View All Items

Title: ANNIHILATORS AND A + B RINGS.
Creator: Epstein, Alexandra Nicole, Klingler, Lee, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: A + B rings are constructed from a ring A and nonempty set of prime ideals of A. Initially, these rings were created to provide examples of reduced rings which satisfy certain annihilator conditions. We describe precisely when A + B rings have these properties, based on the ring A and set of prime ideals of A. We continue by giving necessary and su cient conditions for A + B rings to have various other properties. We also consider annihilators in the context of frames of ideals of reduced rings.
Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013588
Subject Headings: Rings (Algebra)
Format: Document (PDF)

Title: The Cayley-Dickson algebras.
Creator: Khalil, Saidah Hasan, Florida Atlantic University, Yiu, Paul Y., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: This thesis studies the various effects of the nonassociativity of the Cayley-Dickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the Cayley-Dickson algebras, and give a self-contained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v - u(wv...
Show moreThis thesis studies the various effects of the nonassociativity of the Cayley-Dickson algebras At, t>3, especially on the structure of their automorphism groups. Beginning with the problem of composition algebra structures on euclidean spaces, we shall explain the origin of the Cayley-Dickson algebras, and give a self-contained exposition on some important results on such algebras. These algebras being nonassociative, we focus on the study of the associators of the form (u,w,v) = (uw)v - u(wv). The first main result, that if u and v are elements in a Cayley-Dickson algebra for which (u, w, v) = 0 for all w, then u and v generate a 2-dimensional subalgebra isomorphic to C, was conjectured by P. Yiu, and proved by P. Eakin and A. Sathaye. We shall simplify the proof given by these latter authors. This is then used to give a simple proof of R. D. Schafer's theorem on derivations of Cayley-Dickson algebras, and following also Eakin and Sathaye, a proof of the conjecture by R. B. Brown on the structure of the automorphism groups of these algebras. Two simple proofs are presented for the beautiful characterization by H. Brandt that in the Cayley algebra A3 = K, conjugation by a unit element a is an automorphism if and only if a is a 6th root of unity. We shall present a geometric proof by M. A. Zorn and a purely algebraic one. The zero divisors of the Cayley-Dickson algebra A4 are also analyzed in detail.
Show less
Date Issued: 1993
PURL: http://purl.flvc.org/fcla/dt/14993
Subject Headings: Cayley algebras
Format: Document (PDF)

Title: OPERATOR IDENTITIES AND SPITZER'S FORMULA IN NON-COMMUTATIVE ALGEBRAS.
Creator: ELSTNER, EILERT., Florida Atlantic University
Abstract/Description: This thesis was motivated by the idea to generalize Spitzer's identity to the non-commutative case. For this purpose the concept of an "operator type'' is introduced, which reveals in an elementary way the relationship between operator identities and functional equations. Baxter and Reynolds operators are studied using this approach. Then a non-commutative Spitzer identity is derived and applied to generalized shift operators. As another application we give non-commutative analogs of some...
Show moreThis thesis was motivated by the idea to generalize Spitzer's identity to the non-commutative case. For this purpose the concept of an "operator type'' is introduced, which reveals in an elementary way the relationship between operator identities and functional equations. Baxter and Reynolds operators are studied using this approach. Then a non-commutative Spitzer identity is derived and applied to generalized shift operators. As another application we give non-commutative analogs of some formulas of Euler.
Show less
Date Issued: 1971
PURL: http://purl.flvc.org/fcla/dt/13439
Subject Headings: Commutative algebra
Format: Document (PDF)

Title: DERIVATIONS AND DIFFERENTIALS.
Creator: BASTIDA, VICKI C., Florida Atlantic University, Bastida, Julio R.
Abstract/Description: In this thesis we present a detailed study of the foundations of the general theory of derivations and differentials for commutative algebras over commutative rings. We give a direct and natural proof of the existence of the module of differentials, and then discuss some of its basic properties. A considerable part of the work is devoted to the establishing of the two fundamental exact sequences.
Date Issued: 1971
PURL: http://purl.flvc.org/fcla/dt/13447
Subject Headings: Algebra, Abstract
Format: Document (PDF)

