Various strategies can be used to teach precision, rigor, and their importance. Examples of seemingly correct arguments that are wrong In The Man who Knew Infinity: A Life of the Genius Ramanujan, Kanigel gives as an example Ramanujan’s claim of having “found a function which exactly represents the number of prime numbers less than x.” Using this example, Kanigel clearly explains for a lay audience why rigorous proof is essential in mathematics, even (especially) for those with a strong intuitive understanding of mathematics. These pages could be a suitable reading assignment for students. (By Robert Kanigel 1991, pp. 215-224; Readers
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This assignment from the second week of Real Analysis (Fall 2009) prods students to think rigorously. It includes questions requiring students to translate notation and to learn to LaTeX a table. Developed by the 18.100C team, especially Joel Lewis and Craig Desjardins.
Read more →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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