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This article aims to show the mathematical contexts out of which emerged Solow's 1957 article "Technical Change and the Aggregate Production Function." In particular, it seeks to provide some understanding of its most striking feature, namely, the highly aggregate level on which technical change is discussed and the simple way in which it is represented. The approach is similar to Weintraub's (1991) contextualization of Samuelson's Foundations of Economic Analysis (1947), but it will map out the two mathematical contexts in which Solow's 1957 article can be located. Samuelson's concepts of stability provided Solow the tools for the aggregation of technical change. However, Samuelson's concepts were defined in relation to static equilibrium and not to growth. To arrive at his 1957 representation of technical change, Solow successfully applied P. H. Leslie's concepts and tools of population mathematics. The main mathematical concepts around which this development is described are eigenvalue and eigenvector. It is by the use of these two concepts that aggregation of input-output tables was made feasible.

The domain of strategic interaction includes all those decision tasks in which the outcome of a decision depends on the decisions taken by a plurality of individuals, so that each individual must try to devise the most likely moves of the others in order to pursue the best course of action, knowing that all other actors are engaged in the same type of strategic thinking. Problems of strategic interaction in economics have been traditionally modelled using the formal language of game theory, first introduced by von Neumann and Morgenstern's 1944 seminal book Theory of Games and Economic Behavior. Game theory subsequently developed into a highly formal mathematical language used to describe the behavior of hyperrational individuals in strategic contexts. Although born as a branch of applied mathematics and originally developed with the intention of making it the science of military conflict, its diffusion within economics has been extremely rapid, and related fields in the social sciences have recently begun to apply it to model behavior in a variety of social settings.

Katz and King have previously developed a model for predicting or explaining aggregate electoral results in multiparty democracies. Their model is, in principle, analogous to what least-squares regression provides American political researchers in that two-party system. Katz and King applied their model to three-party elections in England and revealed a variety of new features of incumbency advantage and sources of party support. Although the mathematics of their statistical model covers any number of political parties, it is computationally demanding, and hence slow and numerically imprecise, with more than three parties. In this paper we produce an approximate method that works in practice with many parties without making too many theoretical compromises. Our approach is to treat the problem as one of missing data. This allows us to use a modification of the fast EMis algorithm of King, Honaker, Joseph, and Scheve and to provide easy-to-use software, while retaining the attractive features of the Katz and King model, such as thetdistribution and explicit models for uncontested seats.

The hypothesis that engineering graduates are best suited for junior officer positions aboard increasingly sophisticated surface and submarine warships is tested empirically for a subset of 1,560 U.S. Naval Academy graduates from the classes 1976-80. Following the guidelines set by Admiral Rickover, policymakers presume the best preparation for leadership positions is provided by college majors that emphasize mathematics, sciences, and (especially) engineering. The results of the study, based on advanced multivariate regression techniques, fail to support this common notion. For the subset of USNA graduates, neither academic major selection nor achievement within defined academic class groupings is found to be statistically related to performance and retention of junior officers at the completion of their initial tour of duty. The results are applicable to both the conventional surface and nuclear navies for the subset of academy graduates. The study suggests the approach be applied to the Officer Candidate School and the Reserve Officers' Training Corps commissioned officers for a more general test of the Rickover hypothesis.

In the last decade, more and more political scientists have speculated on the possible applications of mathematical analysis to political phenomena. It is the position of this paper that such discussion, when in the abstract, serves little purpose, for the question of whether or not quantitative techniques can fruitfully be so applied is essentially an empirical one and can only be resolved by experiment. Yet even a specifically experimental approach becomes challengeable if it can be shown to misunderstand and hence misemploy otherwise sound techniques. The claim to have solved problems whose mathematical features have not, in fact, been comprehended seems especially harmful in a field where the application of mathematics is as yet in its infancy, and this not only because minor impurities at the base of a growing framework may assume major proportions at its apex, but because exposure of error may breed unjustified disenchantment or give solace to those who prefer a casual, imprecise impressionism in the social sciences.

