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The Most Common Errors in Undergraduate Mathematics

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Author:Eric Schechter
Description: Errors in communication: teacher hostility, student shyness, bad handwriting, not reading directions, loss of invisible parentheses, terms lost inside an ellipsis; Algebra errors: sign errors, everything is additive, everything is commutative, undistributed cancellations, dimensional errors; Confusion about notation: idiosyncratic inverses, square roots, order of operations, ambiguously written fractions, stream-of-consciousness notations; Errors in reasoning: 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: Euler's square root error, x^x; Other common calculus errors: jumping to conclusions about infinity, loss or misuse of constants of integration, loss of differentials.

Levels: High School (9-12), College
Languages: English
Math Topics: Basic Algebra, Number Sense/About Numbers, Calculus (Single Variable), Communicating Math, Logic/Foundations

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