A. Kinds and qualities of writing relevant to mathematics
By the time they graduate, mathematics majors should be competent in the following types of writing:
Building blocks of mathematical writing
- Description of a calculation or series of calculations and presentation of the results.
- Proofs of mathematical statements at a variety of levels of complexity, including details that are suited to a particular audience (experts in the field, novice mathematicians, classmates etc). This type of writing may include
- background information
- clear statements of assumptions and conclusions
- identification of the method of proof (e.g. induction, contraposition, or contradiction)
- Discussion of the implications and limitations of a solution or method.
Synthesis and extended mathematical writing:
- Extended reports that, in addition to the above, may include
- Outlines of the key steps to a problem’s solution in a way that is suited to a particular audience (experts in the field, novice mathematicians, or clients who may or may not be mathematically inclined)
- Descriptions of a problem’s context and origin
- Explanations of the significance of a problem and whether its significance is due to its relationship to a major question in mathematics or its application in a nonmathematical context
- Summaries of and reactions to articles and book excerpts
- Reports on single applications of subject matter from class.
B. Courses through which mathematics majors develop their ability to write in the relevant forms and styles
All mathematics majors will achieve writing competence through three required courses: Introduction to Proof and Problem Solving (Math 200), Abstract Algebra (215), and Analysis I (310). In each of these courses, students will complete frequent written assignments, and revise selected assignments, throughout the semester. Students will also regularly analyze and critique examples of both student and professional mathematical prose.
The focus of much mathematical writing is the proof of a theorem. To become competent in writing proofs, students will have frequent practice writing and revising short individual and group proof assignments. They will also complete short assignments in other styles of mathematical writing. For example, students may compose a paragraph explaining the significance and applications of a theorem, or outline the key steps of a long proof discussed in class. Students will revise and resubmit selected assignments in response to feedback from professors and peers. Finally, they will draw on skills developed throughout the semester to complete at least one term paper per class, which may be supplemented with an oral presentation. Students should write a total of about fifteen pages of polished (i.e. drafted, critiqued and revised) mathematical prose per semester.
To meet professional standards of presentation, students will be required to complete some writing assignments in LaTeX or an equivalent scientific typesetting environment. Proficiency with such software will be largely achieved in Math 200, which is a prerequisite for the other two writing-intensive courses.
C. Writing in statistics and applied mathematics
Communicating statistical results in a clear and concise written report is an essential part of any data analysis project. In particular, reports need to be written in a way that will be meaningful and informative for non-statisticians. Since the ability to communicate results is central to the study of statistics at any level, writing skills are emphasized starting from the introductory statistics level (in homework assignments) and more substantially in the advanced applied statistics courses where students conduct an actual data analysis project and submit a professional written report.
In courses such as Differential Equations, Discrete Dynamical Systems, Cryptography, and Scientific Computing, students will turn in assignments guided by professional standards in applied mathematics, explaining the significance of a problem with regard to a particular application, describing the key steps in its solution and their motivation, and preparing reports that explain technical results to non-specialists. The level of competence in this kind of writing that a student achieves will depend on the elective courses she or he takes.