I'm looking for opinions and advice about an important academic decision I will have to make next year. I'm sorry if this post becomes too long, but I really appreciate your comments. About me: I'm a senior Physics/Computational Math undergrad at a decent state university (top 15 US in both fields). I am highly interested in pursuing an academic career, most likely in the fields of Computational Biophysics or Medical Physics (probably imaging related). I have good grades (clean 4.0) but my research experience is so-so: 6 months in particle physics, 6 months in biophysics, but no publications yet. Nevertheless, I should get good recommendation letters from both professors. I will finish the requirements for my physics degree in Spring 2009, but my math degree will take me an additional semester or two. Therefore, my expected graduation date is currently Spring 2010. (More on this later.) Several of my professors agree that getting into a "Big Name" university for grad school makes getting an academic position at a decent school much easier, so for the moment, that is my intention. The questions is: how? I will be applying to two REU programs at prestigious universities for Summer 2009. Both are universities I would be happy to attend for graduate school, so it seems natural to get directly involved with them before applying. However, I would like to know: how are your chances of getting into a top 5 school affected if you perform well at an REU there? Has anyone here performed well at an REU and later not have been accepted when applying to grad school there? My other option is somewhat more unorthodox: dropping my BS Math degree, graduating with a BS Physics degree in Spring 2009, and getting into a Master's program in Applied and Computational Mathematics at my current school. This would mean I graduate college one year earlier, but enter a PhD program one year later than expected (2 years Master). However, I think that such a degree would be useful and look good on an application if I want to do computational work for my PhD. What are your thoughts on this? Another interesting possibility of the Master's option is that I may be able to work as a RA in the Physics department, because I know many of the professors here. This would allow me to do 2 years of paid research and give me time to land a few publications (hopefully!). One important note: the REU programs and the Master's are mutually exclusive, because I cannot enter one if I graduate (REU) in Spring 2009 and I cannot enter the other one (Master's) if I don't. This is getting long, so the bottom line is: what's better for grad school applications? Meeting and working with professors at a given school and showing them you're competent or preparing yourself better for what you want to do and having some publications to show for it? Thanks a lot for reading.