Mathematics, Department of
http://hdl.handle.net/2027.42/61172
2017-04-23T10:05:43ZA Primer of Commutative Algebra
http://hdl.handle.net/2027.42/136228
A Primer of Commutative Algebra
Milne, James
These notes collect the basic results in commutative algebra used in the rest of my
notes and books. Although most of the material is standard, the notes include a few
results, for example, the affine version of Zariski’s main theorem, that are difficult to
find in books.
2017-03-18T00:00:00ZSymmetry in European Folk Costumes
http://hdl.handle.net/2027.42/136161
Symmetry in European Folk Costumes
James, David A.; James, Alice V.; Root, Martha J.
Ethnomathematics is an interdisciplinary field that explores subconscious and conscious expression of non-formal mathematics within cultures. To explore the mathematics of the designs on European folk costumes, we recorded images of the costumes of 73 cultures displayed in 167 museums throughout Europe, interviewed the directors and curators, and carried out research at the libraries of these museums. We analyze the frequency, similarities and differences in the designs of the 73 cultures, first comparing results culture-by-culture and then repeating the process after combining the cultures into families having characteristic commonalities and similarities of history.
The associated data (Excel spreadsheet and Access database) for the Symmetry in European Folk Costumes paper can be found in Deep Blue Data at: http://dx.doi.org/10.7302/Z2HD7SKC
2017-03-09T00:00:00ZWell-posedness and self-similar asymptotics for a thin-film equation
http://hdl.handle.net/2027.42/117366
Well-posedness and self-similar asymptotics for a thin-film equation
Gnann, Manuel V.
We investigate compactly supported solutions for a thin-film equation with linear mobility in the regime of perfect wetting. This problem has already been addressed by Carrillo and Toscani, proving that the source-type self-similar profile is a global attractor of entropy solutions with compactly supported initial data. Here we study small perturbations of source-type self-similar solutions for the corresponding classical free boundary problem and set up a global existence and uniqueness theory within weighted L2-spaces under minimal assumptions. Furthermore, we derive asymptotics for the evolution of the solution, the free boundary, and the center of mass. As spatial translations are scaled out in our reference frame, the rate of convergence is higher than the one obtained by Carrillo and Toscani.
2015-07-30T00:00:00ZMathematical Knowledge for Teaching High School Geometry
http://hdl.handle.net/2027.42/91279
Mathematical Knowledge for Teaching High School Geometry
Herbst, Patricio; Kosko, Karl W.
This paper documents efforts to develop an instrument to measure mathematical knowledge for teaching high school geometry (MKT-G). We report on the process of developing and piloting questions that purported to measure various domains of MKT-G. Scores on the final set of items had no statistical relationship with total years of experience teaching, but all domain scores were found to have statistically significant correlations with years of experience teaching high school geometry. We use this result to propose ways of conceptualizing how instruction-specific considerations might matter in the design of MKT items.
2012-05-28T00:00:00Z