Title: The prime spectrum of a ring: A survey.
Creator: Fernandez, James Stephen, Florida Atlantic University, Klingler, Lee
Abstract/Description: This thesis has as its motivation the exploration, on an informal level, of a correspondence between Algebra and Topology. Specifically, it considers the prime spectrum of a ring, that is, the set of prime ideals, endowed with the Zariski topology. Questions posed by M. Atiyah and I. MacDonald in their book, "Introduction to Commutative Algebra", serve as a guideline through most of this work. The final section, however, follows R. Heitmann's paper, "Generating Non-Noetherian Modules...
Show moreThis thesis has as its motivation the exploration, on an informal level, of a correspondence between Algebra and Topology. Specifically, it considers the prime spectrum of a ring, that is, the set of prime ideals, endowed with the Zariski topology. Questions posed by M. Atiyah and I. MacDonald in their book, "Introduction to Commutative Algebra", serve as a guideline through most of this work. The final section, however, follows R. Heitmann's paper, "Generating Non-Noetherian Modules Efficiently". This section examines the patch topology on the prime spectrum of a ring where the patch topology has as a closed subbasis the Zariski closed and Zariski quasi-compact open sets. It is proven that the prime spectrum of a ring with the patch topology is a compact Hausdorff space, and several relationships between the patch and Zariski topologies are established. The final section concludes with a technical theorem having a number of interesting corollaries, among which are a stable range theorem and a theorem of Kronecker, both generalized to the non-Noetherian setting.
Show less
Date Issued: 1991
PURL: http://purl.flvc.org/fcla/dt/14763
Subject Headings: Rings (Algebra)
Format: Document (PDF)

Title: A CHARACTERIZATION OF PRODUCT FORMULA FIELDS.
Creator: HELLMAN, ALLEN PAUL, Florida Atlantic University
Abstract/Description: In this thesis we present a characterization of fields which admit a product formula. We prove that a field which admits a product formula consisting of admissible prime spots is a global field. This result was originally proved by Artin and Whaples in 1945. By limiting the admissible prime spots to those that are archimedean or discrete with finite residue class field, we are able to obtain a more elementary proof than that given by Artin and Whaples. The proof given here is, to our...
Show moreIn this thesis we present a characterization of fields which admit a product formula. We prove that a field which admits a product formula consisting of admissible prime spots is a global field. This result was originally proved by Artin and Whaples in 1945. By limiting the admissible prime spots to those that are archimedean or discrete with finite residue class field, we are able to obtain a more elementary proof than that given by Artin and Whaples. The proof given here is, to our knowledge, The render should notice that Artin and Whaples obtain, as a part of their result, that only the two types of prime spots mentioned above can occur in a product formula.
Show less
Date Issued: 1973
PURL: http://purl.flvc.org/fcla/dt/13582
Subject Headings: Algebraic fields, Algebraic number theory
Format: Document (PDF)

Title: Auslander-Reiten theory for systems of submodule embeddings.
Creator: Moore, Audrey., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite...
Show moreIn this dissertation, we will investigate aspects of Auslander-Reiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute Auslander-Reiten quivers of such categories, which among other information, yields valuable information about the indecomposable objects in such a category. A main result of the dissertation is an adaptation to this situation of the Auslander and Ringel-Tachikawa Theorem which states that for an artinian ring R of finite representation type, each R-module is a direct sum of finite-length indecomposable R-modules. In cases where this applies, the indecomposable objects obtained in the Auslander-Reiten quiver give the building blocks for the objects in the category. We also briefly discuss in which cases systems of submodule embeddings form a Frobenius category, and for a few examples explore pointwise Calabi-Yau dimension of such a category.
Show less
Date Issued: 2009
PURL: http://purl.flvc.org/fcla/dt/210496
Subject Headings: Artin algebras, Rings (Algebra), Representation of algebras, Embeddings (Mathematics), Linear algebraic groups
Format: Document (PDF)

