Xiao-Xiong Gan (Morgan State University, Baltimore MD, USA)**From Formal Power Series to Formal Analysis**

For any , a formal power series on a ring is defined to be a mapping from to . A formal power series in from to is usually denoted as a sequence or as a power series , where for every . The set of all formal power series on is denoted by .

If considering a formal power series as a sequence, what is the difference between and ?

If considering a formal power series as a power series, what is the difference between formal power series and the traditional power series? What is the relationship between formal power series and traditional power series?

What is *formal analysis*?

This talk tries to answer those questions and brings discussion of all kinds of questions about formal analysis, a relatively new mathematical subject.