Galois Groups Of Differential Equations And Representing Algebraic Sets, 2018 The Graduate Center, City University of New York
Galois Groups Of Differential Equations And Representing Algebraic Sets, Eli Amzallag
Dissertations, Theses, and Capstone Projects
The algebraic framework for capturing properties of solution sets of differential equations was formally introduced by Ritt and Kolchin. As a parallel to the classical Galois groups of polynomial equations, they devised the notion of a differential Galois group for a linear differential equation. Just as solvability of a polynomial equation by radicals is linked to the equation’s Galois group, so too is the ability to express the solution to a linear differential equation in "closed form" linked to the equation’s differential Galois group. It is thus useful even outside of mathematics to be able to compute and represent these …
Math Active Learning Lab: Math 92 Notebook, 2018 University of North Dakota
Math Active Learning Lab: Math 92 Notebook, Michele Iiams, Gwennie Byron
Open Educational Resources
This course notebook has been designed for students of Math 92 (Algebra Prep II) at the University of North Dakota. It has been designed to help you get the most out of the ALEKS resources and your time.
- Topics in the Notebook are organized by weekly learning module.
- Space for notes from ALEKS learning pages, e-book and videos directs you to essential concepts.
- Examples and “You Try It” problems have been carefully chosen to help you focus on these essential concepts.
- Completed Notebook is an invaluable tool when studying for exams.
High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, 2018 The University of Western Ontario
High Performance Sparse Multivariate Polynomials: Fundamental Data Structures And Algorithms, Alex Brandt
Electronic Thesis and Dissertation Repository
Polynomials may be represented sparsely in an effort to conserve memory usage and provide a succinct and natural representation. Moreover, polynomials which are themselves sparse – have very few non-zero terms – will have wasted memory and computation time if represented, and operated on, densely. This waste is exacerbated as the number of variables increases. We provide practical implementations of sparse multivariate data structures focused on data locality and cache complexity. We look to develop high-performance algorithms and implementations of fundamental polynomial operations, using these sparse data structures, such as arithmetic (addition, subtraction, multiplication, and division) and interpolation. We revisit …
The Effects Of Motivation, Technology And Satisfaction On Student Achievement In Face-To-Face And Online College Algebra Classes, 2018 South Texas College
The Effects Of Motivation, Technology And Satisfaction On Student Achievement In Face-To-Face And Online College Algebra Classes, Hanan Jamal Amro, Marie-Anne Mundy, Lori Kupczynski
TxDLA Journal of Digital Learning
Demand for online learning has increased in recent years due to the convenience of class delivery. However, some students appear to have difficulties with online education resulting in lack of completion. The study utilized a quantitative approach with archival data and survey design. The factors of demographics, motivation, technology, and satisfaction were compared for face-to-face and online students. MANCOVA tests were performed to analyze the data while controlling age and gender to uncover significant differences between the two groups. The sample and population for this study were predominantly Hispanic students.
Motivation and Technology were non-significant, but satisfaction was proven to …
Equations Of Multi-Rees Algebras, 2018 University of Arkansas, Fayetteville
Equations Of Multi-Rees Algebras, Babak Jabbar Nezhad
Graduate Theses and Dissertations
In this thesis we describe the defining equations of certain multi-Rees algebras. First, we determine the defining equations of the multi-Rees algebra $R[I^{a_1}t_1,\dots,I^{a_r}t_r]$ over a Noetherian ring $R$ when $I$ is an ideal of linear type. This generalizes a result of Ribbe and recent work of Lin-Polini and Sosa. Second, we describe the equations defining the multi-Rees algebra $R[I_1^{a_1}t_1,\dots,I_r^{a_r}t_r]$, where $R$ is a Noetherian ring containing a field and the ideals are generated by a subset of a fixed regular sequence.
A Tensor's Torsion, 2018 University of Nebraska-Lincoln
A Tensor's Torsion, Neil Steinburg
Department of Mathematics: Dissertations, Theses, and Student Research
While tensor products are quite prolific in commutative algebra, even some of their most basic properties remain relatively unknown. We explore one of these properties, namely a tensor's torsion. In particular, given any finitely generated modules, M and N over a ring R, the tensor product $M\otimes_R N$ almost always has nonzero torsion unless one of the modules M or N is free. Specifically, we look at which rings guarantee nonzero torsion in tensor products of non-free modules over the ring. We conclude that a specific subclass of one-dimensional Gorenstein rings will have this property.
