Note: This proposal is several years old and is formatted in a way that is not necessarily a good model for current proposals. I.e., it does not include citations and is not a full two pages single spaced with one inch margins. It is included, however, as an example of research in a creative major.
(NOTE: Do not use this sample proposal as a formatting model. Current and future URG applications must be 2 pages single spaced with 1 inch margins, and the use of internal headings is discouraged.) The topic of my project is the logarithmic Sobolev inequality, an inequality for a certain type of integral which has numerous applications in both pure and applied mathematics—including partial differential equations, mathematical statistics, and quantum mechanics. In the course of my research, I will attempt to develop a new proof of this inequality, based on a special integration by parts formula. Such a proof will yield a hitherto unknown approach to the study of the logarithmic Sobolev inequality, as well as that of a family of related inequalities. It may thereby lead to advances in the areas of math and science where these inequalities are applied. Moreover, my project will give me additional experience doing research in analysis, a ﬁeld in which I am considering specializing in my future career.
In a child’s world, nearly everything seems related to play. Every new person, sound, and object is somehow exciting and captivating, and it is from this stimulation that the child develops new cognitive capacities and builds interpersonal relationships. As such, an entire field of psychology is dedicated to studying child play and the ways in which it contributes to psychologically and physically healthier children (Ginsburg, 2007; Vygotsky, 1967). Research among adults, however, is limited and inconclusive. Many news articles, blogs, and self-help books have attempted to inspire awareness on the subject, declaring that adult play is almost nonexistent and deserves attention. Yet adult play research continues to be underrepresented in psychology. The aim of the current proposal is to examine the types of structured ‘play’ or leisure activities adults commonly engage in, and compare them to the less structured and imaginative play most often performed by children. I propose that, just as imaginative play builds cognitive and social resources in children, it continues to do so in adulthood.