Communications in Mathematics
As scientists, we know that the act of communicating our work to others — when writing a research paper, speaking at a seminar, or sketching out our ideas on the blackboard to a colleague — gives us a valuable opportunity to test the validity of our reasoning.
As instructors, much of our time is devoted to teaching students how to learn mathematics, and even how to think mathematically. Comparatively little is done to help students communicate mathematically.
It is often assumed that students will learn to express themselves accurately by osmosis — absorbing good practice throughout their instruction. And some do. But many students communicate poorly, using sloppy notation, disordered presentation, and a lack of attention to detail. Communication is a skill, but it is a skill that needs to be learned, pattern for pattern, convention for convention.
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Course description
Project description
The course was inspired by classes on mathematical writing by Prof. Dr S. Kleiman at the MIT Department of Mathematics.
All undergraduates at MIT have mandatory Communication Requirements. From the official MIT webpage, these requirements
...were developed out of the belief that MIT students, regardless of their field of study, should learn to write prose that is clear, organized, and effective, and to marshal facts and ideas into convincing written and oral presentations.
In contrast, we do not take communication and other "soft skills" so seriously. We require our students to write a Bachelors thesis and a Masters thesis, but offer them little to no instruction how to go about the process.
The problems our students face are compounded by the fact that — unlike at MIT — most of them are not writing in their native tongue. The result is that the quality of the written exposition produced by many of our top students falls below the standards set by other similar internationally renowned universities.
What makes a writing course important?
Writing can be part of the learning process. As Baker explains in The Practical Stylist , writing can be an integral part of the learning process:
In writing you clarify your own thoughts and strengthen your conviction... Writing is a way of thinking. You learn as you write.
A student with only a limited comprehension of the underlying principles may be able to recite a proof, or perform a computation, but it is not possible for them to write convincingly about either. Writing forces students to examine and rectify the gaps in their understanding.
Writing is hard work! It may not be the most glamorous part of our jobs, but much of the day-to-day life of an academic involves writing in some shape or form:
? Research papers,
? Textbooks,
? Presentations and seminars,
? Job and grant applications,
? Press releases and social media...
Even for established scholars and scientists, the art of writing well often remains elusive. As Krantz writes in the preface to his A Primer on Mathematical Writing:
I know many examples of mathematicians A and B, of roughly similar talent, with the property that A has enjoyed much greater success than B, and considerably more recognition for his ideas, because A wrote his work in an appealing and readable fashion and B did not.
Writing is a transferable skill that is valued outside of academia. Our students will thank us for teaching them how to craft clear and effective prose using simple and direct language. Their future employers will thank us too.
Contact information
Additional links
externe Seite Project websitePaper:
1. Sheridan Baker, The Practical Stylist, Pearson/Longman (9th Edition, 2005)
ISBN-10: 0321333497
2. Steven G. Krantz, A Primer on Mathematical Writing, AMS (2nd Edition, 2017)
ISBN-10:1470436582