Open Access. Powered by Scholars. Published by Universities.®

Algebra Commons

Open Access. Powered by Scholars. Published by Universities.®

565 Full-Text Articles 590 Authors 94353 Downloads 81 Institutions

All Articles in Algebra

Faceted Search

565 full-text articles. Page 1 of 19.

Session A-3: Three-Act Math Tasks, Lindsey Herlehy 2017 Illinois Mathematics and Science Academy

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.


Lorentz Transformation From An Elementary Point Of View, Arkadiusz Jadczyk, Jerzy Szulga 2017 Laboratoire de Physique Th\'{e}orique, Universit\'{e} de Toulouse III \& CNRS

Lorentz Transformation From An Elementary Point Of View, Arkadiusz Jadczyk, Jerzy Szulga

Electronic Journal of Linear Algebra

Elementary methods are used to examine some nontrivial mathematical issues underpinning the Lorentz transformation. Its eigen-system is characterized through the exponential of a $G$-skew symmetric matrix, underlining its unconnectedness at one of its extremes (the hyper-singular case). A different yet equivalent angle is presented through Pauli coding which reveals the connection between the hyper-singular case and the shear map.


Links With Finite N-Quandles, Jim Hoste, Patrick D. Shanahan 2017 Pitzer College

Links With Finite N-Quandles, Jim Hoste, Patrick D. Shanahan

Patrick Shanahan

We prove a conjecture of Przytycki which asserts that the n-quandle of a link L in the 3-sphere is finite if and only if the fundamental group of the n-fold cyclic branched cover of the 3-sphere, branched over L, is finite.


Specifications Grading In A First Course In Abstract Algebra, Mike Janssen 2017 Dordt College

Specifications Grading In A First Course In Abstract Algebra, Mike Janssen

Faculty Work: Comprehensive List

Specifications grading offers an alternative to more traditional, points-based grading and assessment structures. In place of partial credit, students are assessed pass/fail on whether or not they have achieved the learning outcomes being assessed on a given piece of work according to certain specifications, with limited opportunities for revision of non-passing work. This talk will describe the learning outcomes and specifications grading system I used in my Fall 2016 abstract algebra course, as well as student responses.


An Introduction To Boolean Algebras, Amy Schardijn 2016 California State University - San Bernardino

An Introduction To Boolean Algebras, Amy Schardijn

Electronic Theses, Projects, and Dissertations

This thesis discusses the topic of Boolean algebras. In order to build intuitive understanding of the topic, research began with the investigation of Boolean algebras in the area of Abstract Algebra. The content of this initial research used a particular notation. The ideas of partially ordered sets, lattices, least upper bounds, and greatest lower bounds were used to define the structure of a Boolean algebra. From this fundamental understanding, we were able to study atoms, Boolean algebra isomorphisms, and Stone’s Representation Theorem for finite Boolean algebras. We also verified and proved many properties involving Boolean algebras and related structures ...


Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson 2016 University of Tennessee, Knoxville

Mathematics Education From A Mathematicians Point Of View, Nan Woodson Simpson

Masters Theses

This study has been written to illustrate the development from early mathematical learning (grades 3-8) to secondary education regarding the Fundamental Theorem of Arithmetic and the Fundamental Theorem of Algebra. It investigates the progression of the mathematics presented to the students by the current curriculum adopted by the Rhea County School System and the mathematics academic standards set forth by the State of Tennessee.


Controllability And Nonsingular Solutions Of Sylvester Equations, Hamid Maarouf 2016 Poly-disciplinary Faculty of Safi

Controllability And Nonsingular Solutions Of Sylvester Equations, Hamid Maarouf

Electronic Journal of Linear Algebra

The singularity problem of the solutions of some particular Sylvester equations is studied. As a consequence of this study, a good choice of a Sylvester equation which is associated to a linear continuous time system can be made such that its solution is nonsingular. This solution is then used to solve an eigenstructure assignment problem for this system. From a practical point view, this study can also be applied to automatic control when the system is subject to input constraints.


Teaching Functions: The Good, The Bad, And The Many Ways To Do Better, Melanie Bayens 2016 Murray State University

Teaching Functions: The Good, The Bad, And The Many Ways To Do Better, Melanie Bayens

Honors College Theses

The way functions are taught in school needs improvement. Many times when students are introduced to functions in Algebra 2, the definition is glossed over, the instruction is lacking, and deeper understanding of the concept is lost. This causes problems when students are required to use this knowledge of functions in later classes, particularly, in Precalculus and Calculus. First, this paper will give the definition of a function and its role in mathematics. Second, this paper will delve into the problems of teaching functions the standard way. Finally, it will present multiple alternative methods for teaching functions. Specifically, it will ...


