So far we mostly dealt with groups for which associativity condition is satisfied (multiplication and addition of numbers, successive symmetry operations, etc.). So on Day 8, we started off with some exercises in which student assessed ambiguity of mathematical expressions which lacked brackets. After going through some examples, we briefly reviewed the order of operations rules for addition, subtraction, multiplication, and division. Having understood the importance of mathematical punctuation, we introduced more interesting binary operations on numbers and practiced how to check whether associativity condition holds. This expanded our horizons because we discovered that we aren’t bound to the familiar operations, but could invent our own.

Resources used: F. J. Budden, *The Fascination of Groups*. Cambridge University Press, 1972. (Reprint with corrections, 1978).