Title: Coset intersection problem and application to 3-nets.
Creator: Pace, Nicola, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all...
Show moreIn a projective plane (PG(2, K) defined over an algebraically closed field K of characteristic p = 0, we give a complete classification of 3-nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3-nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3-nets realizing dihedral groups. We prove that there is no further infinite family and list all possible sporadic examples. If p is larger than the order of the group, the same classification holds true apart from three possible exceptions: Alt4, Sym4 and Alt5.
Show less
Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3355866
Subject Headings: Finite fields (Algebra), Mathematical physics, Field theory (Physics), Curves, Algebraic
Format: Document (PDF)

Title: Weakly integrally closed domains and forbidden patterns.
Creator: Hopkins, Mary E., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: An integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally...
Show moreAn integral domain D is weakly integrally closed if whenever there is an element x in the quotient field of D and a nonzero finitely generated ideal J of D such that xJ J2, then x is in D. We define weakly integrally closed numerical monoids similarly. If a monoid algebra is weakly integrally closed, then so is the monoid. A pattern F of finitely many 0's and 1's is forbidden if whenever the characteristic binary string of a numerical monoid M contains F, then M is not weakly integrally closed. Any stretch of the pattern 11011 is forbidden. A numerical monoid M is weakly integrally closed if and only if it has a forbidden pattern. For every finite set S of forbidden patterns, there exists a monoid that is not weakly integrally closed and that contains no stretch of a pattern in S. It is shown that particular monoid algebras are weakly integrally closed.
Show less
Date Issued: 2009
PURL: http://purl.flvc.org/FAU/199327
Subject Headings: Mathematical analysis, Algebra, Homological, Monoids, Categories (Mathematics), Semigroup algebras
Format: Document (PDF)

Title: ANGULAR RIGIDITY THEORY IN PLANAR FRAMEWORKS.
Creator: Urizar, David Ricardo, Rosen, Zvi, Florida Atlantic University, Department of Mathematical Sciences, Charles E. Schmidt College of Science
Abstract/Description: In this dissertation, we develop analogues to various notion in rigidity theory in the case of angular constraints. Initially, we were interested in angle dependencies. However, by defining a chromatic graph determined by the point-line incidence or angle graph of a given angularity, we were able to determine an assortment of properties. We provide a conjectured angular rigidity matroid involving count matroids, tranversal matroids, and traditional rigidity matroids. We consider realizations...
Show moreIn this dissertation, we develop analogues to various notion in rigidity theory in the case of angular constraints. Initially, we were interested in angle dependencies. However, by defining a chromatic graph determined by the point-line incidence or angle graph of a given angularity, we were able to determine an assortment of properties. We provide a conjectured angular rigidity matroid involving count matroids, tranversal matroids, and traditional rigidity matroids. We consider realizations of chromatic graphs in R2 as well as C similar to the work in [3]. We extend the notions of pure conditions and infinitesimal motions using the chromatic rigidity matrix by applying techniques from algebra geometric as well as classical geometric results, such as Thales’ theorem. Some realizations I computed inspired curiosity in the space of realizations of angle-constrained graphs. We generate uniformly random sets of angle constraints to consider the space of realizations given these angle sets. We provide some results for the maximum number of possible realizations for some chromatic graphs on four vertices. We conclude with some directions for further research to develop our notions of angle-rigid graphs and their properties.
Show less
Date Issued: 2023
PURL: http://purl.flvc.org/fau/fd/FA00014291
Subject Headings: Rigidity (Geometry), Algebraic geometry, Graphs
Format: Document (PDF)

