A Project of Discrete Mathematics
 
You will need to do a project on discrete mathematics. Start your project as soon as possible. Your project must be submitted electronically in the Microsoft Word file by 11:59PM, Tuesday, Dec. 8, 2020 to D2L. Since this is the final week for the semester, please do not be late. Your project will be evaluated based the following rubrics.

1. Excluding the title and reference pages, your paper must have at least 10 pages with double line space. Each missing page will result in a deduction of 15 points in addition to the deductions based on the following rubrics.
2. 2. (5 points) Professional appearance and format of your paper: The margins are not more than 1” from each side; the font size should not be larger than 12; and the font can be Calibri, or Times New Roman. The paper must be numbered. The sizes of tables and pictures need to be reasonable. Your paper should be organized in the following format:
3. Project title, names of authors, emails and affiliations (optional)
4. Project summary, abstract, and/or objectives
5. Project Body (you may use sections, bullets tables, pictures)
6. Acknowledgement (if applicable)
7. References: If you obtained any information from the Internet, include the URL. You need use the MLA (Modern Language Association) citation style, or the Chicago citation style, or the style of a reputable mathematical journal, for example, the Journal of Mathematical Analysis and Applications (http://www.elsevier.com/wps/find/journaldescription.cws_home/622886?generatepdf=true) Your paper must be presentable, or the entire project will receive 0 points.
8. (5 points) Summary or abstract of your project. You may include objective statements. a. Project title, names of authors, emails, affiliations, abstract should be included in the title page.
9. (15 points) Difficulty and complexity: There are four options for your project (see the next page). For Project Option 1 and 2, the difficulty refers to the level of school mathematics from the lowest, arithmetic, to the highest, calculus II. For Project Option 3, your project needs to be at least at the level you taught, teach, or will teach. The appropriate length of the project is also a consideration of difficulty, though the minimum length is 10 pages with double space. An unnecessarily lengthy paper will not be considered more difficult. Difficulty may mean complexity. Use and inclusion of definitions, theorems and proofs will reflect difficulty and complexity. The more difficult the mathematics is, the more points you may earn.
10. (15 points) Originality or creativity: The first meaning of originality is that your paper must be your own work. Plagiarism is prohibited, and hence will result in 0 for the entire project. Any materials taken from the Internet, publications and other people’s work must be well cited. The second meaning of originality is that your work has not been seen on the Internet and in publications. Originality may also mean creativity. The more original work your project has, the more points you may earn.
11. 6. (60 points) Readability and Communication: clear and correct calculation, derivation, proofs, applications and explanation; sufficient and appropriate examples; real world examples, particularly related to your students, school and community (this also contributes to originality); smooth connection and transition among concepts, definitions, theorems, examples, and explanations; use of pictures, diagrams, and tables; easiness for understanding; appropriate citation; completeness of the project; fun to read.
12. 7. Correctness: mathematically your project must be correct. Errors and mistakes in mathematics will be subject to deduction of points you earn. Errors and mistakes in other areas (English, Education, Science…) may or may not cause a deduction, depending on the nature and significance of the errors and mistakes.
13. 8. The instructor retains the final interpretation of the grading rubrics.

 
You can choose one of the following topics for your project:
Option 1, False Proofs: There are many false proofs. For example, the following article is an MIT student project:

• Xing Yuan, Mathematical Fallacy Proofs http://dspace.mit.edu/bitstream/handle/1721.1/100853/18-304- spring-2006/contents/projects/fallacy_yuan.pdf You also see two other examples in our lecture, Proof Techniques (1), Introduction. For this project, you need to search the Internet for more new false proofs. Do not use the examples from our lectures and Yuan’s paper.

For each false proof you use, please explain what lead to the false proof, and how the false proof helps students learn and understand and/or enhance your teaching.
Option 2, Analysis and Classification of Student mistakes and difficulties: Students often have difficulties and make mistakes in arithmetic, algebra, trigonometry, and calculus. Why? What kind of mistakes and difficulties do they make or have? How can you help? You may read the following articles from the following link: https://www.semanticscholar.org/paper/Classifying-students-mistakes-in-Calculus-Hirst/436f1e13390e367c9647d493a5b462561d63b003

• Keith Hirst. Classifying Students’ Mistakes in Calculus
• Nourooz Hashemia,*, Mohd Salleh Abua , Hamidreza Kashefia , Khadijeh Rahimib. Undergraduate students’ difficulties in conceptual understanding of derivation

If you have taught or tutored before, you may collect the mistakes that your students made, then classify and analyze them. You may also develop a plan how you would apply your findings in your classroom.
 
Option 3, Discrete Mathematics in Your Classroom. If you are a pre-service or in-service teacher, you may choose to read the three articles in Section 4 (Pages 187-202, Pages 203-222, and Pages 223-236) and the four in Section 5 (pages 239-254, Pages 255-264, Pages 295-300, and Pages 301-307) in the following book,

• Discrete Mathematics in the Schools, edited by J. Rosenstein, D. Franzblau, and F. Roberts , published by the American Mathematical Society, ISBN-13: 978-0-8218-1137-5, http://bookstore.ams.org/dimacs-36/.

You may also read other articles in the book if you like. After your reading, develop a teaching plan how you can include some topics of discrete mathematics in your classroom.
Or, you may pick a section (or a topic) in the textbook. Develop a lecture note how you would teach it. Your lecture note should include introduction (your understanding of the section(s)), definitions, theorems, examples, and your explanation of the definitions, theorems, applications if there are applications, and homework assignments. Have a description why the section or topic is important.
Option 4: Any other topics of discrete mathematics that you would like to investigate further. Discuss this with your instructor before you work on it. See the following examples:

• David and Elise Price. Complex Numbers: From “Impossibility” to Necessity. The AMATYC 2018 Conference Proceedings https://cdn.ymaws.com/amatyc.site-ym.com/resource/resmgr/2018_proceedings/s038_-_price.pdf
• Sean Saunders, Standing on the Shoulders of Giants. The AMATYC 2019 Conference Proceedings. This is a Power Point Presentation, which gives you ideas what to do. When you write your project, you need to write it as a paper, not a PowerPoint Presentation. https://cdn.ymaws.com/amatyc.siteym.com/resource/resmgr/2019_conference_proceedings/s017_saunders.pdf