Ordinary differential equations (ODE) constitute a significant portion of any engineering or STEM curriculum. However, students often question the relevance to their professional lives of the mathematics they learn ODE courses. This is largely due to the fact that they rarely see real and credible connections to real world phenomena and situations in the math classroom. On the other hand, organizations like the European Society for Engineering Education (SEFI), the Mathematical Association of America (MAA), the American Mathematical Society (AMS), and the Society for Industrial and Applied Mathematics (SIAM) involved with the education of engineering professionals, for decades have regarded modeling as an essential skill to foster in students of engineering and related professions, and have called for including modeling in university mathematics courses. Founded in 2013 by Brian Winkel, Emeritus Professorof Mathematics at the United States Military Academy - West Point, SIMIODE is an open community of teachers and learners committed to a modeling first approach to teaching differential equations. This pedagogical innovation is starting to be known and used in several Latin-American universities, though not yet in Panama. This article informs of a mathematical modeling workshop conducted by Dr. Winkel at the UTP in February 2020. The workshop was directed to UTP professors who regularly teach the ordinary differential equations course, in the hopes of motivating them to incorporate mathematical modeling in their teaching. Mathematics professors from other higher ed institutions, high school teachers, as well as graduate students who needed to hone their mathematical modeling skills to carry out their research, also participated. Subsequently, several teachers implemented modeling scenarios with their students during the fall semester of the 2020-2021 school year. Student response to this pedagogical innovation is briefly described. ; Las ecuaciones diferenciales ordinarias (EDO) constituyen una parte significativa de cualquier currículo de ingeniería o CTIM. No obstante, los estudiantes a menudo cuestionan la relevancia para su vida profesional de las matemáticas que aprenden en los cursos de EDO. En buena medida esto se debe a que pocas veces se establecen nexos reales y creíbles entre los conceptos estudiados en clase y fenómenos y situaciones de la vida real. Por otra parte, organizaciones vinculadas a la formación de profesionales de la ingeniería, como la Sociedad Europea de Formación de Ingenieros (SEFI), la Asociación Matemática de América (MAA), la Sociedad Matemática Americana (AMS), y la Sociedad para Matemática Aplicada e Industrial (SIAM) por décadas han destacado la capacidad de modelación como una competencia esencial a desarrollar en los estudiantes de ingeniería y carreras afines, y han hecho un llamado para incluir la modelación en los cursos básicos de matemáticas a nivel de pregrado. SIMIODE es una comunidad abierta de enseñantes y aprendientes para enseñar y aprender sobre ecuaciones diferenciales a nivel de pregrado fundada en el 2013 por Brian Winkel, profesor emérito del United States Military Academy, West Point. La propuesta pedagógica de SIMIODE, denominada modelado primero, ya empieza a conocerse y ponerse práctica en algunas universidades latinoamericanas, aunque todavía no en Panamá. Este artículo da cuenta de un taller de modelación matemática realizado por el Dr. Winkel en la UTP en febrero de 2020. El taller estaba dirigido a docentes de la UTP que regularmente imparten el curso de ecuaciones diferenciales ordinarias, con el objetivo de motivarlos a incorporar la modelación matemática en su quehacer docente. Participaron también profesores de matemáticas de otras instituciones de educación superior, docentes de secundaria, así como estudiantes de posgrado que requerían afinar sus habilidades de modelación matemática para sus trabajos de investigación. Posteriormente, varios docentes implementaron escenarios de modelación con sus estudiantes durante el primer semestre del año académico 2020-2021. Se describe brevemente la respuesta de los estudiantes a esta innovación pedagógica.

