Engineering Mathematics · topic
Set identities and power sets; relation properties with matrix tests and counts; reflexive, symmetric and transitive closures; equivalence relations, classes and partitions with Bell and Stirling numbers; injective, surjective and bijective functions with counts, composition, inverses and countability.
Set identities, power sets and Cartesian products; the six relation properties with matrix and digraph tests; how many relations on an n-element set have each property or combination (brute-forced for n = 3 and 4); the empty and identity relations; composition of relations; reflexive, symmetric and transitive closures with Warshall's algorithm; which properties survive union and intersection; and a solved past question on a relation defined by a formula.
A partial preview of the top of the sheet. The full sheet is in the Engineering Mathematics cheat sheet pack.
Equivalence classes and the one-to-one match with partitions, Bell numbers and Stirling numbers of the second kind with a small table, counting equivalence relations with k classes or containing a given pair, the equivalence closure; injective, surjective and bijective functions, their counts (including onto maps by inclusion-exclusion), partial functions and involutions, what composition says about each factor, inverses and images, real-valued examples, and countable versus uncountable sets.
A partial preview of the top of the sheet. The full sheet is in the Engineering Mathematics cheat sheet pack.