Title: Unique decomposition of direct sums of ideals.
Creator: Ay, Basak., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: We say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 1-3 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one...
Show moreWe say that a commutative ring R has the unique decomposition into ideals (UDI) property if, for any R-module which decomposes into a finite direct sum of indecomposable ideals, this decomposition is unique up to the order and isomorphism class of the ideals. In a 2001 paper, Goeters and Olberding characterize the UDI property for Noetherian integral domains. In Chapters 1-3 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of one-dimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the Krull-Schmidt property for direct sums of torsion-free rank one modules for a reduced local commutative Noetherian one-dimensional ring R.
Show less
Date Issued: 2010
PURL: http://purl.flvc.org/FAU/2683133
Subject Headings: Algebraic number theory, Modules (Algebra), Noetherian rings, Commutative rings, Algebra, Abstract
Format: Document (PDF)

Title: Rings of integer-valued polynomials and derivatives.
Creator: Villanueva, Yuri., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: For D an integral domain with field of fractions K and E a subset of K, the ring Int (E,D) = {f e K[X]lf (E) C D} of integer-valued polynomials on E has been well studies. In particulare, when E is a finite subset of D, Chapman, Loper, and Smith, as well as Boynton and Klingler, obtained a bound on the number of elements needed to generate a finitely generated ideal of Ing (E, D) in terms of the corresponding bound for D. We obtain analogous results for Int (r) (E, D) - {f e K [X]lf(k) (E) c...
Show moreFor D an integral domain with field of fractions K and E a subset of K, the ring Int (E,D) = {f e K[X]lf (E) C D} of integer-valued polynomials on E has been well studies. In particulare, when E is a finite subset of D, Chapman, Loper, and Smith, as well as Boynton and Klingler, obtained a bound on the number of elements needed to generate a finitely generated ideal of Ing (E, D) in terms of the corresponding bound for D. We obtain analogous results for Int (r) (E, D) - {f e K [X]lf(k) (E) c D for all 0 < k < r} , for finite E and fixed integer r > 1. These results rely on the work of Skolem [23] and Brizolis [7], who found ways to characterize ideals of Int (E, D) from the values of their polynomials at points in D. We obtain similar results for E = D in case D is local, Noetherian, one-dimensional, analytically irreducible, with finite residue field.
Show less
Date Issued: 2012
PURL: http://purl.flvc.org/FAU/3356899
Subject Headings: Rings of integers, Ideals (Algebra), Polynomials, Arithmetic algebraic geometry, Categories (Mathematics), Commutative algebra
Format: Document (PDF)

Title: Minimal zero-dimensional extensions.
Creator: Chiorescu, Marcela, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: The structure of minimal zero-dimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a one-to-one correspondence between isomorphism classes of minimal zero-dimensional extensions of R and sets M, where the elements of M are...
Show moreThe structure of minimal zero-dimensional extension of rings with Noetherian spectrum in which zero is a primary ideal and with at most one prime ideal of height greater than one is determined. These rings include K[[X,T]] where K is a field and Dedenkind domains, but need not be Noetherian nor integrally closed. We show that for such a ring R there is a one-to-one correspondence between isomorphism classes of minimal zero-dimensional extensions of R and sets M, where the elements of M are ideals of R primary for distinct prime ideals of height greater than zero. A subsidiary result is the classification of minimal zero-dimensional extensions of general ZPI-rings.
Show less
Date Issued: 2009
PURL: http://purl.flvc.org/FAU/210447
Subject Headings: Algebra, Abstract, Noetherian rings, Commutative rings, Modules (Algebra), Algebraic number theory
Format: Document (PDF)

