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Articles 1  30 of 16271
FullText Articles in Mathematics
How To Calculate Pi: Buffon's Needle (NonCalculus Version), Dominic Klyve
How To Calculate Pi: Buffon's Needle (NonCalculus Version), Dominic Klyve
Precalculus and Trigonometry
No abstract provided.
Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg
Greatest Common Divisor: Algorithm And Proof, Mary K. Flagg
Number Theory
No abstract provided.
Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao
Brauer's Theorem And Nonnegative Matrices With Prescribed Diagonal Entries, Ricardo L. Soto, Ana I. Julio, Macarena A. Collao
Electronic Journal of Linear Algebra
The problem of the existence and construction of nonnegative matrices with prescribed eigenvalues and diagonal entries is an important inverse problem, interesting by itself, but also necessary to apply a perturbation result, which has played an important role in the study of certain nonnegative inverse spectral problems. A number of partial results about the problem have been published by several authors, mainly by H. \v{S}migoc. In this paper, the relevance of a Brauer's result, and its implication for the nonnegative inverse eigenvalue problem with prescribed diagonal entries is emphasized. As a consequence, given a list of complex ...
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Diagonal Sums Of Doubly Substochastic Matrices, Lei Cao, Zhi Chen, Xuefeng Duan, Selcuk Koyuncu, Huilan Li
Electronic Journal of Linear Algebra
Let $\Omega_n$ denote the convex polytope of all $n\times n$ doubly stochastic matrices, and $\omega_{n}$ denote the convex polytope of all $n\times n$ doubly substochastic matrices. For a matrix $A\in\omega_n$, define the subdefect of $A$ to be the smallest integer $k$ such that there exists an $(n+k)\times(n+k)$ doubly stochastic matrix containing $A$ as a submatrix. Let $\omega_{n,k}$ denote the subset of $\omega_n$ which contains all doubly substochastic matrices with subdefect $k$. For $\pi$ a permutation of symmetric group of degree $n$, the sequence of elements $a_{1\pi(1 ...
InSphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, TinYau Tam, Bich Khue T Vo
InSphere Property And Reverse Inequalities For Matrix Means, Trung Hoa Dinh, TinYau Tam, Bich Khue T Vo
Electronic Journal of Linear Algebra
The insphere property for matrix means is studied. It is proved that the matrix power mean satisfies insphere property with respect to the HilbertSchmidt norm. A new characterization of the matrix arithmetic mean is provided. Some reverse AGM inequalities involving unitarily invariant norms and operator monotone functions are also obtained.
Surjective Additive Rank1 Preservers On Hessenberg Matrices, Prathomjit Khachorncharoenkul, Sajee Pianskool
Surjective Additive Rank1 Preservers On Hessenberg Matrices, Prathomjit Khachorncharoenkul, Sajee Pianskool
Electronic Journal of Linear Algebra
Let $H_{n}(\mathbb{F})$ be the space of all $n\times n$ upper Hessenberg matrices over a field~$\mathbb{F}$, where $n$ is a positive integer greater than two. In this paper, surjective additive maps preserving rank$1$ on $H_{n}(\mathbb{F})$ are characterized.
Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang
Role Of Combinatorial Complexity In Genetic Networks, Sharon Yang
SMU Journal of Undergraduate Research
A common motif found in genetic networks is the formation of large complexes. One difficulty in modeling this motif is the large number of possible intermediate complexes that can form. For instance, if a complex could contain up to 10 different proteins, 210 possible intermediate complexes can form. Keeping track of all complexes is difficult and often ignored in mathematical models. Here we present an algorithm to code ordinary differential equations (ODEs) to model genetic networks with combinatorial complexity. In these routines, the general binding rules, which counts for the majority of the reactions, are implemented automatically, thus the users ...
Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza
Singular Ramsey And Turán Numbers, Yair Caro, Zsolt Tuza
Theory and Applications of Graphs
We say that a subgraph F of a graph G is singular if the degrees d_G(v) are all equal or all distinct for the vertices v of F. The singular Ramsey number Rs(F) is the smallest positive integer n such that, for every m at least n, in every edge 2coloring of K_m, at least one of the color classes contains F as a singular subgraph. In a similar flavor, the singular Turán number Ts(n,F) is defined as the maximum number of edges in a graph of order n, which does not contain F as a ...
Solving The Sylvester Equation AxXb=C When $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, Nebojša Č. Dinčić
Solving The Sylvester Equation AxXb=C When $\Sigma(A)\Cap\Sigma(B)\Neq\Emptyset$, Nebojša Č. Dinčić
Electronic Journal of Linear Algebra
The method for solving the Sylvester equation $AXXB=C$ in complex matrix case, when $\sigma(A)\cap\sigma(B)\neq \emptyset$, by using Jordan normal form is given. Also, the approach via Schur decomposition is presented.
