This web page describes the errors that I have seen most frequently in undergraduate mathematics, the likely causes of those errors, and their remedies. I am tired of seeing these same old errors over and over again. (I would rather see new, original errors!) I caution my undergraduate students about these errors at the beginning of each semester. Outline of this web page:
- ERRORS IN COMMUNICATION, including teacher hostility or arrogance, student shyness, unclear wording, bad handwriting, not reading directions,loss of invisible parentheses, terms lost inside an ellipsis
- ALGEBRA ERRORS, including sign errors, everything is additive, everything is commutative, undistributed cancellations, dimensional errors
- CONFUSION ABOUT NOTATION, including idiosyncratic inverses, square roots, order of operations, ambiguously written fractions, stream-of-consciousness notations.
- ERRORS IN REASONING, including going over your work, overlooking irreversibility, not checking for extraneous roots, confusing a statement with its converse, working backward, difficulties with quantifiers, erroneous methods that work, unquestioning faith in calculators.
- UNWARRANTED GENERALIZATIONS, including Euler's square root error, xx.
- OTHER COMMON CALCULUS ERRORS, including jumping to conclusions about infinity, loss or misuse of constants of integration, loss of differentials.
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