Tea Time Numerical Analysis - Brin, Leon (2013)
Keywords: dept.mat; faculty_collection

A Gentle Introduction to the Art of Mathematics: Version 3.1 - Fields, Joseph (Joseph E. Fields, 2013)
Keywords: Mathematics; Textbooks; dept.mat; faculty_collection

The mathematics for middle school teachers program at Western Oregon University - Beaver, C.; Harrington, R.; Kruczek, K. (Resources for Preparing Middle School Mathematics Teachers, 2013)
Introduction: Although there is some common pedagogical ground for all teachers of mathematics, there is a fundamental difference in the topics and depth of content knowledge required for students preparing to teach elementary, middle, or high school mathematics. The middle school teacher preparation program at Western Oregon University (WOU) seeks to develop foundational content for middle school teachers while exploring best practices such as active learning, appropriate use of technology, and hands-on exploration. WOU offers many courses specifically for middle school teachers that are designed to develop mathematical maturity and content knowledge while connecting the subject matter to the middle school curriculum and standards. This article describes the structure of WOU's middle school mathematics program and the courses designed specifically for middle school mathematics teachers. We point out the difference in the mathematical preparation and requirements for middle school mathematics teachers compared to elementary teachers and high school mathematics teachers and explain the licensure requirements for middle school mathematics teachers in Oregon. Background and Philosophy of the Program: Western Oregon University's math curriculum for K–8 teacher preparation was among ten programs singled out as meeting critical coursework needs by the National Council on Teacher Quality [5]. The teacher preparation program as a whole was named the 2010 recipient of the Christa McAuliffe Award for Excellence in Teacher Education by the American Association of State Colleges and Universities (AASCU). © 2013 by The Mathematical Association of America (Incorporated).
Journal Abbreviation: Resources for Preparing Middle School Mathematics Teachers
Keywords: dept.mat

Visual College Algebra for Teachers - Burton, L.J.; Kruczek, K.T. (Resources for Preparing Middle School Mathematics Teachers, 2013)
At Western Oregon University, we offer a College Algebra for Teachers course using the Visual Algebra for College Students [3] materials that we wrote and class tested. Visual Algebra is designed to help middle school teachers gain a deep understanding of basic algebraic skills. Students visually show algebra using a concrete model (algebra pieces), verbally describe the meaning of each algebra piece move, symbolically connect the ideas to standard algebraic algorithms and procedures, and graphically connect the ideas of the visual models and symbolic work. Overall, students think deeply about topics, do not rely on rote memorization or rote rules, and understand ideas so well that they can easily describe, model, and teach core algebraic ideas to their middle grade students in a variety of ways. This allows our future teachers to meet the needs of the different learning styles in their classrooms. Visual Algebra takes students through modeling integer operations with black and red tiles to modeling linear and quadratic patterns with tiles and variable algebra pieces, looking at the general forms of the patterns and then connecting all the ideas to symbolic manipulation, creating data sets, graphing, and finding intercepts and points of intersection. Ideas are then extended to higher order polynomial functions and then to modeling complex number operations with black, red, yellow, and green tiles. Throughout the course, students are able to relate what they learned using visual methods to the standard methods and algorithms they will see every day in their classroom. For example, after factoring quadratic equations using visual methods, students learn factoring by grouping and factoring using the “ac” method. © 2013 by The Mathematical Association of America (Incorporated).
Journal Abbreviation: Resources for Preparing Middle School Mathematics Teachers
Keywords: dept.mat

Academic Freedom and Tenure: National Louis University (Illinois) - Grant, K.E.; Simpson, P.A.; Zannoni, D.C. (Academe, 2013)
Keywords: dept.mat; ⛔ No DOI found

Extremal rees Algebras - Hong, J.; Simis, A.; Vasconcelos, W.V. (Journal of Commutative Algebra, 2013)
We study almost complete intersection ideals whose Rees algebras are extremal in the sense that some of their fundamental metrics depth or relation type have maximal or minimal values in the class. The focus is on those ideals that lead to almost Cohen-Macaulay algebras, and our treatment is wholly concentrated on the nonlinear relations of the algebras. Several classes of such algebras are presented, some of a combinatorial origin. We offer a different prism to look at these questions with accompanying techniques. The main results are effective methods to calculate the invariants of these algebras. © 2013 Rocky Mountain Mathematics Consortium.
6 citations (Crossref) [2023-10-31]
Keywords: Almost Cohen-Macaulay algebra; Almost complete intersection; Birational mapping; Castelnuovo regularity; Extremal Rees algebra; Hilbert function; Module of nonlinear relations; Rees algebra; Relation type; Sally module; dept.mat

Rank numbers of graphs that are combinations of paths and cycles - Blake, Brianna; Field, Elizabeth; Jacob, Jobby (Involve, A Journal of Mathematics, 2013)
1 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/006-267-107-161-586 tex.type: [object Object]
Keywords: dept.mat

Variation of hilbert coefficients - Ghezzi, Laura; Goto, Shiro; Hong, Jooyoun; Vasconcelos, Wolmer V (Proceedings of the American Mathematical Society, 2013)
For a Noetherian local ring (R, m), the first two Hilbert coefficients, e0 and e1, of the I-adic filtration of an m-primary ideal I are known to code for properties of R, of the blowup of Spec(R) along V (I), and even of their normalizations. We give estimations for these coefficients when I is enlarged (in the case of e1 in the same integral closure class) for general Noetherian local rings. © American Mathematical Society.
3 citations (Crossref) [2023-10-31] Citation Key Alias: lens.org/035-873-690-231-781
Keywords: dept.mat

Guarding orthogonal polygons with h holes: A bound independent of h - Michael, T S; Pinciu, Val (Fall Workshop on Computational Geometry, 2013)
Hoffmann and Kriegel showed that an orthogonal gallery with n vertices and an unspecified number of holes can be protected by at most n/3 vertex guards. We improve this bound to (17n − 8)/52.
Citation Key Alias: lens.org/128-915-841-672-555
Keywords: dept.mat; ⛔ No DOI found