# Mathematics Commons™

## All Articles in Mathematics

4,882 full-text articles. Page 1 of 99.

Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, 2015 Boise State University

#### Castelnuovo–Mumford Regularity And Arithmetic Cohen–Macaulayness Of Complete Bipartite Subspace Arrangements, Zach Teitler, Douglas A. Torrence

##### Mathematics Faculty Publications and Presentations

We give the Castelnuovo–Mumford regularity of arrangements of (n−2)-planes in Pn whose incidence graph is a sufficiently large complete bipartite graph, and determine when such arrangements are arithmetically Cohen–Macaulay.

Global Holomorphic Functions In Several Noncommuting Variables, 2015 University of California - San Diego

#### Global Holomorphic Functions In Several Noncommuting Variables, Jim Agler, John E. Mccarthy

##### Mathematics Faculty Publications

We define a free holomorphic function to be a function that is locally, with respect to the free topology, a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an Oka-Weil theorem for free analytic functions.

Real Linear Maps Preserving Some Complex Subspaces, 2015 Indiana University - Purdue University Fort Wayne

#### Real Linear Maps Preserving Some Complex Subspaces, Adam Coffman

##### Mathematical Sciences Faculty Publications

We find configurations of subspaces of a complex vector space such that any real linear map with sufficiently high rank that maps the subspaces into complex subspaces of the same dimension must be complex linear or antilinear.

Session B-3: Mathematical Games, Puzzles, And Diversions, 2015 Illinois Mathematics and Science Academy

#### Session B-3: Mathematical Games, Puzzles, And Diversions, Steven M. Condie

##### Professional Learning Day

Delve into the exciting world of math through games, puzzles and other sources! Participants shall try their luck and test their skill at these diversions. Participants will leave this session with a wealth of mathematical activities appropriate for students of all ages.

Session B-1: Pipelines And Oil Spills!, 2015 Illinois Mathematics and Science Academy

#### Session B-1: Pipelines And Oil Spills!, Patrick Young

##### Professional Learning Day

Don’t miss this hands-on approach to middle school math. Participants will construct an actual pipeline from inexpensive materials and record evidence of leakage. They will then conduct an experiment and create a model relating liquid volume and spill area. They will apply their model to determine how much liquid leaked from their pipeline.

Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, 2015 Illinois Mathematics and Science Academy

#### Session B-2: The “Roll” Of Statistics In Modeling - It All Adds Up, Richard Stalmack, Janice Krouse

##### Professional Learning Day

The common core practice standards ask us to teach students to propose mathematical models and test their viability. Participants will do an experiment, collect data and use technological tools to combine modeling, analysis and basic statistics. Participants should bring a laptop, if possible; otherwise, bring a graphing calculator.

2015 Illinois Mathematics and Science Academy

#### Session A-2: From Polynomial To Rational Functions: Flip!, Ruth Dover

##### Professional Learning Day

Ah HA! Making the connection between polynomial functions, rational functions and using reciprocals! Join us to flip, not flop, with trig for your classroom.

Session A-1: Implementing Common Core In Middle School Math, 2015 Illinois Mathematics and Science Academy

#### Session A-1: Implementing Common Core In Middle School Math, Karen Togliatti

##### Professional Learning Day

This session will focus on implementing Common Core Middle-School Mathematics Standards using student-centered activities. Participants will receive three hands-on activities (one each at grades six, seven, and eight) to take back to their classrooms.

2015 ian.anderson@usu.edu

#### Non-Isomorphic Real Simple Lie Algebras Of The Same Complex Type And Character, Ian M. Anderson

##### Tutorials on... in 1 hour or less

Complex simple Lie algebras are classified by their root types. The type of a real simple Lie algebra is the root type of the associated complex algebra. The character of a real simple Lie algebra is the signature of its Killing form.

For many root types, the character is sufficient to uniquely classify the corresponding real Lie algebras. However, one should not take this statement to be literally true – there are a few cases where the character does not suffice to distinguish all possible real forms.

In this worksheet we will show that the 2 real non-isomorphic Lie algebras so ...

2015 University of North Georgia

#### Spontaneous Dimension Reduction And The Existence Of A Local Lagrange-Hamilton Formalism For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda, Beata A. Hebda

##### Faculty Publications

A partially explicit construction of a Lagrange-Hamiltonian formalism for an arbitrary n -dimensional Newtonian system of equations of motion is given. Additional variables used in the construction are spontaneously reduced by the Dirac’s constraints resulting from degeneracy of the proposed Lagrangian, so that only the variables that appear in the original system of equations remain. A Hamiltonian and dynamical Dirac’s brackets are calculated.

