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Document includes a bibliography listing post doctoral research performed at the Center for Mathematics System Theory at the University of Florida. Additional keywords: Linear systems; Nonlinear realization theory; Applied algebraic geometry.

As an attempt to confirm the view that the relationships between certain classroom process variables and student achievement are curvilinear, first grade reading and mathematics data from the Stallings and Kaskowitz (1974) Project Follow Through Classroom Observation Evaluation were reanalyzed using orthogonal polynomial regression methods. Seventy-five classroom process variables were selected from Stallings and Kaskowitz data and entered into poly-nomial regression analyses. Thirty-two of ninety-five relationships tested were found to be nonlinear. (This, of course, is well beyond chance.) Fourteen of the nonlinear functions were quadratic in nature, eleven were cubic, and seven were quartic. Fifteen of these functions were related to mathematics achievement, and seventeen were related to reading achievement. These results generally support the view that relationships between some classroom process variables and student achievement are probably curvilinear. In turn, this finding seems to raise a question about recommendations for instructional improvement that are made based solely on linear analyses of process-product study data. This finding also provides additional support for the argument to employ both linear and nonlinear analyses in classroom process-product research. (Author/MP)

Includes bibliography

Includes bibliography

Includes bibliography

Includes bibliography

Includes bibliography

We analyze 5 years of student records at the University of Oregon to estimate the probability of success (as defined by superior undergraduate record; sufficient for admission to graduate school) in Physics and Mathematics as a function of SAT-M score. We find evidence of a nonlinear threshold: below SAT-M score of roughly 600, the probability of success is very low. Interestingly, no similar threshold exists in other majors, such as Sociology, History, English or Biology, whether on SAT combined, SAT-R or SAT-M. Our findings have significant implications for the demographic makeup of graduate populations in mathematically intensive subjects, given the current distribution of SAT-M scores.

We analyze 5 years of student records at the University of Oregon to estimate the probability of success (as defined by superior undergraduate record; sufficient for admission to graduate school) in Physics and Mathematics as a function of SAT-M score. We find evidence of a nonlinear threshold: below SAT-M score of roughly 600, the probability of success is very low. Interestingly, no similar threshold exists in other majors, such as Sociology, History, English or Biology, whether on SAT combined, SAT-R or SAT-M. Our findings have significant implications for the demographic makeup of graduate populations in mathematically intensive subjects, given the current distribution of SAT-M scores.

Mathematics 10B, 001 - Spring 2014 Creative Commons 3.0: Attribution-NonCommercial-NoDerivs

This report gives a brief discussion of the different problem areas under which research papers have been published during the term of the grant as well as a short description of the main results. In this research finite element methods were applied to a simple model of shear band formation. They were also used for elliptic and parabolic problems that arise in optimal control and for equations that simulate phase transitions. These finite element schemes were analyzed and implemented. Also, studies of space-time schemes where the Galerkin technique is used to discretize time as well as space were the focus of several papers. Finally, a last paper contains a thorough analysis of an adaptive time discretization technique.

This grant provided partial support for IMA academic year programs on nonlinear waves (1988-89), Dynamical Systems (1989-90), and Phase Transitions (1990-91). Each program involved approximately 700 researchers. A total of approximately 400 preprints and approximately 25 proceedings volumes of research results were produced. Of particular note were the 8 one week workshops supported by ARO which focused attention on special subject areas in these fields which are of particular interest at the present time.

Work which involved both error estimates and computations on a time dependent problem modeling the deformations of a viscoelastic solid was completed during the term of this report. Also two algorithm were derived and implemented for the Kdv equation with wavemaker boundary conditions.

Special emphasis was given to the following areas: (1) Finite-dimensional linear system theory by algebraic methods: linear systems over a ring, algebraic methods in the study of feedback, polynomial methods for the study of linear systems, F mod G invariant subspaces; (2) Infinite-dimensional linear systems: realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory: basic properties of polynomial (discrete-time) systems and their realization theory; and (4) Identification problems in economics: study of econometric model building.

Special emphasis was given to the following areas: (1) Finite-dimensional linear system theory by algebraic methods: linear systems over a ring, algebraic methods in the study of feedback, polynomial methods for the study of linear systems, F mod G invariant subspaces; (2) Infinite-dimensional linear systems: realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory: basic properties of polynomial (discrete-time) systems and their realization theory; and (4) Identification problems in economics: study of econometric model building.

Special emphasis was given to the following areas: (1) Finite-dimensional linear system theory by algebraic methods: linear systems over a ring, algebraic methods in the study of feedback, polynomial methods for the study of linear systems, F mod G invariant subspaces; (2) Infinite-dimensional linear systems: realization theory of infinite-dimensional linear systems; (3) Nonlinear system theory: basic properties of polynomial (discrete-time) systems and their realization theory; and (4) Identification problems in economics: study of econometric model building.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

The purpose of this study is to equate Trends in International Mathematics and Science Study (TIMSS) mathematics subtest scores obtained from TIMSS 2011 to scores obtained from TIMSS 2007 form with different nonlinear observed score equating methods under Non-Equivalent Anchor Test (NEAT) design where common items are used to link two or more test forms. The ultimate goal is to determine whether different forms of mathematics tests that administered in different years with anchor (common) items caused any inequalities with respect to students. In addition, results obtained from chained and frequency estimation based on equipercentile equating methods were compared to four different methods (Tucker, Levine, Braun-Holland and chained) based on a new nonlinear equating approach called circle-arc equating in order to see which method is the most appropriate for equating these forms. The results of different nonlinear equating methods were compared with respect to Root Mean Squared Error (RMSE) index, mean of bootstrap standard errors (MBSE) and mean of bootstrap bias. Results indicates that TIMSS 2007 mathematics tests were easier than TIMSS 2011 mathematics across the score scale which indicates that results were biased against to students participated to TIMSS 2007. Moreover, equating methods based on nonlinear circle-arc equating outperformed the equipercentile equating methods and presmoothing decreased both standard error and bias associated with each method.

Includes index

Includes index

Projection from a Business Mathematics course (2005 - 6) by KIT

Lecture from a Business Mathematics course (2005 - 6) by KIT

Introductive backgrounds of a new mathematical physics discipline - Quantum Mathematics - are discussed and analyzed both from historical and analytical points of view. The magic properties of the second quantization method, invented by V. Fock in 1932, are demonstrated, and an impressive application to the nonlinear dynamical systems theory is considered.

Lecture from a Business Mathematics course (2005 - 6) by KIT

Projection from a Business Mathematics course (2005 - 6) by KIT