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily CilliTurner, Gail Tang, Gulden Karakok, Houssein El Turkey
Special Issue Call For Papers: Creativity In Mathematics, Milos Savic, Emily CilliTurner, Gail Tang, Gulden Karakok, Houssein El Turkey
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics is pleased to announce a call for papers for a special issue on Creativity in Mathematics. Please send your abstract submissions via email to the guest editors by March 1, 2019. Initial submission of complete manuscripts is due August 1, 2019. The issue is currently scheduled to appear in July 2020.
What The Wasp Said, Hugh C. Culik
What The Wasp Said, Hugh C. Culik
Journal of Humanistic Mathematics
On a bright spring day, the ancient building housing the English and Logic Departments begins to slowly collapse on itself, trapping McMann (an inept English professor) and Lucy Curt (a logician) in the office they share. As the Fibonacci repetitions of the building’s brickwork slowly peel away, McMann seizes the moment to tell Lucy stories about skunks, stories whose recurrent pattern finally leads to the unrecognized connection between a “message” burned into his ear by a wasp and the orderly universe for which he cannot find a language. At last, he looks up only to see Lucy descending a ...
An 1883 Faery Tale, Scott W. Williams
An 1883 Faery Tale, Scott W. Williams
Journal of Humanistic Mathematics
A poem about the construction of Georg Cantor's famous set.
Irrational Infinity, Ricky Chen
Irrational Infinity, Ricky Chen
Journal of Humanistic Mathematics
A short whimsical poem on the cardinality of irrational numbers.
Cosmology, Craig W. Steele
A Mathematician's Travel Memories, Michael Holcomb
A Mathematician's Travel Memories, Michael Holcomb
Journal of Humanistic Mathematics
No abstract provided.
Geometry Of Night, Jenny Patton
Geometry Of Night, Jenny Patton
Journal of Humanistic Mathematics
No abstract provided.
Ecstatic Syllabi: Four Poems, Mary Peelen
Ecstatic Syllabi: Four Poems, Mary Peelen
Journal of Humanistic Mathematics
Four poems with mathematical themes. Poems are entitled: Algebra I, Algebra II, Plane Geometry, Number Theory.
A Selection Of Poems From Ode To Numbers, Sarah Glaz
A Selection Of Poems From Ode To Numbers, Sarah Glaz
Journal of Humanistic Mathematics
My first poetry collection, Ode to Numbers, was published by Antrim House in September 2017 (http://www.antrimhousebooks.com/glaz.html). The book contains poems written over a quarter of a century and inspired by mathematics and my life as a mathematician. The poems in this folder are a small selection from the book—a series of seven poems focusing on events from the history of mathematics.
Book Review: Ode To Numbers: Poems By Sarah Glaz, Eveline Pye
Book Review: Ode To Numbers: Poems By Sarah Glaz, Eveline Pye
Journal of Humanistic Mathematics
This review explores the issues surrounding mathematics poetry and its role in challenging stereotypes about mathematics and mathematicians. In Ode to Numbers Sarah Glaz takes us from her childhood in Romania to her work as a professor at the University of Connecticut in the USA, with the constant thread of her love of mathematics. It is an intense emotional journey through time and place, arriving at mature reflection. The reader will encounter a wide range of poetic forms; some traditional, others inspired by mathematics. Glaz writes with originality, courage, insight, and generosity and this collection secures her reputation as an ...
Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn
Teaching History Of Mathematics: A Dialogue, Benjamin Braun, Eric Kahn
Journal of Humanistic Mathematics
Many colleges and universities offer a course in the history of mathematics. While the potential benefits for students taking such a course might be apparent, it is often less clear how teaching a history of mathematics course can be a transformational experience for faculty. We present a dialogue between the authors regarding their experiences teaching history of mathematics courses, including their motivation for doing so, the impact these experiences have had on their classroom practices and assessment methods, and the opportunities history of mathematics courses offer for incorporating social justice, equity, and inclusion into the study of mathematics. Our goal ...
Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren
Finding Teaching Inspiration From Gorgias: Mathematics Lessons From A Sophist, Ann L. Von Mehren
Journal of Humanistic Mathematics
The logos or rational language of the fifthcentury BCE teacher, Gorgias, as contained in the fragment On the Nonexistent, challenges a reader to understand the relationship between the existent and the nonexistent; yet the text also offers an accessible idea of logos. Inspired by William M. Priestley's approach to the study of logos through ratios, and by Ivor GrattanGuinness's recommendation to broaden the study of historical texts in the history of mathematics and mathematics education, and pursue their significance in a heritage sense, this article suggests that this ancient nonmathematics text by Gorgias may inspire and refresh elementary ...