2015 University of North Georgia

#### Spontaneous Dimension Reduction And The Existence Of A Local Lagrangian For Given N-Dimensional Newtonian Equations Of Motion, Piotr W. Hebda, Beata A. Hebda

##### Faculty Publications

A partially explicit construction of a Lagrangian for an n -dimensional Newtonian system of equations of motion is given. Extra variables used in the construction are spontaneously reduced by the constraints resulting from degeneracy of the proposed Lagrangian, so that only the variables that appear in the original system of equations remain. An explicit example of a Lagrangian for a system not satisfying Helmholtz conditions is given.

Transition To Higher Mathematics: Structure And Proof (Second Edition), 2015 University of Washington - Seattle Campus

#### Transition To Higher Mathematics: Structure And Proof (Second Edition), Bob A. Dumas, John E. Mccarthy

##### Books and Monographs

This book is written for students who have taken calculus and want to learn what “real mathematics" is. We hope you will find the material engaging and interesting, and that you will be encouraged to learn more advanced mathematics.

This is the second edition of our text. It is intended for students who have taken a calculus course, and are interested in learning what higher mathematics is all about. It can be used as a textbook for an "Introduction to Proofs" course, or for self-study.

Chapter 1: Preliminaries, Chapter 2: Relations, Chapter 3: Proofs, Chapter 4: Principles of Induction, Chapter ...

My Finite Field, 2015 Idaho State University

#### My Finite Field, Matthew Schroeder

##### Journal of Humanistic Mathematics

A love poem written in the language of mathematics.

Prisoner's Dilemma, 2015 Hofstra University

#### Prisoner's Dilemma, Raymond N. Greenwell

##### Journal of Humanistic Mathematics

No abstract provided.

Abscissas And Ordinates, 2015 Mimar Sinan Güzel Sanatlar Üniversitesi

#### Abscissas And Ordinates, David Pierce

##### Journal of Humanistic Mathematics

In the manner of Apollonius of Perga, but hardly any modern book, we investigate conic sections as such. We thus discover why Apollonius calls a conic section a parabola, an hyperbola, or an ellipse; and we discover the meanings of the terms abscissa and ordinate. In an education that is liberating and not simply indoctrinating, the student of mathematics will learn these things.

2015 University of Kentucky

#### The Symbolic And Mathematical Influence Of Diophantus's Arithmetica, Cyrus Hettle

##### Journal of Humanistic Mathematics

Though it was written in Greek in a center of ancient Greek learning, Diophantus's Arithmetica is a curious synthesis of Greek, Egyptian, and Mesopotamian mathematics. It was not only one of the first purely number-theoretic and algebraic texts, but the first to use the blend of rhetorical and symbolic exposition known as syncopated mathematics. The text was influential in the development of Arabic algebra and European number theory and notation, and its development of the theory of indeterminate, or Diophantine, equations inspired modern work in both abstract algebra and computer science. We present, in this article, a selection of ...

Love Games: A Game-Theory Approach To Compatibility, 2015 Georg-August Universität Göttingen

#### Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett

##### Journal of Humanistic Mathematics

In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's ...

On The Persistence And Attrition Of Women In Mathematics, 2015 Central Michigan University

#### On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez

##### Journal of Humanistic Mathematics

The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women ...

2015 Utah State University

#### The Game Of Thrones: A Study Of Power Networks And How They Change, Trevor Williams

##### Research on Capitol Hill

No abstract provided.

Minimum Rank Of Graphs With Loops, 2015 Iowa State University

#### Minimum Rank Of Graphs With Loops, Chassidy Bozeman, Annavictoria Ellsworth, Leslie Hogben, Jephian Chin-Hung Lin, Gabi Maurer, Kathleen Nowak, Aaron Rodriguez, James Strickland

##### Electronic Journal of Linear Algebra

A loop graph $\mf G$ is a finite undirected graph that allows loops but does not allow multiple edges. The set $\sym(\lG)$ of real symmetric matrices associated with a loop graph $\lG$ of order $n$ is the set of symmetric matrices $A=[a_{ij}]\in\Rnn$ such that $a_{ij}\ne 0$ if and only if $ij\in E(\lG)$. The minimum (maximum) rank of a loop graph is the minimum (maximum) of the ranks of the matrices in $\sym(\lG)$. We characterize loop graphs having minimum rank at most two (by forbidden induced subgraphs and graph complements) and ...