In mathematics an argument is a series of statements typically used to present reasons for accepting a conclusion. Two common examples are mathematical proofs and solution processes for solving equations or inequalities. Arguments in mathematics are required to adhere to the rules of Formal Logic. For that reason we should learn some very elementary logic.
Hypothesis has different interrelating meanings in different contexts, but no overarching simple definition that describes all of them exactly. In The Scientific Method The steps of the scientific method are nicely diagrammed: HERE and are displayed at the right. In this context: A hypothesis (plural hypotheses) is a proposed explanation for a phenomenon. For a