Adviser: Roger Wiegand and Tom …
Factorization In Integral Domains., 2018 University of Louisville
Factorization In Integral Domains., Ryan H. Gipson
Electronic Theses and Dissertations
We investigate the atomicity and the AP property of the semigroup rings F[X; M], where F is a field, X is a variable and M is a submonoid of the additive monoid of nonnegative rational numbers. In this endeavor, we introduce the following notions: essential generators of M and elements of height (0, 0, 0, . . .) within a cancellative torsion-free monoid Γ. By considering the latter, we are able to determine the irreducibility of certain binomials of the form Xπ − 1, where π is of height (0, 0, 0, . . .), in the monoid domain. Finally, …
Developments In Multivariate Post Quantum Cryptography., 2018 University of Louisville
Developments In Multivariate Post Quantum Cryptography., Jeremy Robert Vates
Electronic Theses and Dissertations
Ever since Shor's algorithm was introduced in 1994, cryptographers have been working to develop cryptosystems that can resist known quantum computer attacks. This push for quantum attack resistant schemes is known as post quantum cryptography. Specifically, my contributions to post quantum cryptography has been to the family of schemes known as Multivariate Public Key Cryptography (MPKC), which is a very attractive candidate for digital signature standardization in the post quantum collective for a wide variety of applications. In this document I will be providing all necessary background to fully understand MPKC and post quantum cryptography as a whole. Then, I …
Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, 2018 Chapman University
Partially-Ordered Multi-Type Algebras, Display Calculi And The Category Of Weakening Relations, Peter Jipsen, Fei Liang, M. Andrew Moshier, Apostolos Tzimoulis
Mathematics, Physics, and Computer Science Faculty Articles and Research
"We define partially-ordered multi-type algebras and use them as algebraic semantics for multi-type display calculi that have recently been developed for several logics, including dynamic epistemic logic [7], linear logic[10], lattice logic [11], bilattice logic [9] and semi-De Morgan logic [8]."
Local Higher Category Theory, 2018 The University of Western Ontario
Local Higher Category Theory, Nicholas Meadows
Electronic Thesis and Dissertation Repository
The purpose of this thesis is to give presheaf-theoretic versions of three of the main extant models of higher category theory: the Joyal, Rezk and Bergner model structures. The construction of these model structures takes up Chapters 2, 3 and 4 of the thesis, respectively. In each of the model structures, the weak equivalences are local or ‘stalkwise’ weak equivalences. In addition, it is shown that certain Quillen equivalences between the aforementioned models of higher category theory extend to Quillen equivalences between the various models of local higher category theory.
Throughout, a number of features of local higher category theory …
Determining The Determinant, 2018 Xavier University
Webwork Problems For Linear Algebra, 2018 University of North Georgia
Webwork Problems For Linear Algebra, Hashim Saber, Beata Hebda
Mathematics Ancillary Materials
This set of problems for Linear Algebra in the open-source WeBWorK mathematics platform was created under a Round Eleven Mini-Grant for Ancillary Materials Creation. The problems were created for an implementation of the CC-BY Lyrix open textbook A First Course in Linear Algebra. Also included as an additional file are the selected and modified Lyryx Class Notes for the textbook.
Topics covered include:
- Linear Independence
- Linear Transformations
- Matrix of a Transformation
- Isomorphisms
- Eigenvalues and Eigenvectors
- Diagonalization
- Orthogonality
Finding Meaning In A Multivariable World: A Conceptual Approach To An Algebra-Based Second Course In Statistics, 2018 Dordt College
Finding Meaning In A Multivariable World: A Conceptual Approach To An Algebra-Based Second Course In Statistics, Karen Mcgaughey, Beth Chance, Nathan L. Tintle, Soma Roy, Todd Swanson, Jill Vander Stoep
Faculty Work Comprehensive List
Although the teaching of the first course in statistics has improved dramatically in recent years, there has been less focus on a similarly conceptual-based second course aimed at non-majors. We present a curriculum for the second course, designed to expand statistical literacy across disciplines, which focuses on conceptual understanding of multivariable relationships through data visualization, study design, the role of confounding variables, reduction of unexplained variation, and simulation-based inference, rather than the mathematically-based discourse often used in the second course. Our curriculum uses a student-centered pedagogical approach, utilizing guided discovery activities based on real-world case studies, facilitated by student-focused technology …
Dimers On Cylinders Over Dynkin Diagrams And Cluster Algebras, 2018 Louisiana State University and Agricultural and Mechanical College
Dimers On Cylinders Over Dynkin Diagrams And Cluster Algebras, Maitreyee Chandramohan Kulkarni
LSU Doctoral Dissertations
This dissertation describes a general setting for dimer models on cylinders over Dynkin diagrams which in type A reduces to the well-studied case of dimer models on a disc. We prove that all Berenstein--Fomin--Zelevinsky quivers for Schubert cells in a symmetric Kac--Moody algebra give rise to dimer models on the cylinder over the corresponding Dynkin diagram. We also give an independent proof of a result of Buan, Iyama, Reiten and Smith that the corresponding superpotentials are rigid using the dimer model structure of the quivers.
