# Mathematics Commons™

## All Articles in Mathematics

11912 full-text articles. Page 1 of 320.

Roman Domination In Complementary Prisms, 2017 East Tennessee State University

#### Roman Domination In Complementary Prisms, Alawi I. Alhashim

##### Electronic Theses and Dissertations

The complementary prism GG of a graph G is formed from the disjoint union of G and its complement G by adding the edges of a perfect match- ing between the corresponding vertices of G and G. A Roman dominating function on a graph G = (V,E) is a labeling f : V(G) → {0,1,2} such that every vertex with label 0 is adjacent to a vertex with label 2. The Roman domination number γR(G) of G is the minimum f(V ) = Σv∈V f(v) over all such functions of G. We study the Roman domination number ...

#### Session A-3: Three-Act Math Tasks, Lindsey Herlehy

##### Professional Learning Day

Participants will engage in a Three-Act Math task highlighting the application of properties of geometrical figures. Developed by Dan Meyer, an innovative and highly regarded mathematics instructor, Three-Act Math tasks utilize pedagogical skills that elicit student curiosity, collaboration and questioning. By posing a mathematical problem through active storytelling, this instructional approach redefines real-world mathematics and clarifies the role that a student plays in the learning process. Participants will be given multiple resources where they can access Three-Act Math tasks appropriate for upper elementary grades through Algebra and Geometry courses.

Generalized Left And Right Weyl Spectra Of Upper Triangular Operator Matrices, 2017 University of Nis

#### Generalized Left And Right Weyl Spectra Of Upper Triangular Operator Matrices, Guojun Hai, Dragana S. Cvetkovic-Ilic

##### Electronic Journal of Linear Algebra

In this paper, for given operators $A\in\B(\H)$ and $B\in\B(\K)$, the sets of all $C\in \B(\K,\H)$ such that $M_C=\bmatrix{cc} A&C\\0&B\endbmatrix$ is generalized Weyl and generalized left (right) Weyl, are completely described. Furthermore, the following intersections and unions of the generalized left Weyl spectra $$\bigcup_{C\in\B(\K,\H)}\sigma^g_{lw}(M_C) \;\;\; \mbox{and} \;\;\; \bigcap_{C\in\B(\K,\H)}\sigma^g_{lw}(M_C)$$ are also described, and necessary and sufficient conditions which two operators $A\in\B(\H)$ and $B\in\B(\K)$ have to satisfy in order for $M_C$ to be a generalized left Weyl operator for each $C\in\B(\K,\H)$, are presented.

On The Graceful Cartesian Product Of Alpha-Trees, 2017 Clayton State University

#### On The Graceful Cartesian Product Of Alpha-Trees, Christian Barrientos, Sarah Minion

##### Theory and Applications of Graphs

A \emph{graceful labeling} of a graph $G$ of size $n$ is an injective assignment of integers from the set $\{0,1,\dots,n\}$ to the vertices of $G$ such that when each edge has assigned a \emph{weight}, given by the absolute value of the difference of the labels of its end vertices, all the weights are distinct. A graceful labeling is called an $\alpha$-labeling when the graph $G$ is bipartite, with stable sets $A$ and $B$, and the labels assigned to the vertices in $A$ are smaller than the labels assigned to the vertices in $B$. In ...

Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, 2017 Humboldt-Universität zu Berlin

#### Breaking Spaces And Forms For The Dpg Method And Applications Including Maxwell Equations, Carsten Carstensen, Leszek Demkowicz, Jay Gopalakrishnan

##### Jay Gopalakrishnan

Discontinuous Petrov Galerkin (DPG) methods are made easily implementable using `broken' test spaces, i.e., spaces of functions with no continuity constraints across mesh element interfaces. Broken spaces derivable from a standard exact sequence of first order (unbroken) Sobolev spaces are of particular interest. A characterization of interface spaces that connect the broken spaces to their unbroken counterparts is provided. Stability of certain formulations using the broken spaces can be derived from the stability of analogues that use unbroken spaces. This technique is used to provide a complete error analysis of DPG methods for Maxwell equations with perfect electric boundary ...

2017 University of California, Irvine School of Law

#### The Subject Librarian Newsletter, Mathematics, Spring 2017, Sandy Avila

No abstract provided.

On The Closure Of The Completely Positive Semidefinite Cone And Linear Approximations To Quantum Colorings, 2017 CWI (Centrum Wiskunde & Informatica) Amsterdam

#### On The Closure Of The Completely Positive Semidefinite Cone And Linear Approximations To Quantum Colorings, Sabine Burgdorf, Monique Laurent, Teresa Piovesan

##### Electronic Journal of Linear Algebra

We investigate structural properties of the completely positive semidefinite cone $\mathcal{CS}_+$, consisting of all the $n \times n$ symmetric matrices that admit a Gram representation by positive semidefinite matrices of any size. This cone has been introduced to model quantum graph parameters as conic optimization problems. Recently it has also been used to characterize the set $\mathcal Q$ of bipartite quantum correlations, as projection of an affine section of it. We have two main results concerning the structure of the completely positive semidefinite cone, namely about its interior and about its closure. On the one hand we construct ...

Arithmetic: Math As 'Pure' And 'Applied', 2017 College of Saint Benedict/Saint John's University

#### Arithmetic: Math As 'Pure' And 'Applied', Sunil Chetty

##### Forum Lectures

One often hears mathematics classified into two categories: pure or applied, abstract or concrete, elementary or modern. We explore how arithmetic can dismantle such highly artificial distinctions. More specifically, we play with tiles and draw pictures to highlight how arithmetic can be both good mental exercise and a very useful tool for modern communication.