Title: CONNECTED MULTI-DOMAIN AUTONOMY AND ARTIFICIAL INTELLIGENCE: AUTONOMOUS LOCALIZATION, NETWORKING, AND DATA CONFORMITY EVALUATION.
Creator: Tountas, Konstantinos, Pados, Dimitris, Florida Atlantic University, Department of Computer and Electrical Engineering and Computer Science, College of Engineering and Computer Science
Abstract/Description: The objective of this dissertation work is the development of a solid theoretical and algorithmic framework for three of the most important aspects of autonomous/artificialintelligence (AI) systems, namely data quality assurance, localization, and communications. In the era of AI and machine learning (ML), data reign supreme. During learning tasks, we need to ensure that the training data set is correct and complete. During operation, faulty data need to be discovered and dealt with to...
Show moreThe objective of this dissertation work is the development of a solid theoretical and algorithmic framework for three of the most important aspects of autonomous/artificialintelligence (AI) systems, namely data quality assurance, localization, and communications. In the era of AI and machine learning (ML), data reign supreme. During learning tasks, we need to ensure that the training data set is correct and complete. During operation, faulty data need to be discovered and dealt with to protect from -potentially catastrophic- system failures. With our research in data quality assurance, we develop new mathematical theory and algorithms for outlier-resistant decomposition of high-dimensional matrices (tensors) based on L1-norm principal-component analysis (PCA). L1-norm PCA has been proven to be resistant to irregular data-points and will drive critical real-world AI learning and autonomous systems operations in the future. At the same time, one of the most important tasks of autonomous systems is self-localization. In GPS-deprived environments, localization becomes a fundamental technical problem. State-of-the-art solutions frequently utilize power-hungry or expensive architectures, making them difficult to deploy. In this dissertation work, we develop and implement a robust, variable-precision localization technique for autonomous systems based on the direction-of-arrival (DoA) estimation theory, which is cost and power-efficient. Finally, communication between autonomous systems is paramount for mission success in many applications. In the era of 5G and beyond, smart spectrum utilization is key.. In this work, we develop physical (PHY) and medium-access-control (MAC) layer techniques that autonomously optimize spectrum usage and minimizes intra and internetwork interference.
Show less
Date Issued: 2020
PURL: http://purl.flvc.org/fau/fd/FA00013617
Subject Headings: Artificial intelligence, Machine learning, Tensor algebra
Format: Document (PDF)

Title: Polynomials that are integer valued on the image of an integer-valued polynomial.
Creator: Marshall, Mario V., Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: Let D be an integral domain and f a polynomial that is integer-valued on D. We prove that Int(f(D);D) has the Skolem Property and give a description of its spectrum. For certain discrete valuation domains we give a basis for the ring of integer-valued even polynomials. For these discrete valuation domains, we also give a series expansion of continuous integer-valued functions.
Date Issued: 2009
PURL: http://purl.flvc.org/FAU/216411
Subject Headings: Polynomials, Ring of integers, Ideals (Algebra)
Format: Document (PDF)

Title: Maximally Prüfer rings.
Creator: Sharma, Madhav, Klingler, Lee, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
Abstract/Description: In this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong...
Show moreIn this dissertation, we consider six Prufer-like conditions on acommutative ring R. These conditions form a hierarchy. Being a Prufer ring is not a local property: a Prufer ring may not remain a Prufer ring when localized at a prime or maximal ideal. We introduce a seventh condition based on this fact and extend the hierarchy. All the conditions of the hierarchy become equivalent in the case of a domain, namely a Prufer domain. We also seek the relationship of the hierarchy with strong Prufer rings.
Show less
Date Issued: 2015
PURL: http://purl.flvc.org/fau/fd/FA00004465, http://purl.flvc.org/fau/fd/FA00004465
Subject Headings: Approximation theory, Commutative algebra, Commutative rings, Geometry, Algebraic, Ideals (Algebra), Mathematical analysis, Prüfer rings, Rings (Algebra), Rings of integers
Format: Document (PDF)