Ordinary differential equations (ODE) constitute a significant portion of any engineering or STEM curriculum. However, students often question the relevance to their professional lives of the mathematics they learn ODE courses. This is largely due to the fact that they rarely see real and credible connections to real world phenomena and situations in the math classroom. On the other hand, organizations like the European Society for Engineering Education (SEFI), the Mathematical Association of America (MAA), the American Mathematical Society (AMS), and the Society for Industrial and Applied Mathematics (SIAM) involved with the education of engineering professionals, for decades have regarded modeling as an essential skill to foster in students of engineering and related professions, and have called for including modeling in university mathematics courses. Founded in 2013 by Brian Winkel, Emeritus Professorof Mathematics at the United States Military Academy - West Point, SIMIODE is an open community of teachers and learners committed to a modeling first approach to teaching differential equations. This pedagogical innovation is starting to be known and used in several Latin-American universities, though not yet in Panama. This article informs of a mathematical modeling workshop conducted by Dr. Winkel at the UTP in February 2020. The workshop was directed to UTP professors who regularly teach the ordinary differential equations course, in the hopes of motivating them to incorporate mathematical modeling in their teaching. Mathematics professors from other higher ed institutions, high school teachers, as well as graduate students who needed to hone their mathematical modeling skills to carry out their research, also participated. Subsequently, several teachers implemented modeling scenarios with their students during the fall semester of the 2020-2021 school year. Student response to this pedagogical innovation is briefly described. ; Las ecuaciones diferenciales ordinarias (EDO) constituyen una parte significativa de cualquier currículo de ingeniería o CTIM. No obstante, los estudiantes a menudo cuestionan la relevancia para su vida profesional de las matemáticas que aprenden en los cursos de EDO. En buena medida esto se debe a que pocas veces se establecen nexos reales y creíbles entre los conceptos estudiados en clase y fenómenos y situaciones de la vida real. Por otra parte, organizaciones vinculadas a la formación de profesionales de la ingeniería, como la Sociedad Europea de Formación de Ingenieros (SEFI), la Asociación Matemática de América (MAA), la Sociedad Matemática Americana (AMS), y la Sociedad para Matemática Aplicada e Industrial (SIAM) por décadas han destacado la capacidad de modelación como una competencia esencial a desarrollar en los estudiantes de ingeniería y carreras afines, y han hecho un llamado para incluir la modelación en los cursos básicos de matemáticas a nivel de pregrado. SIMIODE es una comunidad abierta de enseñantes y aprendientes para enseñar y aprender sobre ecuaciones diferenciales a nivel de pregrado fundada en el 2013 por Brian Winkel, profesor emérito del United States Military Academy, West Point. La propuesta pedagógica de SIMIODE, denominada modelado primero, ya empieza a conocerse y ponerse práctica en algunas universidades latinoamericanas, aunque todavía no en Panamá. Este artículo da cuenta de un taller de modelación matemática realizado por el Dr. Winkel en la UTP en febrero de 2020. El taller estaba dirigido a docentes de la UTP que regularmente imparten el curso de ecuaciones diferenciales ordinarias, con el objetivo de motivarlos a incorporar la modelación matemática en su quehacer docente. Participaron también profesores de matemáticas de otras instituciones de educación superior, docentes de secundaria, así como estudiantes de posgrado que requerían afinar sus habilidades de modelación matemática para sus trabajos de investigación. Posteriormente, varios docentes implementaron escenarios de modelación con sus estudiantes durante el primer semestre del año académico 2020-2021. Se describe brevemente la respuesta de los estudiantes a esta innovación pedagógica.

"This innovative book proposes new methodologies for the measurement of entrepreneurship by applying techniques of demography, engineering, mathematics and statistics. Using the data from the Global Entrepreneurship Monitor (GEM), statistical demographic techniques are used for the evaluation of data quality and for the estimation of key indicators, a new methodology for the calculation of Specific Entrepreneurship Rates and Global Entrepreneurship Rate is proposed, at the same time the authors present artificial intelligence techniques such as Fuzzy Time Series to forecast data series of the entrepreneurial population. Finally, they present a case study of the implementation of Big Data in Entrepreneurship using GEM Data, that shows the latest technological trends for the management of data, in support of making more accurate decisions. Being a methodological book, the techniques presented can be applied to any data set in different areas. Readers will learn new methodologies of analysis and measurement of entrepreneurship using data from the Global Entrepreneurship Monitor. They will be able to access the experience of the authors through each of the applied cases in which the reader is taken by the hand both in the scientific method and in the methodology of construction of more accurate metrics in entrepreneurship or with less error. This book will be of value to students at an advanced level, academics, and researchers in the fields of Entrepreneurship, Business analytics and Research Methodology."

This revised edition presents the relevant aspects of transformational geometry, matrix algebra, and calculus to those who may be lacking the necessary mathematical foundations of applied multivariate analysis. It brings up-to-date many definitions of mathematical concepts and their operations. It also clearly defines the relevance of the exercises to concerns within the business community and the social and behavioral sciences. Readers gain a technical background for tackling applications-oriented multivariate texts and receive a geometric perspective for understanding multivariate methods. Mathematical Tools for Applied Multivariate Analysis, Revised Edition illustrates major concepts in matrix algebra, linear structures, and eigenstructures geometrically, numerically, and algebraically. The authors emphasize the applications of these techniques by discussing potential solutions to problems outlined early in the book. They also present small numerical examples of the various concepts. Key Features * Provides a technical base for tackling most applications-oriented multivariate texts * Presents a geometric perspective for aiding ones intuitive grasp of multivariate methods * Emphasizes technical terms current in the social and behavioral sciences, statistics, and mathematics * Can be used either as a stand-alone text or a supplement to a multivariate statistics textbook * Employs many pictures and diagrams to convey an intuitive perception of matrix algebra concepts * Toy problems provide a step-by-step approach to each model and matrix algebra concept * Provides solutions for all exercises

Mathematics and Physics are different research cultures. In comparison with
mathematicians, physicists in some cases try to simplify and to introduce new cultural context into conventional pure mathematics. Cross-cultural differences between these cultures can be essential and some attempts to do alternative mathematics in the physical academic context could be defined as the new fields of ethnomathematics. Einstein's Relativity as this kind of ethnomathematics is the first considered .

