College-level mathematics encompasses a wide range of principles, from those based in relatively basic math to those that are very complex. Accordingly, it's important to tailor your math project to the content you wish students to use in its completion. The best way to design your project is to first identify several objectives. What do you wish students to learn or master through the process of completing the project? For instance, do you wish for your students to perform operationalized calculations, or do you wish for them to synthesize information in order to determine the best approach of several options? Clarifying your goals as you begin will not only make the next step clearer, but also will make the later planning stages simpler.
For those who are interested in creating a math project pertaining to basic math, there are many options. This type of project may be appropriate for business, marketing, science or health studies students as well as math students. When creating an algebraic project, consider these fields. For instance, you could create a case study using medication dosages (requiring algebra to calculate) or a marketing budget. Moreover, algebra is used in many daily life tasks. Consider projects that pertain to personal financial management or nutrition to emphasize for students how important it is for everyone to develop skill in algebra.
Another option may be to incorporate famous theorems into your project. An interesting approach may be to ask students to find practical applications where well-known curves apply. For example, students may perform tasks with a ball and identify the famous curves to which the data correspond.
Because higher-level mathematics focus not just on finding solutions but on the critical thinking that underlies problem solving, choosing a project based upon complex reasoning may be an excellent option. For instance, students may play the chaos game and report back with a verbal explanation of its operation. You may also choose to create a project based upon Bayesian reasoning, or using a technological interface, such as a makeshift Turing machine (see example below under Resources).
Differential equations are an important aspect of collegiate mathematics. Fortunately, they are also conducive to projects because many differential equations correspond to physical occurrences. Many projects can be created based upon the simple motion of a ball or other object, or based upon the simulated motion of a particle. For example, you might ask students to create equations for the velocity, acceleration, distance traveled and so forth, of several trials throwing a baseball.