2017 Utrecht University

#### Ichme-5: Fifth International Conference On The History Of Mathematics Education, Jenneke Krüger

##### Journal of Humanistic Mathematics

No abstract provided.

##### Journal of Humanistic Mathematics

"Lady" Jane is an expert at her racket. The Joint Statistical Meetings are in Vegas, and she reckons it's payday. But she's taking on the professionals.

2017 Westminster College (Salt Lake City)

#### The University Of Montana Department Of Mathematics Post-Apocalyptic Working Seminar, Kenan A. Ince

##### Journal of Humanistic Mathematics

No abstract provided.

16, 2017 Norwich University

#### 16, Dan Mcquillan

##### Journal of Humanistic Mathematics

This 15 word poem suggests that the reader count the words of the poem. Since every line has half as many words as the previous line, and since the poem urges the reader to keep counting forever, one imagines a total of 16 words.

The Geometry Of Morning, 2017 Claremont Colleges

#### The Geometry Of Morning, Greg Huteson

##### Journal of Humanistic Mathematics

No abstract provided.

2017 Pennsylvania State University, University Park

#### Book Review: Realizing Reason: A Narrative Of Truth And Knowing By Danielle Macbeth, Emily R. Grosholz

##### Journal of Humanistic Mathematics

This review examines Danielle Macbeth’s novel and compelling account of the formal languages of mathematics, from Euclid’s geometrical diagrams to the algebraic equations of Descartes and the differential equations of Newton and Leibniz, to the much more abstract language of Galois, Bolzano and Riemann. She argues that the practice of those 19th century mathematicians, reasoning deductively from abstract concepts like ‘group’ and ‘manifold’, inspired the philosophical logician Gottlob Frege, whose Begriffsschrift captures the procedures of those who reasoned in concepts. However, his way of formalizing mathematical reasoning was obscured by the success of Bertrand Russell and Alfred ...

#### Solving Equations: A Make-Work Project For Math Teachers And Students, Egan J. Chernoff

##### Journal of Humanistic Mathematics

The purpose of this article is to share a particular view that I have towards solving equations in the school mathematics classroom. Specifically, I contend that solving equations in the math classroom is a make-work project for math teachers and students. For example, math teachers take a predetermined value that makes a statement true, and then proceed to make it harder and harder and harder for their students to determine the value that makes the statement true. However, math teachers do so with the explicit purpose of teaching their students how to reveal the solution that they themselves have concealed ...

Does Society Need Imo Medalists?, 2017 Department of Mathematics, University of Hong Kong

#### Does Society Need Imo Medalists?, Man Keung Siu

##### Journal of Humanistic Mathematics

With a title that sounds provocative but with no intention to embarrass the organizers and participants of the event of IMO (International Mathematical Olympiad) this article should be seen as the sharing of some thoughts on this activity, or more generally on mathematical competitions, by a teacher of mathematics who had once helped in the coaching of the first Hong Kong Team to take part in the 29th IMO held in Canberra in 1988 and in the coordination work of the 35th IMO held in Hong Kong in 1994. The author tries to look at the issue in ...

Basketball, Algebra, And Probabilities, 2017 New Jersey City University

#### Basketball, Algebra, And Probabilities, Gunhan Caglayan

##### Journal of Humanistic Mathematics

This article is an attempt to illustrate some humanistic aspects of mathematics in context, in particular, sports and scoring (basketball). The intriguing and dynamic illustrations demonstrate innovative and creative ways of integrating basketball snapshots into the pedagogy of a high school or college-level mathematics-in-context course. I have used this activity with several mathematics education students in a mathematics-in-context class as they worked in groups of five. I include here a presentation and a discussion of their explorations and analyses.

The Battle Against Malaria: A Teachable Moment, 2017 Schoolcraft College

#### The Battle Against Malaria: A Teachable Moment, Randy K. Schwartz

##### Journal of Humanistic Mathematics

Malaria has been humanity’s worst public health problem throughout recorded history. Mathematical methods are needed to understand which factors are relevant to the disease and to develop counter-measures against it. This article and the accompanying exercises provide examples of those methods for use in lower- or upper-level courses dealing with probability, statistics, or population modeling. These can be used to illustrate such concepts as correlation, causation, conditional probability, and independence. The article explains how the apparent link between sickle cell trait and resistance to malaria was first verified in Uganda using the chi-squared probability distribution. It goes on to ...

The Hidden Symmetries Of The Multiplication Table, 2017 None

#### The Hidden Symmetries Of The Multiplication Table, Zoheir Barka

##### Journal of Humanistic Mathematics

In this article we explore some of the symmetries that hide in the distribution of numbers in the multiplication table of positive integers when viewed through modulo k arithmetic as we vary k.

Some Comments On Multiple Discovery In Mathematics, 2017 Queen Mary University of London

#### Some Comments On Multiple Discovery In Mathematics, Robin W. Whitty

##### Journal of Humanistic Mathematics

Among perhaps many things common to Kuratowski's Theorem in graph theory, Reidemeister's Theorem in topology, and Cook's Theorem in theoretical computer science is this: all belong to the phenomenon of simultaneous discovery in mathematics. We are interested to know whether this phenomenon, and its close cousin repeated discovery, give rise to meaningful questions regarding causes, trends, categories, etc. With this in view we unearth many more examples, find some tenuous connections and draw some tentative conclusions.