By Joseph A. Gallian, University of Minnesota Duluth The ability to do a PowerPoint (or equivalent) presentation well is a valuable skill that many students will find useful in connection with their academic work and employment. Preparation 1. Determine the level of knowledge of the target audience. 2. Choose a subject that will appeal to the intended audience. 3. Don’t overestimate what the audience knows about your subject. 4. Don’t try to do too much. 5. Use simple examples and concrete special cases. A “non-example” often helps to clarify a concept. For instance, if you use the integers modulo 7 […]

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Paul R. Halmos (1916-2006) had strong views on the communication of mathematics, whether in written form, in the classroom, or in lectures. See, for example, “Paul Halmos on Writing Mathematics.” Here’s his reminder to lecturers: “Some lecturers defend complications and technicalities by saying that that’s what their subject is like, and there is nothing they can do about it. I am skeptical, and I am willing to go so far as to say that such statements indicate incomplete understanding of the subject and of its place in mathematics. Every subject, and even every small part of a subject, if it […]

Read more →By Katharine Merow In the waning hours of MAA MathFest 2013, in Room 12 of Hartford’s Connecticut Convention Center, James Freeman addresses a sparse crowd he has dubbed “the few, the proud, and the brave.” Then, as if to determine whether “the candid” ought to be added to that list, the Cornell College professor poses a touchy question: “How many of you have heard bad talks at MathFest?” Getting some mathematicians to admit the impenetrability of, say, an invited lecture borders on impossible, but folks at this session—“Great Talks for a General Audience: Coached Presentations by Graduate Students”—have no qualms […]

Read more →By Aaron Luttman and Rachel Schwell A number of years ago a graduate student was asked to give a 20-minute presentation at the Montana Academy of Sciences annual meeting describing his research on using partial differential equations to model a botanical process. The student thought to himself, “The audience will consist of graduate students and faculty from a wide range of sciences, who aren’t necessarily familiar with PDE modeling or the numerical issues involved. I’ll make sure to spend plenty of time going through the numerical details of my computation, so the audience will understand the computational subtleties.” This student […]

Read more →“Active learning” hit the news this week with the publication of a study suggesting that undergraduate students generally do better in classes that engage them through activities or discussion than in lecture-based courses. Scott Freeman (University of Washington) and his colleagues describe their results in the paper “Active learning increases student performance in science, engineering, and mathematics,” published online in the Proceedings of the National Academy of Sciences. Freeman and his team analyzed 225 studies conducted between 1942 and 2010 that reported data on exam scores or failure rates when comparing traditional lecturing versus active learning in undergraduate science, engineering, […]

Read more →An abstract plays a key role in calling attention to a research paper in a journal or an oral or poster presentation at a conference or colloquium. It serves as a short introduction to the subject at hand. Typically, the prospective reader or listener has only your title and abstract available to decide whether your topic is worth his or her attention. And a title by itself, whether vague (“On a Theorem of Hilbert”) or specific (“A Complete Description of Θ-Continuous Functions”), doesn’t do the job. Without an abstract, there usually isn’t enough information for someone to decide that what follows will be of […]

Read more →Exercise: You Be the Editor I Can you figure out why the suggested answer (or answers) shown below each statement or phrase is an improvement on the original (in bold)? Suggested Answers: 1. These results were obtained jointly by Hilbert and myself. These results were obtained jointly by Hilbert and me. Hilbert and I obtained these results jointly. 2. If x > 0, then Euler proved in 1756 that . . . Euler proved in 1756 that if x > 0, then . . . 3. Since this limit exists, then the series converges. Since this limit exists, the series converges. […]

Read more →Test your mathematical communication skills. Each of the following sentences or phrases has at least one flaw. How would you edit each one to improve its style or syntax? These results were obtained jointly by Hilbert and myself. If x > 0, then Euler proved in 1756 that . . . Since this limit exists, then the series converges. Obviously, every group G of prime order is simple. Occurrences were observed in which . . . It has been noticed that . . . The best one of those are in the book. She is one of those who enjoys mathematics. How […]

Read more →Leslie Lamport of Microsoft Research is the 2013 recipient of the prestigious A.M. Turing Award, presented by the Association for Computing Machinery. Lamport was honored for “fundamental contributions to the theory and practice of distributed and concurrent systems, notably the invention of concepts such as causality and logical clocks, safety and liveness, replicated state machines, and sequential consistency.” Lamport has also been keenly interested in technical communication. In 1987, he presented a guest lecture in a course on “Mathematical Writing” (CS209) conducted at Stanford University by Donald Knuth. Recordings of the course lectures are still available (Lamport’s lecture was on […]

Read more →Scrawl a shape on a piece of paper. Really. Any shape. Now draw a curve tightly around your shape, as close as you can. Do this again. And again. Do you notice anything as you draw more outlines? Is the doodle getting more circular? Will this always happen, no matter what shape you start with? This is the question Stanford mathematician Ravi Vakil tackles in the American Mathematical Monthly paper that has garnered him the 2014 Chauvenet Prize, awarded by the Mathematical Association of America (MAA) at the Joint Mathematics Meetings in Baltimore. Named for a professor of mathematics at […]

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