Title: Characterization of optimal normal bases.
Creator: Munoz-Connolly, Leonela, Florida Atlantic University, Mullin, Ronald C., Hoffman, Frederick
Abstract/Description: Recent interest in cryptographic systems has generated many mathematical results involving computations in finite fields. In particular, it is known that the use of optimal normal bases significantly reduces the complexity of computations in certain finite fields. This thesis examines three specific aspects of optimal normal bases. First, the effect of optimal normal bases on computations in finite fields is analyzed. Second, the known constructions of optimal normal bases are presented....
Show moreRecent interest in cryptographic systems has generated many mathematical results involving computations in finite fields. In particular, it is known that the use of optimal normal bases significantly reduces the complexity of computations in certain finite fields. This thesis examines three specific aspects of optimal normal bases. First, the effect of optimal normal bases on computations in finite fields is analyzed. Second, the known constructions of optimal normal bases are presented. Finally, the generators of optimal normal bases are discussed in terms of their order in the field.
Show less
Date Issued: 2000
PURL: http://purl.flvc.org/fcla/dt/15755
Subject Headings: Finite fields (Algebra), Normal basis theorem
Format: Document (PDF)

Title: EFFECTIVENESS OF THE USE OF BEHAVIORAL OBJECTIVES WITH AND WITHOUT STUDENT SELF-EVALUATION TESTS IN THE TEACHING OF INTERMEDIATE ALGEBRA AT THE COMMUNITY COLLEGE.
Creator: EVERETT, EUNICE FLEMING., Florida Atlantic University, Cook, Joseph B.
Abstract/Description: The literature reveals some studies dealing with behavioral objectives, but few of these concern the community college. Almost no research has dealt directly with student self-evaluation testing. The purpose of this study was to determine whether the use of behavioral objectives with and without student self-evaluation testing could improve achievement and reduce attrition in Intermediate Algebra at the community college. Three Intermediate Algebra sections at Broward Community College, Ft....
Show moreThe literature reveals some studies dealing with behavioral objectives, but few of these concern the community college. Almost no research has dealt directly with student self-evaluation testing. The purpose of this study was to determine whether the use of behavioral objectives with and without student self-evaluation testing could improve achievement and reduce attrition in Intermediate Algebra at the community college. Three Intermediate Algebra sections at Broward Community College, Ft. Lauderdale, were each randomly subdivided into two classes. The investigator and a colleague each taught three classes, each class by a different instructional method. The control method LR involved traditional lecture and test review. In the experimental treatment LOR, references were made to stated lists of behavioral objectives during the lectures and review sessions. Treatment LOS was identical to LOR, except that review was replaced by self-evaluation testing. Students returned the self-evaluation tests after keying them and noting the objectives missed. A comprehensive pretest was administered the first class meeting. This same test served as a posttest and course final examination. Six unit tests were administered during the term. Student achievement was measured by the raw posttest score (A(,1)) and by a composite score of unit test and posttest percentages (A(,2)). Seven research hypotheses relating to the independent variables instructional method, instructor, and sex, and their interactions, were tested for both measures. Separate analyses of covariance with the covariates age and pretest score were performed to test the seven hypotheses for A(,1) and A(,2). No significant differences were found for A(,1). Sex, however, was found to be significant in affecting A(,2), F (1, 81) = 5.150, p (LESSTHEQ) .026, with females achieving higher scores than males. Differences in A(,2) due to method were near significance, F (2, 81) = 2.928, p (LESSTHEQ) .059. The mean A(,2) score for method LR was 1.39 above that of LOR and 6.99 above that of LOS. The analyses of covariance indicated that pretest scores did significantly affect both A(,1) and A(,2), p (LESSTHEQ) .001. Six research hypotheses tested the effects of method, instructor, sex, method and instructor acting together, method and sex acting together, and course time interval upon withdrawal rate, WR. Chi-square tests were applied to the withdrawal data. Withdrawal rate varied significantly with respect to sex at the .05 level; 56.3% of the males withdrew; 41.1% of the females withdrew. Method and sex acting together were found to affect WR. Females withdrew significantly less than males within method LR, (chi)('2)(1) = 8.978, p (LESSTHEQ) .01. Finally, 25.5% of the students taking the pretest withdrew between Unit Tests 1 and 3, prior to the completion of the review of Elementary Algebra. It was concluded that for Intermediate Algebra, composite scores are better measures of achievement than single posttest scores, that pretest scores can be used as predictors of achievement, that female students are more persistent and achieve better than males, and that students tend to withdraw during the review units of the course. Further, the use of behavioral objectives did not significantly affect student achievement in lecture-taught classes. Self-evaluation testing had a negative effect on achievement--perhaps due to anxiety resulting from the testing format. Research needs to further explore the use of self-evaluation testing as a learning tool. The causes of heavy attrition in Intermediate Algebra, particularly the attrition of males, need to be found. Also, more research is necessary to verify the usefulness of pretest scores as predictors and composite scores as measures of achievement in Intermediate Algebra.
Show less
Date Issued: 1980
PURL: http://purl.flvc.org/fcla/dt/11770
Subject Headings: Algebra--Study and teaching (Higher)
Format: Document (PDF)