On Mathematical Conjectures And Counterexamples, Ali Barahmand
On Mathematical Conjectures And Counterexamples, Ali Barahmand
Journal of Humanistic Mathematics
This article provides an overview of the limitations of checking out a few cases to prove conjectures in mathematics. To that end, I present a purposeful collection of numbertheoretic conjectures where extensive checking of cases has found counterexamples, with emphasis on the historical backgrounds. Historical examples of longterm attempts to prove or disprove such conjectures could help individuals to realize more deeply that a limited number of observations does not guarantee the correctness of a conjecture, even though there may be many examples in its favor.
Cartegory Theory: Framing Aesthetics Of Mathematics, Maria Mannone
Cartegory Theory: Framing Aesthetics Of Mathematics, Maria Mannone
Journal of Humanistic Mathematics
Mathematics can help investigate hidden patterns and structures in music and visual arts. Also, math in and of itself possesses an intrinsic beauty. We can explore such a specific beauty through the comparison of objects and processes in math with objects and processes in the arts. Recent experimental studies investigate the aesthetics of mathematical proofs compared to those of music. We can contextualize these studies within the framework of category theory applied to the arts (cARTegory theory), thanks to the helpfulness of categories for the analysis of transformations and transformations of transformations. This approach can be effective for the pedagogy ...
Fun With Math On Valentine's Day, Kristin T. Kennedy
Fun With Math On Valentine's Day, Kristin T. Kennedy
Journal of Humanistic Mathematics
This article describes various lovethemed activities the department of mathematics at Bryant University hosted during a collegewide celebration of love called "The Arts and Science of Love", held during Valentine's Day 2018. Inspired by Susan D'Agustino's article "To Fall in Love with Math, Do This" [1], Bryant mathematicians came up with many creative and engaging activities that brought mathematics and its practitioners closer to the students on campus. Much fun was had.
Incorporating Philosophy, Theology, And The History Of Mathematics In An Introduction To Proof Course, Steven Deckelman
Incorporating Philosophy, Theology, And The History Of Mathematics In An Introduction To Proof Course, Steven Deckelman
Journal of Humanistic Mathematics
In this article I describe a project activity for an undergraduate introduction to proof course aimed at mathematics and computer science majors that combines logic and philosophy with a significant dimension of writing. Pedagogically, the project involves a broader range of critical thinking skills than is usual in such courses. Undergraduate students analyze Anselm of Canterbury's and Kurt Gödel's proofs of the existence of God using modal logic.
SpiritWise Math: Two Examples From A Collection Of Mathaphors, Sarah Voss
SpiritWise Math: Two Examples From A Collection Of Mathaphors, Sarah Voss
Journal of Humanistic Mathematics
This article consists of two examples of loosely spiritual insights drawn from mathematics, both of which are from a workinprogress  a collection of mathematical metaphors.
Comforting With Mathematics: A Case Study, Michael J. Goldstein
Comforting With Mathematics: A Case Study, Michael J. Goldstein
Journal of Humanistic Mathematics
Death by suicide often leaves behind grieving family members with unanswered questions. Of these concerns, fear that their loved one suffered or felt regret is common. When the method of suicide was jumping from height, that answer can easily be determined using basic kinematics. Despite the perception that mathematics is a cold, calculating field, it can provide a clear, definitive answer and comfort those left behind.
What Is Humanistic Stem And Why Do We Need It?, Debra T. Bourdeau, Beverly L. Wood
What Is Humanistic Stem And Why Do We Need It?, Debra T. Bourdeau, Beverly L. Wood
Journal of Humanistic Mathematics
Getting students who are planning on technical careers to value their general education courses, particularly in the humanities, is not an easy task. The experiences of two professors from disciplines that cross the socalled divide between STEM and Humanities motivate not only a series of courses blending the two to the advantage of their own students but also a virtual pedagogical community to support efforts taking place elsewhere.
Out Of The Vacuum: A Hidden Assumption, Richard Delaware
Out Of The Vacuum: A Hidden Assumption, Richard Delaware
Journal of Humanistic Mathematics
In writing a proof, a student surprises her sense of reality and logic.
Untangling Knots: Embodied Diagramming Practices In Knot Theory, Kate Mccallum
Untangling Knots: Embodied Diagramming Practices In Knot Theory, Kate Mccallum
Journal of Humanistic Mathematics
The low visibility and specialised languages of mathematical work pose challenges for the ethnographic study of communication in mathematics, but observationbased study can offer a realworld grounding to questions about the nature of its methods. This paper uses theoretical ideas from linguistic pragmatics to examine how mutual understandings of diagrams are achieved in the course of conference presentations. Presenters use shared knowledge to train others to interpret diagrams in the ways favoured by the community of experts, directing an audience’s attention so as to develop a shared understanding of a diagram’s features and possible manipulations. In this way ...