In this assignment from M.I.T.’s communication-intensive offering of Real Analysis, students develop and evaluate various definitions for the notion of a “gap” in a set. The assignment was developed by the 18.100C team, especially Craig Desjardins and Joel Lewis, with modifications by Kyle Ormsby and Susan Ruff. This is the first assignment of the term that requires students to use LaTeX, so students must submit at least one LaTeXed page two days before the assignment is due. This “draft” due date ensures that they devote time to figuring out the basics of LaTeX early enough that they can devote time
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The language of mathematics can throw up barriers to broad dissemination of information about mathematics. Mathematical statements are supposed to be precise, devoid of the ambiguities of ordinary speech. The language is unusually dense and relies heavily on a specialized vocabulary. The meaning and position of every word and symbol make a difference. Mathematician William Thurston once expressed the difference between reading mathematics and reading other subject matter in this way: “Mathematicians attach meaning to the exact phrasing of a sentence, much more than is conventional. The meanings of words are more precisely delimited. When I read articles or listen to speeches
Read more →To learn the wording and punctuation conventions of mathematics, students benefit from individualized feedback on their writing and presentations. Resources for Undergraduates Stephen Maurer’s Undergraduate Guide to Writing Mathematics contains a glossary of mathematical terms as well as sections on when to use displays, saying what you mean, style, words vs. symbols, etc. Some students may find math dictionaries to be helpful. E. J. Borowski and J. M. Borwein’s Collins dictionary of mathematics is also available as the online database The MathResource Dictionary. Searching is free; browse for a fee. J. A. Glenn and G. H. Littler, A dictionary of
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