Title: A comparison of a special purpose processor with a general purpose processor and a numerical approach in generating helicopter dynamics equations.
Creator: Ravichandran, S., Florida Atlantic University, Gaonkar, Gopal H., College of Engineering and Computer Science, Department of Ocean and Mechanical Engineering
Abstract/Description: Presently three schemes are used to generate the governing equations of motion. These schemes are: (1) general purpose processors such as REDUCE, MACSYMA and MAPLE, (2) a special purpose symbolic processor DEHIM--Dynamic Equations for Helicopter Interpretive Models and (3) completely numerical approaches such as AGEM--Automatic Generation of Equations of Motion. With REDUCE as a representative multipurpose processor in scheme 1, comparative aspects of these three schemes have been studied by...
Show morePresently three schemes are used to generate the governing equations of motion. These schemes are: (1) general purpose processors such as REDUCE, MACSYMA and MAPLE, (2) a special purpose symbolic processor DEHIM--Dynamic Equations for Helicopter Interpretive Models and (3) completely numerical approaches such as AGEM--Automatic Generation of Equations of Motion. With REDUCE as a representative multipurpose processor in scheme 1, comparative aspects of these three schemes have been studied by applying them to the same set of problems. These problems range from a linear model of a single blade with one degree of freedom to a mildly nonlinear three-bladed rotor model with several degrees of freedom. The derivation process includes the nonlinear equations and the perturbed linear equations about a user-supplied equilibrium state in a rotating frame and then the multiblade equations, which represent transformation into a nonrotating frame using multiblade coordinates. (Abstract shortened with permission of author.)
Show less
Date Issued: 1989
PURL: http://purl.flvc.org/fcla/dt/14517
Subject Headings: Algebra--Computer programs, Helicopters--Dynamics
Format: Document (PDF)

Title: A computation of the Hall coefficient g(q)[('6,4,2)(,42)(,4,2)].
Creator: Anez, Myriam T., Florida Atlantic University, Schmidmeier, Markus
Abstract/Description: Let L be a uniserial ring of length n, with maximal ideal r , and finite residue field Λ/ r . We consider Λ-modules which possess a finite composition series. We note that a Λ-module has the form B ≅ ⨁i=1m Λ/ rli , where the type of B is the partition l = ( l1,&ldots;,lm ) denoted by t(B). For Λ-modules A, B, C with t(A) = m , t(B) = l , t(C) = n , if A ⊆ B, and B/A ≅ C, we define GBAC = |{U ⊆ B : U ≅ A and B/U ≅ C}|. We show that GBAC = MonoA,B,C Aut A = | S (A, B, C)/∼| = glmn (q),...
Show moreLet L be a uniserial ring of length n, with maximal ideal r , and finite residue field Λ/ r . We consider Λ-modules which possess a finite composition series. We note that a Λ-module has the form B ≅ ⨁i=1m Λ/ rli , where the type of B is the partition l = ( l1,&ldots;,lm ) denoted by t(B). For Λ-modules A, B, C with t(A) = m , t(B) = l , t(C) = n , if A ⊆ B, and B/A ≅ C, we define GBAC = |{U ⊆ B : U ≅ A and B/U ≅ C}|. We show that GBAC = MonoA,B,C Aut A = | S (A, B, C)/∼| = glmn (q), where |Λ/ r | = q, and the last equality comes from evaluating the Hall polynomial glmn (t) ∈ Z [t] at q, as stated in Hall's Theorem. We note that GBAC make up the coefficients of the Hall algebra. We provide a proof that the Hall algebra is a commutative and associative ring. Using the property of associativity of the Hall algebra and I. G. MacDonald's formula: glb1l =qnl -nb-n 1li≥ 1l'i -b'i,b' i-l'i+1 q-1 we develop a procedure to generate arbitrary Hall polynomials and we compute g6,4,2 4,24,2 (q).
Show less
Date Issued: 2005
PURL: http://purl.flvc.org/fcla/dt/13289
Subject Headings: Mathematical statistics, Algebra, Abstract, Abelian groups
Format: Document (PDF)

