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The most common errors in undergraduate mathematics
This page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies.
Eric Schechter
Handbook of Analysis & its Foundations (paper 1996, CD 1999), Academic Press. If a mathematical object is not constructible, we should say so; the student who is unable to visualize some object will be reassured upon hearing that no one else can visualize it either. S.I.A.M. Review called this book " daring and…
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What are the 'real numbers', really?
The short, simple answer used in calculus courses is that a real number is a point on the number line . That's not the whole truth, but it is adequate for the needs of freshman calculus. The freshman calculus course (at most universities nowadays) follows the 17th century style of Newton and Leibniz, emphasizing…