Florida International University (FIU) is the only public research university in Miami-Dade County. It is a Hispanic serving institution of higher education which attracts the best of the high school students in the region, many of whom – descendants from allover the Caribbean region. FIU has particularly motivated students in Mathematics and Natural Sciences. Every year, a strong group of students prepare for the annual W. L. Putnam Math Competition with remarkable, compared to the level of education they have, results on that competition: team's best rankings 89th (2004), 96th (2007), 114th (2008). The students actively participate also in the work of the Math Club, and the Students Seminar on Commutative Algebra and Algebraic Geometry at the Department of Mathematics and Statistics of FIU. There is a very strong trend in the academic achievements of our students in the recent years: a number of senior undergraduates in Mathematics have been successful in doing research as McNair post-baccalaureate (summer) program fellows at FIU (we have for the last three years had 8 such students). Many of the McNair fellows get accepted and actually do their research in various prestiges universities (such as Notre Dame and Princeton). A particular success for our Department was the accepting of two of our students in the Math in Moscow program for Fall'09 and Spring'10 (the former semester – on a grant from NSF for both students). Due to the fact that we do not have a mathematics related Ph.D. program, our best students are forced to pursue doctoral degrees in other universities. We are happy to see former participants in the Math Club and Student Seminar doing research in Analysis, Number Theory, Algebraic Geometry in the graduate schools of such universities as the University of Maryland, UCSD, FSU, Purdue University, Stanford University. This year is strongly revealing another trend in the interests of our best students: attracted by what we do at the Math & Stats Department, many physics majors join our activities and demand that we cover topics related to what they learn in the Physics courses. This motivates us to discuss with them a variety of geometric, topological, and categorical theories going far beyond the scope of what we have to teach them in our standard math classes. Five of the senior students have applied for a McNair fellowship this year. Knowing how important it is to keep the learning process uninterrupted, we, the faculty, are applying for research funding for our sophomore students for Summer'11. This proposal is a result of that.