Algebra--Study and teaching (Higher) (7)	+ -
Abelian groups (5)	+ -
Algebra, Abstract (5)	+ -
Ideals (Algebra) (5)	+ -
Algebraic number theory (4)	+ -

Finite fields (Algebra) (4)	+ -
Polynomials (4)	+ -
Categories (Mathematics) (3)	+ -
Commutative algebra (3)	+ -
Commutative rings (3)	+ -
Curves, Algebraic (3)	+ -
Finite groups (3)	+ -
Linear algebraic groups (3)	+ -
Mathematical analysis (3)	+ -
Mathematical physics (3)	+ -
Modules (Algebra) (3)	+ -
Rings (Algebra) (3)	+ -
Rings of integers (3)	+ -
Algebra (2)	+ -
Algebra, Homological (2)	+ -
Artificial intelligence (2)	+ -
Combinatorial designs and configurations (2)	+ -
Combinatorial group theory (2)	+ -
Computer-assisted instruction (2)	+ -
Cryptography (2)	+ -
Data encryption (Computer science) (2)	+ -
Indecomposable modules (2)	+ -
Lie groups (2)	+ -
Mathematical optimization (2)	+ -
Mathematical recreations (2)	+ -

Florida Atlantic University (32)	+ -
Charles E. Schmidt College of Science (21)	+ -
Department of Mathematical Sciences (21)	+ -
Klingler, Lee (6)	+ -
Burgess, Ernest E. (2)	+ -

College of Engineering and Computer Science (2)	+ -
Mullin, Ronald C. (2)	+ -
Schmidmeier, Markus (2)	+ -
Amento, Brittanney Jaclyn (1)	+ -
Anez, Myriam T. (1)	+ -
Ay, Basak. (1)	+ -
BASTIDA, VICKI C. (1)	+ -
Barella, Michelle Elizabeth. (1)	+ -
Barney, Zalmond C. (1)	+ -
Bastida, Julio R. (1)	+ -
Boynton, Jason (1)	+ -
Bozovic, Vladimir. (1)	+ -
Brumbaugh, Douglas K. (1)	+ -
Bulj, Djordje. (1)	+ -
CHINN, BEVERLY DUKE (1)	+ -
Caliskan, Cafer. (1)	+ -
Chiorescu, Marcela (1)	+ -
College of Education (1)	+ -
Cook, Joseph B. (1)	+ -
Cox, Gregg Clayton (1)	+ -
DIEM, DENNIS CHARLTON. (1)	+ -
Decker, Larry E. (1)	+ -
Department of Computer and Electrical Engineering and Computer Science (1)	+ -
Department of Curriculum, Culture, and Educational Inquiry (1)	+ -
Department of Ocean and Mechanical Engineering (1)	+ -

Search In

Pages

Pages

Sort Results By:

Narrow results by:

Collection

Topical Subject

Genre

Type of Resource

Language

Creator

Format

Owner