The ongoing revolution in communication technology and cloud computing is driving demand for information security tools and specialists. Likewise the revolution in molecular and cell biology is driving a rapidly emerging demand to mathematize biology and for professionals competent in both mathematics and biology. The nature of computing and complexity are central themes for both. Important mathematical problems relevant to the concerns of information security or biology are within the intellectual grasp of talented undergraduate students. The REU Site: Complexity in Algebra, Geometry and Applications will introduce undergraduate students to research in mathematics motivated by applications to information security or genome biology. An objective of this program is to produce a cohort of young researchers whose work and vision will transcend the artificial boundary between mathematics and real world applications of mathematics.
Over the course of eight weeks 8 undergraduate students alongside their faculty mentors will be engaged in mathematics-based interdisciplinary research. In addition to targeted research projects the program will provide a broad array of associated program elements designed to draw students into and prepare them for STEM careers. These include: research workshops where students will build their backgrounds for their projects, computing workshops where students will develop programming skills needed for progress on their research projects, meetings as a group where they will report their current research and a research symposium at the end of the program where all students will present their research results. Using our cloud resources the program will implement collaborative spaces that blend face-to-face and online modes of activity for our workshops, seminars and student research teams. This technological capability is a key component of our follow-through plan to sustain the subsequent research experience of alumni of our REU program.
" funded by NSF grant DMS 1062857 hosted 28 undergraduate students during the summers of 2011-2013. The site also accepted three qualified international students whose institutions provided alternative funding (one in 2012 and two in 2013), and embedded one student from the NIH funded Idea Network in Biomolecular Research Excellence program in one of the REU research teams during Summer 2012. The site received 655 applications, of which 31.7% were women. 38.7% of the recruited participants female. Participants were recruited from 28 different institutions nationwide. Of these institutions 64% offered no undergraduate research opportunities in mathematics. The site is a founding member of the Alliance of Summer Undergraduate Research Programs at Boise State University, a consortium of seven programs including the Mathematics REU site. This consortium organized several supplementary social networking and professional development activities that resulted in a diverse community of undergraduate researchers and faculty mentors. The Mathematics REU site spearheaded the founding of the Summer Undergraduate Research Conference at Boise State University. This poster conference is open for participation by undergraduate students from all disciplines, and is open to attendance by the public. The Mathematics REU site also founded the Summer Undergraduate Research Symposium in Mathematics. It is open to all undergraduate students in Mathematics, and to attendance by the public. During the three year period the site hosted 11 invited speakers that are experts in mathematics, the life sciences and information security. The site hosted, in collaboration with the Division of Extended Studies, a workshop on research for high school students. The site mentors hosted two workshops on cryptology for the summer academy of the NASA funded Idaho Science and Aerospace Scholars Program for high schools in Idaho. The site’s research program engaged students in interdisciplinary mathematics-based research projects that advanced the frontiers of knowledge in fields related to information security and genome biology. Accomplishments include: Design and analysis of generalized versions of the Data Encryption Standard. Generalization and study of the algebraic structure of Rijndael-like ciphers and the Whirlpool hash function over an arbitrary finite fields. Reducing the problem of the existence of infinitely many elliptic primes to the classical Bunyakowski Conjecture. Discovery of elliptic cycles of length 6, contrary to the expectations of experts. The discovery of a technique to generate infinitely many labeled oriented trees that are not diagrammatically irreducible. The discovery that most quotients of knot groups are infinite. The conjecture that all such quotients are infinite emerged from this work. An algorithm that determines the number of ciliate operations needed to sort a given permutation into a fixed point. The algorithm provably halts, is efficient, and can be used it to construct phylogenies for permuted chromosomes. Characterizing the unique permutations that are optimized for sorting by ciliate operations. Characterizing the permutations sortable by the ciliate operations. Determining the optimal number of sorting steps required for a wide class of patterns. The research projects from the REU site resulted in 35 oral presentations at national venues. Four of these presentations were awarded for excellence at national conferences. The research projects also produced eight manuscripts of which two are accepted for publication in peer reviewed journals, one is submitted to a peer reviewed journal and the rest are being prepared for submission.