There is increasing pressure for STEM education to reform in the direction of student-centered learning approaches, active learning, interdisciplinarity, and data-driven evaluations and assessments of student learning. These requirements derive from the need for STEM education to facilitate economic development, national health, technological innovation, and appropriate demographic representation. These contingencies create the need and opportunity for the integration of applied linguistic expertise within STEM education. In this chapter, a senior project officer from a major funding instituti.

The Handbook of Simulation Optimizationpresents an overview of the state of the art of simulation optimization, providing a survey of the most well-established approaches for optimizing stochastic simulation models and a sampling of recent research advances in theory and methodology. Leading contributors cover such topics as discrete optimization via simulation, ranking and selection, efficient simulation budget allocation, random search methods, response surface methodology, stochastic gradient estimation, stochastic approximation, sample average approximation, stochastic constraints, variance reduction techniques, model-based stochastic search methods and Markov decision processes.This single volume should serve as a reference for those already in the field and as a means for those new to the field for understanding and applying the main approaches. The intended audience includes researchers, practitioners and graduate students in the business/engineering fields of operations research, management science, operations management and stochastic control, as well as in economics/finance and computer science. Dr. Michael C. Fu received his Ph.D. in applied mathematics from Harvard University and master's and bachelor's degrees in EECS and mathematics from MIT. Since 1989, he has been at the University of Maryland in the Robert H. Smith School of Business, where he is currently Ralph J. Tyser Professor of Management Science, with a joint appointment in the Institute for Systems Research (ISR) and an affiliate appointment in the Electrical and Computer Engineering Department, A. James Clark School of Engineering. At the University of Maryland, he was named a Distinguished Scholar-Teacher and received the ISR's Outstanding Systems Engineering Faculty Award and the Business School's Allen J. Krowe Award for Teaching Excellence. He served as the Stochastic Models and Simulation Department Editor of Management Science from 2006-2008, as Simulation Area Editor of Operations Research from 2000-2005 and on the Editorial Boards of the INFORMS Journal on Computing, Mathematics of Operations Research, Production and Operations Managementand IIE Transactions. He served as Program Chair of the 2011 Winter Simulation Conference and as Operations Research Program Director at the National Science Foundation from 2010-2012. His co-authored book, Conditional Monte Carlo: Gradient Estimation and Optimization Applications received the INFORMS College on Simulation Outstanding Publication Award. He also co-authored the research monograph Simulation-based Algorithms for Markov Decision Processesand co-edited the books Perspectives in Operations Research, Advances in Mathematical Financeand the 3rd edition of the Encyclopedia of Operations Research and Management Science. He is a Fellowof IEEE and the Institute of Operations Research and the Management Sciences (INFORMS).

Gymnasium as a school and as one of the levels in education has changed for decades both in the curriculum and in its duration. Nevertheless, the common goal in each period of Gymnasium education was and remains to provide students with the widest possible general education and to prepare them for further education at various universities of technical, social and natural sciences. In the last stage of socialism in Bosnia and Herzegovina, all high schools in their curriculum aimed to train students for one of the working professions so that each student after graduating from high school acquired a certain knowledge and could be employed in the sector for which educated. During that period, grammar schools were formally abolished. Instead, secondary administrative schools were most often formed, which were most similar to Gymnasiumin terms of their curriculum. In the present age, the gymnasium as a school exists with the fact that the curriculum is common to all first and second grades, while the third and fourth grades are divided into directions: mathematics-informatics, natural, social, linguistic and information-communication. Without going into the purpose of the existence of other directions, it should be emphasized that the mathematics-informatics direction aims to bring the students of the final grades of grammar school closer to technical and informatics universities, ie to acquaint them with technical and informatics. One of the key subjects at some technical colleges is descriptive geometry. These would primarily be the universities of architecture, civil engineering and mechanical engineering. In informal conversations between fourth graders regardless of direction and their teachers from time to time the topic is the subject of descriptive geometry. From the mentioned conversations, two mutually opposing hypotheses crystallized in terms of the importance of descriptive geometry, ie whether or not descriptive geometry should be introduced in all directions of Gymnasium. In order to determine which of these two hypotheses prevails, a generic / developmental method was applied, ie a survey was used as one of the research techniques. The survey was conducted in February 2020. A sample of 80 fourth-grade students from the "Muhsin Rizvić" Gymnasium in Kakanj and the "Visoko" Gymnasium in Visoko, who are not in the mathematics and computer science trend, was selected for the survey. As can be seen, the importance of descriptive geometry as a subject will be expressed by those students who do not have descriptive geometry as a subject according to the curriculum

