They really have very little in common. Elementary algebra (the kind you learn in high school) is mostly about equations such as [math]y = x^2 + 4x + 1[/math]. Polynomials occupy a lot of the syllabus. read more
Polynomials occupy a lot of the syllabus. In abstract algebra (usually studied by math majors in college, after a calculus sequence) things are made much more abstract and you study things such as rings and fields. Statistics can be divided (roughly) into data analysis and mathematical statistics. read more
Statistics is a mathematical science pertaining to the collection, analysis, interpretation or explanation, and presentation of data.It also provides tools for prediction and forecasting based on data. Algebra deals with the study of structure, relation, and quantity. read more
The diferences between those people was just a matter of personal preference, as Professor Blitzstein goes into more detail, usually statistics students thinking that pure math was a little to abstract for their liking. You would then see the exact same sentiment said about them from the engineers. read more