protect your company’s creations and personnel data so that hackers cannot attack you. Present the various ways cybercriminals can attack MFI, statistical data that shows what, how, and who is doing this, and ways MFI can protect itself. What are your recommendations? Briefly explain the social and economic trends of encryption and decryption systems.