Motivation: This article is a tribute to Johannes Boersma, amathematician who made an indelible impression upon all those who got to know him professionally. Yet, he never aimed to become a star among the stars. Indeed, only the relatively small group who knew him and interacted with him will be able to judge the extremely high level at which he was used to working. He deliberately kept himself out of the limelight. The joy of doing his kind ofmathematics sufficed for him. He also seemed to derive great pleasure from helping others who got stuck in their research and showing them ways on how to solve their mathematical problems. I was one of those. Below are testimonials written by some of the colleagues, peers and others who either greatly benefited from collaborating with him or were awed by the way he handled his particular brand of mathematics. The suggestion to write this tribute came from Professor Tony Rawlins of Brunel, a contributor to the special Wiener–Hopf issue (Vol. 59/4) for which this paper was originally planned. This is the kind of mathematics Boersma loved, along with the whole gamut of special functions and complex-function theory that many applied mathematicians now consider obsolete and superseded by numerics. How wrong they are, if only in view of the handling of singularities and the development of asymptotic constructs it affords! At a recent conference Prof. Rawlins spoke to me of his amazement that nothing of the kind seemed to have been done so far. Even so, the Mathematics Department in Eindhoven offered to organize a scientific conference on the occasion of Boersma's early retirement and he refused. Had he agreed, a book of symposium proceedings might have rendered this present paper superfluous. Although Boersma probably would have frowned upon the publication of a paper like this one, in which his person features so prominently, I believe it will serve a useful purpose. It may show what a life devoted to mathematics may look like, irrespective of career prospects and political in-fighting. Whatever career he may have had came naturally. It ended prematurely, since modern academic times and the emphasis it puts on funding had caught up with him. I start with a section on testimonials written by some of Boersma's colleagues, both in The Netherlands and outside it, who knew him and his work well. They will emphasize different aspects of his activities and persona. Clearly, there will be some duplication of views, but this is understandable and serves to emphasize those points. In a later section I will present my own views, imperfect as these may be. The growth of the scientist will be sketched and his contributions and collaborations will be put in a, hopefully, proper perspective.With only 6 weeks, the time I had for this was fairly short. But then, the Internet and e-mail communication spares one weeks and weeks in dusty library vaults. This contribution will be completed by an incomplete list of Boersma's publications.

The aim of the article is to analyse a number of short answer questions at the unified state examination (higher level) in. The article explores the possibility of solving these tasks by certain categories of pupils who have chosen mathematics examination of higher level. The following research methods were applied – statistical processing of the results of the Unified State Examination (USE), including the so-called "unsuccessful" graduates, dynamic analysis of interdependence between test failure rate and various task types. By "unsuccessful" graduates, the authors mean those examinees who, having scored enough to obtain a certificate of secondary general education, nevertheless did not overcome the threshold of set by the Ministry of Science and Higher Education of the Russian Federation for admission to subordinate higher educational institutions. The obtained data allows to conclude that lowering the above-mentioned score threshold is impractical, since relaxation in the requirements will open the gate to applicants unable to attain any academic achievement. Even in case of successful course completion graduates will not have sufficient competency to work, for example, in important areas of economy, in the field of high technology and, moreover, in the field of education, where any gaps in mathematical training is fraught with negative consequences. At the same time, there is a huge personnel shortage, especially in the periphery, where teachers' salary is several times lower than in the capital's schools. The current situation leads to increased staff turnover in the field of teacher education and a catastrophic reduction in Mathematics teachers able to teach this discipline in secondary schools at an advanced level. The article also emphasises the need to change the scale of conversion of primary USE scores into test scores based on the actual results of the 2022 exam in order to eliminate the competitive advantage of graduates of the previous two years, since the results of the USE are valid for three years.