Exploring and noticing
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problemPolite numbers
A polite number can be written as the sum of two or more consecutive positive integers, for example 8+9+10=27 is a polite number. Can you find some more polite, and impolite, numbers? -
problemWhat do functions do for tiny x?
Looking at small values of functions. Motivating the existence of the Maclaurin expansion.
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problemFavouriteIt's only a minus sign
Solve these differential equations to see how a minus sign can change the answer
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problemFarey neighbours
Farey sequences are lists of fractions in ascending order of magnitude. Can you prove that in every Farey sequence there is a special relationship between Farey neighbours?
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problemInverting rational functions
Consider these questions concerning inverting rational functions
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