Linear Algebra Writing Project
This project is due at the end of week 8 of the course.
In this course, we have used the weekly forum discussions to delve into Linear Algebra’s applications, asking such questions as: How is Linear Algebra used in the real world? Is it a common or uncommon technique? Is it used to cut costs? Increase computational power? Solve problems not otherwise easily (or cost effectively) solvable? Unfortunately, the weekly forum discussions by their nature have provided only limited opportunity to learn about how Linear Algebra is used in the real world.
With that in mind, for this writing project we are going to delve in more depth into this issue.
Please choose one Linear Algebra topic. You can choose any of the topics we’ve covered in this course, or even a topic that we did not cover. As long as it relates to Linear Algebra, it is fine. For a quick list of the topics we’ve covered, just look at the titles of the subsections of each chapter in the textbook.
Then associate your chosen topic with an example from the real world of how that topic can be applied to solve problems. Examples include (but are by no means limited to):
– Orthogonal Diagonalization in Statistics
– Linear Models in Civil Engineering
– Least Squares and GPS
There are numerous examples of Linear Algebra applications scattered throughout our textbook: in the first introductory pages of each chapter, in selected chapter sections (e.g., 1.10), and contained within the description of many homework problems located throughout the chapter. You can also find examples at any of the websites mentioned in the weekly forum descriptions, or at websites you research and find yourself.
Once you have picked a topic and application, you are ready to do research and write up your findings. For your chosen “Topic + Application” combination, be ready to answer the following questions:
1. Describe the Linear Algebra topic in general. Give a brief overview of the mathematics involved. If you are writing about (for example) orthogonal diagonalization in statistics, then your topic is orthogonal diagonalization and you would write an overview of it, much as you would find in a textbook.
2. Describe the full range of applications for your chosen topic. Although the rest of your paper will be devoted to the single application of your chosen topic, for this section the idea is to paint a picture of the full range of applications that are possible. For example, orthogonal diagonalization can be used anywhere that you have large collections of data, and this occurs not only in statistics but also in image processing, weather forecasting, satellite surveillance, and the like.
Be sure to list each of the different application areas and briefly (a sentence or two for each different application) indicate how your chosen topic is used for each type of application. For example, in weather modeling orthogonal diagonalization is used to model how the atmosphere will behave when the atmosphere is divided into small cells and each cell is treated as an individual data point.
3. Now it is time to zero in on the specific “topic + application” combination that you have chosen. In this part of the paper, you should describe how the specific topic you chose is applied to real world problems. Essentially this is the same idea as item 2 above, but because you are focusing here on only your one single chosen application, you can go into it in much more depth and detail than you did for the brief overviews you wrote in item 2.
Continuing with our example, you might describe in detail how orthogonal diagonalization is used within statistics. What kinds of statistical applications is it used for? Could the statistical problems be solved any other way, and if so what is the advantage of using orthogonal diagonalization? To what extent, if any, is the process computerized and what changes, if any, are made to it in order to accommodate computerization? These particular questions probably do not apply directly to your own particular topic+application, but I am sure you can think of many similar aspects to discuss once you have done the research.
4. The last part of the paper centers on doing some illustrative calculations. Create a numerical problem (the kind you might find in the textbook as a homework problem) – and then fully solve it. The problem you create should illustrate how the “topic + application” combination you chose is used in the real world. You may if you wish model your problem on one you find online or in the textbook, but you must use your own original numbers (not the numbers in the problem you modeled your version after) and then solve the problem yourself using your own numbers. Or you can write your own problem from scratch, in fact this is preferable if possible.
For an example of the kind of homework problem that could serve as a “role model” for section 4, see the textbook problems found on p.430 no. 9, p.145 no. 11, or p.90 no. 25.
The total paper should be approximately 4-5 pages in length (not counting the cover page, references page, or any exhibits), and include a full set of references in APA format (including the textbook if you use it, as I assume you will, other books, and all websites). APA format requires that the font used should be Arial or Times New Roman, 10 or 12 point only; the pages be double spaced; and the margins should be no more than one inch all around.
