Current Search: Algebra (x)
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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 CayleyDickson 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 CayleyDickson 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 CayleyDickson algebras, and give a selfcontained 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 CayleyDickson 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 CayleyDickson algebras, and give a selfcontained 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 CayleyDickson algebra for which (u, w, v) = 0 for all w, then u and v generate a 2dimensional 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 CayleyDickson 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 CayleyDickson algebra A4 are also analyzed in detail.
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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 NONCOMMUTATIVE ALGEBRAS.

Creator

ELSTNER, EILERT., Florida Atlantic University

Abstract/Description

This thesis was motivated by the idea to generalize Spitzer's identity to the noncommutative 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 noncommutative Spitzer identity is derived and applied to generalized shift operators. As another application we give noncommutative analogs of some...
Show moreThis thesis was motivated by the idea to generalize Spitzer's identity to the noncommutative 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 noncommutative Spitzer identity is derived and applied to generalized shift operators. As another application we give noncommutative analogs of some formulas of Euler.
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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 NonNoetherian 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 NonNoetherian 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 quasicompact 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 nonNoetherian setting.
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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.
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Date Issued

1973

PURL

http://purl.flvc.org/fcla/dt/13582

Subject Headings

Algebraic fields, Algebraic number theory

Format

Document (PDF)


Title

AuslanderReiten 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 AuslanderReiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute AuslanderReiten 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 RingelTachikawa Theorem which states that for an artinian ring R of finite...
Show moreIn this dissertation, we will investigate aspects of AuslanderReiten theory adapted to the setting of systems of submodule embeddings. Using this theory, we can compute AuslanderReiten 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 RingelTachikawa Theorem which states that for an artinian ring R of finite representation type, each Rmodule is a direct sum of finitelength indecomposable Rmodules. In cases where this applies, the indecomposable objects obtained in the AuslanderReiten 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 CalabiYau dimension of such a category.
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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 3nets.

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 3nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3nets 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 3nets realizing a finite group. The known infinite family, due to Yuzvinsky, arised from plane cubics and comprises 3nets realizing cyclic and direct products of two cyclic groups. Another known infinite family, due to Pereira and Yuzvinsky, comprises 3nets 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.
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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.
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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 pointline 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 pointline 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 angleconstrained 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 anglerigid graphs and their properties.
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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 Rmodule 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 13 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 Rmodule 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 13 the UDI property for reduced Noetherian rings is characterized. In Chapter 4 it is shown that overrings of onedimensional reduced commutative Noetherian rings with the UDI property have the UDI property, also. In Chapter 5 we show that the UDI property implies the KrullSchmidt property for direct sums of torsionfree rank one modules for a reduced local commutative Noetherian onedimensional ring R.
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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 integervalued 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 integervalued 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 integervalued 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, onedimensional, analytically irreducible, with finite residue field.
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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 zerodimensional extensions.

Creator

Chiorescu, Marcela, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences

Abstract/Description

The structure of minimal zerodimensional 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 onetoone correspondence between isomorphism classes of minimal zerodimensional extensions of R and sets M, where the elements of M are...
Show moreThe structure of minimal zerodimensional 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 onetoone correspondence between isomorphism classes of minimal zerodimensional 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 zerodimensional extensions of general ZPIrings.
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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 MULTIDOMAIN 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 outlierresistant decomposition of highdimensional matrices (tensors) based on L1norm principalcomponent analysis (PCA). L1norm PCA has been proven to be resistant to irregular datapoints and will drive critical realworld AI learning and autonomous systems operations in the future. At the same time, one of the most important tasks of autonomous systems is selflocalization. In GPSdeprived environments, localization becomes a fundamental technical problem. Stateoftheart solutions frequently utilize powerhungry or expensive architectures, making them difficult to deploy. In this dissertation work, we develop and implement a robust, variableprecision localization technique for autonomous systems based on the directionofarrival (DoA) estimation theory, which is cost and powerefficient. 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 mediumaccesscontrol (MAC) layer techniques that autonomously optimize spectrum usage and minimizes intra and internetwork interference.
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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 integervalued 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 integervalued 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 integervalued even polynomials. For these discrete valuation domains, we also give a series expansion of continuous integervalued 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 Pruferlike 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 Pruferlike 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.
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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

MunozConnolly, 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.
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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 SELFEVALUATION 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 selfevaluation testing. The purpose of this study was to determine whether the use of behavioral objectives with and without student selfevaluation 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 selfevaluation testing. The purpose of this study was to determine whether the use of behavioral objectives with and without student selfevaluation 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 selfevaluation testing. Students returned the selfevaluation 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. Chisquare 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 lecturetaught classes. Selfevaluation testing had a negative effect on achievementperhaps due to anxiety resulting from the testing format. Research needs to further explore the use of selfevaluation 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.
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Date Issued

1980

PURL

http://purl.flvc.org/fcla/dt/11770

Subject Headings

AlgebraStudy 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 DEHIMDynamic Equations for Helicopter Interpretive Models and (3) completely numerical approaches such as AGEMAutomatic 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 DEHIMDynamic Equations for Helicopter Interpretive Models and (3) completely numerical approaches such as AGEMAutomatic 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 threebladed rotor model with several degrees of freedom. The derivation process includes the nonlinear equations and the perturbed linear equations about a usersupplied 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.)
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Date Issued

1989

PURL

http://purl.flvc.org/fcla/dt/14517

Subject Headings

AlgebraComputer programs, HelicoptersDynamics

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 Λmodules which possess a finite composition series. We note that a Λmodule 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 Λmodules 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 Λmodules which possess a finite composition series. We note that a Λmodule 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 Λmodules 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 nbn 1li≥ 1l'i b'i,b' il'i+1 q1 we develop a procedure to generate arbitrary Hall polynomials and we compute g6,4,2 4,24,2 (q).
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Date Issued

2005

PURL

http://purl.flvc.org/fcla/dt/13289

Subject Headings

Mathematical statistics, Algebra, Abstract, Abelian groups

Format

Document (PDF)
Pages