Egoism and utilitarianism are two moral philosophy with broad constituencies and can both be categorized as forms of moral realism.  To differentiate, egotism is the practice of being absorbed with the self.  Egotism is another word for vanity.

In a perfect world utilitarianism and egoism would be compatible.  If everyone does everything they can to better themselves, this would lead to maximum utility (happiness) among people.  I don't think the world is perfect and some would argue utilitarianism and egoism are in fact incompatible and to be perfectly moral, you need to weigh the moral calculus of utilitarianism.  

What utilitarianism is is an actual mathematical attempt to quantify utility received by goods in a society and so to measure the relative measure of contentment and well-being of a people as quantified by their consumption of goods (housing, food, entertainment, etc).  Since the basis of knowledge is rooted in mathematics, it is important to provide quantities when discussing morality since it is a topic that is already so confounding.  I do applaud utilitarians in this regard and regardless of whether you are more an egoist or more a utilitarian, I do think we will all benefit from clear data and a robust understanding of mathematics.