Group Inverse Extensions Of Certain $M$-Matrix Properties, Appi Reddy K., Kurmayya T., K. C. Sivakumar 2016 National Institute of Technology Warangal

Group Inverse Extensions Of Certain $M$-Matrix Properties, Appi Reddy K., Kurmayya T., K. C. Sivakumar

Electronic Journal of Linear Algebra

In this article, generalizations of certain $M$-matrix properties are proved for the group generalized inverse. The proofs use the notion of proper splittings of one type or the other. In deriving certain results, we make use of a recently introduced notion of a $B_{\#}$-splitting. Applications in obtaining comparison results for the spectral radii of matrices are presented.


On The Characterization And Parametrization Of Strong Linearizations Of Polynomial Matrices, Efstathios Antoniou, Stavros Vologiannidis 2016 Alexander Technological Education Institute of Thessaloniki

On The Characterization And Parametrization Of Strong Linearizations Of Polynomial Matrices, Efstathios Antoniou, Stavros Vologiannidis

Electronic Journal of Linear Algebra

In the present note, a new characterization of strong linearizations, corresponding to a given regular polynomial matrix, is presented. A linearization of a regular polynomial matrix is a matrix pencil which captures the finite spectral structure of the original matrix, while a strong linearization is one incorporating its structure at infinity along with the finite one. In this respect, linearizations serve as a tool for the study of spectral problems where polynomial matrices are involved. In view of their applications, many linearization techniques have been developed by several authors in the recent years. In this note, a unifying approach is ...


The Inverse Along An Element In Rings, Julio Benitez, Enrico Boasso 2016 Universidad Politecnica de Valencia

The Inverse Along An Element In Rings, Julio Benitez, Enrico Boasso

Electronic Journal of Linear Algebra

Several properties of the inverse along an element are studied in the context of unitary rings. New characterizations of the existence of this inverse are proved. Moreover, the set of all invertible elements along a fixed element is fully described. Furthermore, commuting inverses along an element are characterized. The special cases of the group inverse, the (generalized) Drazin inverse and the Moore-Penrose inverse (in rings with involutions) are also considered.


Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta 2016 University of Houston

Exploring Mathematical Strategies For Finding Hidden Features In Multi-Dimensional Big Datasets, Tri Duong, Fang Ren, Apurva Mehta

STAR (STEM Teacher and Researcher) Presentations

With advances in technology in brighter sources and larger and faster detectors, the amount of data generated at national user facilities such as SLAC is increasing exponentially. Humans have a superb ability to recognize patterns in complex and noisy data and therefore, data is still curated and analyzed by humans. However, a human brain is unable to keep up with the accelerated pace of data generation, and as a consequence, the rate of new discoveries hasn't kept pace with the rate of data creation. Therefore, new procedures to quickly assess and analyze the data are needed. Machine learning approaches ...


Algebra Tutorial For Prospective Calculus Students, Matthew McKain 2016 Governors State University

Algebra Tutorial For Prospective Calculus Students, Matthew Mckain

All Capstone Projects

Many undergraduate degrees require students to take one or more courses in calculus. Majors in mathematics, science, and engineering are expected to enroll in several rigorous calculus courses, but those majoring in social and behavioral sciences and business must also have some basic understanding of calculus. The goal of this project is to create a web-based tutorial that can be used by the GSU Mathematics faculty to reinforce the algebra skills needed for introductory or Applied Calculus. The tutorial covers the concepts of the slopes of lines, polynomial arithmetic, factoring polynomials, rational expressions, solving quadratic equations, linear and polynomial inequalities ...


Some 2-Categorical Aspects In Physics, Arthur Parzygnat 2016 The Graduate Center, City University of New York

Some 2-Categorical Aspects In Physics, Arthur Parzygnat

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

2-categories provide a useful transition point between ordinary category theory and infinity-category theory where one can perform concrete computations for applications in physics and at the same time provide rigorous formalism for mathematical structures appearing in physics. We survey three such broad instances. First, we describe two-dimensional algebra as a means of constructing non-abelian parallel transport along surfaces which can be used to describe strings charged under non-abelian gauge groups in string theory. Second, we formalize the notion of convex and cone categories, provide a preliminary categorical definition of entropy, and exhibit several examples. Thirdly, we provide a universal description ...


