Writing Projects in Mathematics
In many courses, I ask my students to write about mathematics. This may be rather informal, such as a paragraph on an assignment or quiz. On other occasions, it may occur in the form of a writing project, in which students spend 1-3 weeks applying their mathematics knowledge to a "practical" problem. Or it may form a course project, often at the end of the semester to cap what they have mastered in our course. Below, I offer examples of these projects from the last few years.
Writing Projects for Calculus
| Class | Description | Topic | Difficulty |
| Calculus I | from spring 2013 | tba | |
| Calculus II | Area of a Leaf | Riemann sums | * |
| Water in a glass | Volumes by integration | ***** | |
| Area of a Leaf | Coyote & Roadrunner | ** | |
| Calculus III | Blasting Former Planets | Gradients | * |
| When does a can tip over? (the bottle part was too messy/hard) | Volume of mass; 3-d integration | **** |
Projects for a Liberal Arts Mathematics Course
| Description | Topic | Difficulty | Comments |
| Divisors Table (as a Google Doc) | Prime Divisors | * | Cloud-based projects are worth considering |
| Traveling Salesman & AP football | Graph Theory | ** | Distance discrepancies will occur unless standardized |
| Conducting Your Own Election (a favorite!) | Voting | *** | I really like the Ranked Pairs method |
| Choosing the Next Topics | Voting | * | students vote on our next topics |
| Miscellaneous ideas | various | * | offered as extra-credit in 2012 |
| Flatland Topics | Geometry | * | |
| Rabbits & Rectangles | Fibonacci & golden ratio | * | actually offered first to a calc class for extra credit |
Course Projects
These are usually large lists of potential topics; some are more refined and detailed than others.| Undergraduate Topology | Project list |
| Axiomatic Geometry | Project list |
| Knot theory (master's level) | Project list |
| Geometric Topology (master's level) | Project list |
Sources and Disclaimers
I first was introduced to writing projects at Project Next at a workshop by Gavin LaRose. See his website listing of projects.Best source: the book Writing Projects for Mathematics Courses: Crushed Clowns, Cars & Coffee to Go, by Crannell, LaRose, Ratliff, and Rykken. Several writing projects below are directly adapted from these.
Disclaimers: I have drawn inspiration for the projects listed below from many sources. Most projects are in need of a serious proofreading. My own style for the writing projects is incredibly corny. Educators are welcome to standard fair-use of these in their own courses. What I ask for in exchange is for you to share your materials and tell me how they went. I'm willing, where possible, to share examples from my own students' work. (A recent rash of plagiarism here suggests that I should not post examples on the web.) Some of these projects are clearly a 'first draft' -- I'll improve them for the next time around.
