By Steven G. Krantz

This ebook is set writing within the expert mathematical surroundings. whereas the ebook is nominally approximately writing, it is also approximately the right way to functionality within the mathematical career. in lots of methods, this article enhances Krantz's past bestseller, easy methods to educate arithmetic. people who are conversant in Krantz's writing will realize his energetic, inimitable style.

In this quantity, he addresses those nuts-and-bolts issues:

– Syntax, grammar, constitution, and style
– Mathematical exposition
– Use of the pc and TeX
– email etiquette
– All points of publishing a magazine article

Krantz's frank and simple process makes this ebook really appropriate as a textbook. He doesn't stay away from tough themes. His purpose is to illustrate to the reader the right way to effectively function in the occupation. He outlines easy methods to write supply proposals which are persuasive and compelling, tips to write a letter of advice describing the learn skills of a candidate for promoting or tenure, and what a dean is seeking in a letter of advice. He extra addresses a few uncomplicated matters resembling writing a ebook idea to a writer or utilising for a role. Readers will locate in studying this article that Krantz has produced a high quality paintings which makes glaring the facility and value of writing within the arithmetic career.

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Additional info for A Primer of Mathematical Writing: Being a Disquisition on Having Your Ideas Recorded, Typeset, Published, Read, and Appreciated

Example text

For example, Let / be a function. / is said to be semicontinuous if ... * and For most points x, x € S. * Even in these two simple examples you can begin to apprehend the problem: the eye balks at a sentence or clause that is begun with a symbol. You find yourself rereading the passage a couple of times in order to discern the correct sense. Much better is: A function / is said to be semicontinuous if ... and We see that x e S for most points x. 8. MORE SPECIFICS OF MATHEMATICAL WRITING 25 Observe that both of these revisions are easily comprehended the first time through.

The main thing, and this advice applies to spelling and to many other choices, is to select a standard and to be consistent. Obviously, Clearly, Trivially These words have become part of standard mathematical jargon. This is too bad. In the best of circumstances, when you use these phrases you are endeavoring to push the reader around. In the worst of circumstances you are throwing up a smoke screen for something that you yourself have not thought through. It would be embarrassing to count the number of major published mathematical errors that have been prefaced with “Obviously” or “Clearly” (no doubt the supreme deity’s way of reminding us that “pride goeth before the fall” ).

Of course mathematical notation allows us to write lim ^ o V — to in­ stead of either of these; this abbreviated presentation will, in many contexts, be more desirable. 6, then the set of points at which / •g is differentiable is a set of the second category, provided that the space of definition of / is metrizable and separable. 6. COMPOUND SENTENCES, PASSIVE VOICE 15 instead say Let X be a separable metric space. Let / be a continuous function that is defined on an open subset of X . Suppose that g is any positive function.

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