Describe a particular problem from another discipline that can be addressed through the use of one or more of the linear algebra techniques was have studied this semester.
You should:
pose one or more specific and sufficiently interesting questions relevant to your problem and make the case that these techniques could help someone answer those questions.
not attempt to use these techniques to actually solve the problem you describe in this part of the project (yet).
complete the statement: “In this project I/we will…”
convince me that you have the resources to complete your project.
do more than argue that linear algebra can be applied to a certain area (e.g. physics, engineering, computer graphics, etc.)
You are welcome to explore an interesting problem that has already been solved (see below for suggestions where to look for one of these) or pose an original problem that has not yet been solved. You should include any data relevant to the problem you choose—or instructions for how someone could obtain such data.
The proposal should be submitted in one of the following two formats:
a one page paper, 12 point Times New Roman or similar font, double-spaced with proper formatting, references (required – and cite in text if and only if you list in the bibliography) and citations, OR
a face-to-face (possibly on Zoom) presentation.
The proposal should be given as if to a fellow student in Math 3305. Thus you may assume that your audience is familiar with the material we have covered together as a class this semester.
CITING YOUR SOURCES
You must cite your sources appropriately in text or in your slides, and a list of references must appear at the end of your paper or presentation, formatted appropriately. It does not matter which formatting style you use (APA, MLA, etc.), but you should be consistent in your formatting. Be sure to format your citations (footnotes, endnotes, etc.) correctly according to the formatting style you choose. (Just including a footnote with a link to a Web page is not sufficient.) Make clear what references you use and how you use them. I will look up all of your references so make it clear for me how to find them. If you include a website url include the whole thing.
Did most of your paper come from a single journal article? If so, then there is no need to cite it in every paragraph, but you should explain your use of the article clearly in your paper and cite direct quotations from the article. At most 20% of your paper can be cited from other work; you need to write the majority of the content yourself. Do not cut and paste paragraphs or computations from your sources into your paper. You cannot cite examples from other papers; create your own examples to demonstrate your understanding.
Did your paper come from a variety of sources? Make it clear what ideas (facts, computations, analysis, etc.) came from which sources through proper citations. That is the spirit of not plagiarizing—making it clear where you obtained your ideas. Whatever else you do, do not plagiarize! If your life is falling apart and you are tempted to plagiarize to save time or get a good grade, please talk to me instead.
Also, pay attention to the quality of any sources you reference. Determine if you have a reputable source or not. Wikipedia is not an acceptable source—not because its entries are user-generated, but because no encyclopedia is an acceptable source. You’re welcome to use Wikipedia as a starting point for your research, however. Most statements in Wikipedia are referenced at the bottom of the Web page. Follow these references for sources to use instead of Wikipedia itself. Another student’s project is also not an acceptable source. Again, it could give some ideas of where to start only. Use an in text citation if and only if the work being cited appears in your bibliography. Do not list sources in the bibliography without specifying in the text of the paper how you used them. In general your paper should cite at least one textbook or other scholarly or professionally reviewed source.
TOPIC IDEAS (You should not re-use a project done in any other class.) Note that you must apply in some way a topic that has been introduced in the class post-exam 2: coordinate systems, eigenvalues, diagonalization, etc.
- Markov Chains – Model a board game, sport, or real-world situation using a Markov chain, then determine optimal strategies through an analysis of the model. Or use the basic ideas behind Google’s PageRank algorithm for ranking the popularity of Web pages to rank some other set of connected items. If you choose this topic you may need to model a very simplified version due to computational constraints. These can also be applied to biology, for example, model inheritance of genetic traits
- Discrete Dynamical Systems – Analyze a population, perhaps using actual birth, survival, and death rates, using the eigenvalue approach to dynamical systems (this is covered later in our textbook in Chapter 5—you can read ahead if you are interested in this). Use the Leslie model to solve a problem in ecology; e.g. look at Hawaii’s population and analyze it with actual birth, survival and death rates
- Social networks analysis using graphs and adjacency matrices.
- Obtaining a closed formula for the Fibonacci Sequence. (This and other “pure math” applications are acceptable.)
- Explain the proof or application of the Jordan Canonical Form of a matrix. This is a deep theorem of interest to those in pure mathematics, as well as a very useful formula that appears in a variety of applied mathematics scenarios.
- Choose one of the applied mathematics projects from the Boyce Applied Mathematics textbook. (Knowledge of differential equations required!) Or look at 5.7 in our book about applications of differential equations.
- Use real-life season data to create a win-loss differential matrix and obtain the rankings of sports teams.
- Section 5.6 : Discrete Dynamical Systems and predatory-prey models
- Learn how to tell when a linear transformation is 1-1 and onto. Show that any finite dimensional vector space is isomorphic to ℝn using the coordinate map.