Please format the paper in APA style. You can find an online APA style guide in the APUS Library. Navigate to APUS Log in » Online Library: CampusGuides » Library Tutorial Center »Writing Help or you can use the link http://apus.campusguides.com/writing/citation and then click on APUS APA Style Guide.
Another excellent APA resource is found by googling “The Owl at Purdue” (OWL is the Online Writing center at Purdue University) – there you will find not only a style guide but a sample paper that you can use as a model for what your own completed paper should look like.
Please post your completed papers in the Assignments area (Assignments tab on the left hand side of the Sakai classroom). Your assignment is automatically submitted to TurnItIn with your submission.
Be sure that you attach your assignment in the Assignment area, attached as a file attachment in doc or docx format (Word format). Do not paste or write your assignment into the text box, as this cannot be run through TurnItIn (which is required).
Note that no work is accepted once the course is over, so for all practical purposes, you cannot submit this assignment late. Be sure to plan your work and your time accordingly.
Grading Rubric (total 100 points)
Excellent Competent Needs Work
(20 pts total) Topic description is detailed and accurate. A generous amount of information is conveyed.
Numerous examples are provided which illustrate the topic.
The mathematical concepts are clearly explained including generous use of mathematical equations and concepts. (19-20 pts) Topic description is accurately portrayed.
Some examples are provided.
Enough math concepts are explained to convey the required topic information. (12-18 pts) Inaccurate statements are made in the topic description and/or math concepts and/or examples.
Topic description may be too superficial or too brief to accurately portray the topic, and/or key math concepts may be missing. (0-11 pts)
(25 pts total) Application descriptions are detailed and accurate. A generous amount of information is conveyed.
Numerous examples are provided which illustrate the application areas.
Associated mathematical concepts are clearly explained including generous use of mathematical equations and concepts. (24-25 pts) Application descriptions are accurately portrayed.
Some examples are provided.
Enough math concepts are explained to convey the required applications information. (15-23 pts) Inaccurate statements are made in the applications description and/or math concepts and/or examples.
Applications descriptions may be too superficial or too brief to accurately portray them, and/or key math concepts may be missing. (0-14 pts)
(25 pts total) Topic+application description is detailed and accurate. A generous amount of information is conveyed.
Numerous examples are provided which illustrate the combination.
The mathematical concepts are clearly explained including generous use of mathematical equations and concepts. (24-25 pts) Topic+application description is accurately portrayed.
Some examples are provided.
Enough math concepts are explained to convey the required information. (15-23 pts) Inaccurate statements are made in the topic+application description and/or math concepts and/or examples.
The description may be too superficial or too brief to accurately portray the topic+application, and/or key math concepts may be missing. (0-14 pts)
(20 pts total) Homework problem represents the topic+application accurately.
Homework problem is original (not copied from any prior model).
Homework problem is robust in nature, not a simplistic example.
All calculations are complete and correct. Explanations are accurate, clear and easy to understand. (19-20 pts) Homework problem represents the topic+application accurately.
Homework problem may have been copied from an existing online or textbook model but the numbers are original.
All calculations are accurate.
Explanations are accurate. (12-18 pts) Homework problem does not represent the topic+application accurately, or was copied from an existing model without changing the numbers.
Calculations may be inaccurate.
Explanations may not be accurate. (0-11 pts)
Writing Style and Mechanics
(10 pts total) Paper is formatted in APA format.
References are included and correctly formatted.
All grammar and spelling is correct.
Paper is at least 4 full pages of text, excluding cover page and references. (9-10 pts) Paper is formatted in APA format.
References are included and correctly formatted.
All grammar and spelling is correct with only very minor errors.
Paper may be marginally less than 4 full pages of text, excluding cover page and references. (6-8 pts) Paper may not be formatted in APA format.
References may not be included.
There may be significant grammar and/or spelling errors.
Paper is significantly less than 4 full pages of text, excluding cover page and references.