On The Derivative Of 2-Holonomy For A Non-Abelian Gerbe, Cheyne J. Miller 2016 The Graduate Center, City University of New York

On The Derivative Of 2-Holonomy For A Non-Abelian Gerbe, Cheyne J. Miller

All Graduate Works by Year: Dissertations, Theses, and Capstone Projects

The local 2-holonomy for a non abelian gerbe with connection is first studied via a local zig-zag Hochschild complex. Next, by locally integrating the cocycle data for our gerbe with connection, and then glueing this data together, an explicit definition is offered for a global version of 2-holonomy. After showing this definition satisfies the desired properties for 2-holonomy, its derivative is calculated whereby the only interior information added is the integration of the 3-curvature. Finally, for the case when the surface being mapped into the manifold is a sphere, the derivative of 2-holonomy is extended to an equivariant closed form ...


Generalizations Of The Cauchy And Fujiwara Bounds For Products Of Zeros Of A Polynomial, Rajesh Pereira, Mohammad Ali Vali 2016 University of Guelph

Generalizations Of The Cauchy And Fujiwara Bounds For Products Of Zeros Of A Polynomial, Rajesh Pereira, Mohammad Ali Vali

Electronic Journal of Linear Algebra

The Cauchy bound is one of the best known upper bounds for the modulus of the zeros of a polynomial. The Fujiwara bound is another useful upper bound for the modulus of the zeros of a polynomial. In this paper, compound matrices are used to derive a generalization of both the Cauchy bound and the Fujiwara bound. This generalization yields upper bounds for the modulus of the product of $m$ zeros of the polynomial.


Cycle Structures Of Orthomorphisms Extending Partial Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski, John S. Caughman IV 2016 Portland State University

Cycle Structures Of Orthomorphisms Extending Partial Orthomorphisms Of Boolean Groups, Nichole Louise Schimanski, John S. Caughman Iv

Mathematics and Statistics Faculty Publications and Presentations

A partial orthomorphism of a group GG (with additive notation) is an injection π:S→G for some S⊆G such that π(x)−x ≠ π(y) for all distinct x,y∈S. We refer to |S| as the size of π, and if S=G, then π is an orthomorphism. Despite receiving a fair amount of attention in the research literature, many basic questions remain concerning the number of orthomorphisms of a given group, and what cycle types these permutations have.

It is known that conjugation by automorphisms of G forms a group action on the set of orthomorphisms ...


A Survey Of Graphs Of Minimum Order With Given Automorphism Group, Jessica Alyse Woodruff 2016 University of Texas at Tyler

A Survey Of Graphs Of Minimum Order With Given Automorphism Group, Jessica Alyse Woodruff

Math Theses

We survey vertex minimal graphs with prescribed automorphism group. Whenever possible, we also investigate the construction of such minimal graphs, confirm minimality, and prove a given graph has the correct automorphism group.


Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz 2016 University of Nebraska - Lincoln

Homological Characterizations Of Quasi-Complete Intersections, Jason M. Lutz

Dissertations, Theses, and Student Research Papers in Mathematics

Let R be a commutative ring, (f) an ideal of R, and E = K(f; R) the Koszul complex. We investigate the structure of the Tate construction T associated with E. In particular, we study the relationship between the homology of T, the quasi-complete intersection property of ideals, and the complete intersection property of (local) rings.

Advisers: Luchezar L. Avramov and Srikanth B. Iyengar


Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces, Sean A. Broughton 2016 Rose-Hulman Institute of Technology

Topological And Hq Equivalence Of Prime Cyclic P-Gonal Actions On Riemann Surfaces, Sean A. Broughton

Mathematical Sciences Technical Reports (MSTR)

Two Riemann surfaces S1 and S2 with conformal G-actions have topologically equivalent actions if there is a homeomorphism h : S1 -> S2 which intertwines the actions. A weaker equivalence may be defined by comparing the representations of G on the spaces of holomorphic q-differentials Hq(S1) and Hq(S2). In this note we study the differences between topological equivalence and Hq equivalence of prime cyclic actions, where S1/G and S2/G have genus zero.


Digital Commons powered by bepress