Invariant Of Noncommutative Algebras And Poisson Geometry, 2018 Louisiana State University and Agricultural and Mechanical College
Invariant Of Noncommutative Algebras And Poisson Geometry, Bach Van Nguyen
LSU Doctoral Dissertations
In this dissertation, we describe the structure of discriminant of noncommutative algebras using the theory of Poisson quantization and ring theoretic properties of Poisson algebra. In particular, under appropriate conditions, we express the discriminant of specialization of K[q^{+-1}]-algebras as product of Poisson prime elements in some Poisson central subalgebra. In addition, we provide methods for computing noncommutative discriminant in various settings using results obtained for specialization of K[q^{+-1}]-algebras. Further, to demonstrate, we explicitly compute the discriminant of algebra of quantum matrices and quantum Schubert cell algebras specializing at roots of unity. This dissertation is part of the collaboration with Trampel …
Study Of Pseudo Bl–Algebras In View Of Left Boolean Lifting Property, 2018 Islamic Azad University
Study Of Pseudo Bl–Algebras In View Of Left Boolean Lifting Property, B. Barani Nia, A. B. Saeid
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we define left Boolean lifting property (right Boolean lifting property) LBLP (RBLP) for pseudo BL–algebra which is the property that all Boolean elements can be lifted modulo every left filter (right filter) and next, we study pseudo BL-algebra with LBLP (RBLP). We show that Quasi local, local and hyper Archimedean pseudo BL–algebra that have LBLP (RBLP) has an interesting behavior in direct products. LBLP (RBLP) provides an important representation theorem for semi local and maximal pseudo BL–algebra.
Symmetric Presentations, Representations, And Related Topics, 2018 California State University - San Bernardino
Symmetric Presentations, Representations, And Related Topics, Adam Manriquez
Electronic Theses, Projects, and Dissertations
The purpose of this thesis is to develop original symmetric presentations of finite non-abelian simple groups, particularly the sporadic simple groups. We have found original symmetric presentations for the Janko group J1, the Mathieu group M12, the Symplectic groups S(3,4) and S(4,5), a Lie type group Suz(8), and the automorphism group of the Unitary group U(3,5) as homomorphic images of the progenitors 2*60 : (2 x A5), 2*60 : A5, 2*56 : (23 : 7), and 2*28 : (PGL(2,7):2), respectively. We have also discovered the groups 2 …
Galois Theory And The Quintic Equation, 2018 Union College
Galois Theory And The Quintic Equation, Yunye Jiang
Honors Theses
Most students know the quadratic formula for the solution of the general quadratic polynomial in terms of its coefficients. There are also similar formulas for solutions of the general cubic and quartic polynomials. In these three cases, the roots can be expressed in terms of the coefficients using only basic algebra and radicals. We then say that the general quadratic, cubic, and quartic polynomials are solvable by radicals. The question then becomes: Is the general quintic polynomial solvable by radicals? Abel was the first to prove that it is not. In turn, Galois provided a general method of determining when …
Homomorphism Of Fuzzy Multigroups And Some Of Its Properties, 2018 University of Agriculture, Nigeria
Homomorphism Of Fuzzy Multigroups And Some Of Its Properties, P. A. Ejegwa
Applications and Applied Mathematics: An International Journal (AAM)
In a way, the notion of fuzzy multigroups is an application of fuzzy multisets to the theory of group. The concept of fuzzy multigroups is a new algebraic structure of uncertainty which generalizes fuzzy groups. Fuzzy multigroup is a multiset of X x [0; 1] satisfying some set of axioms, where X is a classical group. In this paper, we propose the concept of homomorphism in fuzzy multigroups context. Some homomorphic properties of fuzzy multigroups are explicated. Again, we show that the homomorphic image and homomorphic preimage of fuzzy multigroups are also fuzzy multigroups. Finally, we present some homomorphic properties …
Simple Groups, Progenitors, And Related Topics, 2018 California State University - San Bernardino
Simple Groups, Progenitors, And Related Topics, Angelica Baccari
Electronic Theses, Projects, and Dissertations
The foundation of the work of this thesis is based around the involutory progenitor and the finite homomorphic images found therein. This process is developed by Robert T. Curtis and he defines it as 2^{*n} :N {pi w | pi in N, w} where 2^{*n} denotes a free product of n copies of the cyclic group of order 2 generated by involutions. We repeat this process with different control groups and a different array of possible relations to discover interesting groups, such as sporadic, linear, or unitary groups, to name a few. Predominantly this work was produced from transitive groups …