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Physical Sciences and Mathematics Commons™
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Full-Text Articles in Physical Sciences and Mathematics
Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Clique-Relaxed Graph Coloring, Charles Dunn, Jennifer Firkins Nordstrom, Cassandra Naymie, Erin Pitney, William Sehorn, Charlie Suer
Faculty Publications
We define a generalization of the chromatic number of a graph G called the k-clique-relaxed chromatic number, denoted χ(k)(G). We prove bounds on χ(k)(G) for all graphs G, including corollaries for outerplanar and planar graphs. We also define the k-clique-relaxed game chromatic number, χg(k)(G), of a graph G. We prove χg(2)(G)≤ 4 for all outerplanar graphs G, and give an example of an outerplanar graph H with χg(2)(H) ≥ 3. Finally, we prove that if H is a member …
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Higher Dimensional Lattice Chains And Delannoy Numbers, John S. Caughman, Charles L. Dunn, Nancy Ann Neudauer, Colin L. Starr
Faculty Publications
Fix nonnegative integers n1 , . . ., nd, and let L denote the lattice of points (a1 , . . ., ad) ∈ ℤd that satisfy 0 ≤ ai ≤ ni for 1 ≤ i ≤ d. Let L be partially ordered by the usual dominance ordering. In this paper we use elementary combinatorial arguments to derive new expressions for the number of chains and the number of Delannoy paths in L. Setting ni = n (for all i) in these expressions yields a new …
Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave
Perspectives On Deepening Teachers’ Mathematics Content Knowledge: The Case Of The Oregon Mathematics Leadership Institute, Libby Knott, Martha Vancleave
Faculty Publications
The Oregon Mathematics Leadership Institute (OMLI) project served 180 Oregon teachers, and 90 administrators, across the K-12 grades from ten partner districts. OMLI offered a residential, three-week summer institute. Over the course of three consecutive summers, teachers were immersed in a total of six mathematics content classes– Algebra, Data & Chance, Discrete Mathematics, Geometry, Measurement & Change, and Number & Operations—along with an annual collegial leadership course. Each content class was designed and taught by a team of expert faculty from universities, community colleges, and K-12 districts. Each team chose a few “big ideas” on which to focus the course. …
Providing Preservice Teachers With Worthwhile Field-Based Experiences In Mathematics, Glenn Nelson
Providing Preservice Teachers With Worthwhile Field-Based Experiences In Mathematics, Glenn Nelson
Faculty Publications
Providing preservice teachers with worthwhile field-based experiences is recognized as an important component in their development as good teachers. Because mathematics instruction in general has moved from a teacher-directed, procedurally-focused process to a more student-centered, conceptually-oriented approach, preservice mathematics education classes – especially methods courses - should reflect this shift as well. Field-based opportunities can be instances for preservice teachers to personally experience such a shift to real-world relevance.
Explicit Constructions Of Rip Matrices And Related Problems, Jean Bourgain, S J. Dilworth, Kevin Ford, Sergei Konyagin, Denka Kutzarova
Explicit Constructions Of Rip Matrices And Related Problems, Jean Bourgain, S J. Dilworth, Kevin Ford, Sergei Konyagin, Denka Kutzarova
Faculty Publications
We give a new explicit construction of n×N matrices satisfying the Restricted Isometry Property (RIP). Namely, for someε > 0, largeN, and any n satisfyingN1−ε ≤ n ≤ N, we construct RIP matrices of order k ≥ n1/2+ε and constant δ = n−ε. This overcomesthe natural barrier k = O(n1/2) for proofs based on small coherence, which areused in all previous explicit constructions of RIP matrices. Key ingredients in ourproof are new estimates for sumsets in product sets and for exponential sums with theproducts of sets possessing special additive structure. We also give a construction ofsets of n complex numbers whose …
Understanding Streaming In Dictyostelium Discoideum: Theory Versus Experiments, J. C. Dallon, Brittany Dalton, Chelsea Malani
Understanding Streaming In Dictyostelium Discoideum: Theory Versus Experiments, J. C. Dallon, Brittany Dalton, Chelsea Malani
Faculty Publications
Recent experimental work involving Dictyostelium discoideum seems to contradict several theoretical models. Experiments suggest that localization of the release of the chemoattractant cyclic adenosine monophosphate to the uropod of the cell is important for stream formation during aggregation. Yet several mathematical models are able to reproduce streaming as the cells aggregate without taking into account localization of the chemoattractant. A careful analysis of the experiments and the theory suggests the two major features of the system which are important to stream formation are random cell motion and chemotaxis to regions of higher cell density. Random cell motion acts to reduce …