Relevant bibliographies by topics / Group theory – Mathematics

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Group theory – Mathematics'

Author: Grafiati
Published: 4 June 2021
Last updated: 16 February 2022

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Journal articles on the topic "Group theory – Mathematics"

1

Huetinck, Linda. "Group Theory: It's a SNAP." Mathematics Teacher 89, no. 4 (April 1996): 342–46. http://dx.doi.org/10.5951/mt.89.4.0342.

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Martin Gardner has compared the concept of a mathematical group to the grin of the Cheshue Cat. “The body of the cat (algebra as traditionally taught) vanishes, leaving only an abstract grin. A grin implies something amusing. Perhaps we can make group theory less mysterious if we do not take it too seriously” (Gardner 1966). A game like “It's a SNAP” can be used to introduce mathematical groups and make them appear less mysterious. This mathematics manipulative allows students to play with the concepts of group theory and develop an understanding of modern algebra.
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Stonehewer, Stewart. "MATHEMATICAL WORKS I: GROUP THEORY." Bulletin of the London Mathematical Society 28, no. 2 (March 1996): 219–20. http://dx.doi.org/10.1112/blms/28.2.219.

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Pride, Stephen J. "CONTRIBUTIONS TO GROUP THEORY (Contemporary Mathematics, 33)." Bulletin of the London Mathematical Society 17, no. 6 (November 1985): 610–12. http://dx.doi.org/10.1112/blms/17.6.610.

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Gordon, Gary. "USING WALLPAPER GROUPS TO MOTIVATE GROUP THEORY." PRIMUS 6, no. 4 (January 1996): 355–65. http://dx.doi.org/10.1080/10511979608965838.

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Alperin, J. L. "Book Review: Group theory." Bulletin of the American Mathematical Society 17, no. 2 (October 1, 1987): 339–41. http://dx.doi.org/10.1090/s0273-0979-1987-15583-2.

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Knapp, A. W., Andrew Baker, and Wulf Rossmann. "Matrix Groups: An Introduction to Lie Group Theory." American Mathematical Monthly 110, no. 5 (May 2003): 446. http://dx.doi.org/10.2307/3647845.

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SAPIR, MARK V. "SOME GROUP THEORY PROBLEMS." International Journal of Algebra and Computation 17, no. 05n06 (August 2007): 1189–214. http://dx.doi.org/10.1142/s0218196707003925.

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This is a survey of some problems in geometric group theory that I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some necessary definitions and motivations, problems and some discussions of them. For each problem, I try to mention the author. If the author is not given, the problem, to the best of my knowledge, was formulated by me first.
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Steingart, Alma. "A group theory of group theory: Collaborative mathematics and the ‘uninvention’ of a 1000-page proof." Social Studies of Science 42, no. 2 (February 23, 2012): 185–213. http://dx.doi.org/10.1177/0306312712436547.

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Streater, R. F. "APPLICATIONS OF GROUP THEORY IN PHYSICS AND MATHEMATICAL PHYSICS (Lectures in Applied Mathematics 21)." Bulletin of the London Mathematical Society 19, no. 5 (September 1987): 500. http://dx.doi.org/10.1112/blms/19.5.500a.

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Beardon, Alan F. "Complex Exponents and Group Theory." Mathematics Magazine 93, no. 3 (May 20, 2020): 186–92. http://dx.doi.org/10.1080/0025570x.2020.1736876.

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Dissertations / Theses on the topic "Group theory – Mathematics"

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McSorley, J. P. "Topics in group theory." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.376929.

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Isenrich, Claudio Llosa. "Kähler groups and Geometric Group Theory." Thesis, University of Oxford, 2017. https://ora.ox.ac.uk/objects/uuid:4a7ab097-4de5-4b72-8fd6-41ff8861ffae.

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In this thesis we study Kähler groups and their connections to Geometric Group Theory. This work presents substantial progress on three central questions in the field: (1) Which subgroups of direct products of surface groups are Kähler? (2) Which Kähler groups admit a classifying space with finite (n-1)-skeleton but no classifying space with finitely many n-cells? (3) Is it possible to give explicit finite presentations for any of the groups constructed in response to Question 2? Question 1 was raised by Delzant and Gromov. Question 2 is intimately related to Question 1: the non-trivial examples of Kähler subgroups of direct products of surface groups never admit a classifying space with finite skeleton. The only known source of non-trivial examples for Questions 1 and 2 are fundamental groups of fibres of holomorphic maps from a direct product of closed surfaces onto an elliptic curve; the first such construction is due to Dimca, Papadima and Suciu. Question 3 was posed by Suciu in the context of these examples. In this thesis we: provide the first constraints on Kähler subdirect products of surface groups (Theorem 7.3.1); develop new construction methods for Kähler groups from maps onto higher-dimensional complex tori (Section 6.1); apply these methods to obtain irreducible examples of Kähler subgroups of direct products of surface groups which arise from maps onto higher-dimensional tori and use them to show that our conditions in Theorem 7.3.1 are minimal (Theorem A); apply our construction methods to produce irreducible examples of Kähler groups that (i) have a classifying space with finite (n-1)-skeleton but no classifying space with finite n-skeleton and (ii) do not have a subgroup of finite index which embeds in a direct product of surface groups (Theorem 8.3.1); provide a new proof of Biswas, Mj and Pancholi's generalisation of Dimca, Papadima and Suciu's construction to more general maps onto elliptic curves (Theorem 4.3.2) and introduce invariants that distinguish many of the groups obtained from this construction (Theorem 4.6.2); and, construct explicit finite presentations for Dimca, Papadima and Suciu's groups thereby answering Question 3 (Theorem 5.4.4)).
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Evans, D. M. "Some topics in group theory." Thesis, University of Oxford, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.355748.

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Alp, Murat. "GAP, crossed inodules, Cat'1-groups : applications of computational group theory." Thesis, Bangor University, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.361168.

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Grenham, Dermot. "Some topics in nilpotent group theory." Thesis, University of Oxford, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.329954.

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Cornwell, Christopher R. "On the Combinatorics of Certain Garside Semigroups." Diss., CLICK HERE for online access, 2006. http://contentdm.lib.byu.edu/ETD/image/etd1381.pdf.

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Gatward, Sally Morrell. "On a new construction in group theory." Thesis, Queen Mary, University of London, 2011. http://qmro.qmul.ac.uk/xmlui/handle/123456789/2342.

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My supervisors Ian Chiswell and Thomas M¨uller have found a new class of groups of functions defined on intervals of the real line, with multiplication defined by analogy with multiplication in free groups. I have extended this idea to functions defined on a densely ordered abelian group. This doesn’t give rise to a class of groups straight away, but using the idea of exponentiation from a paper by Myasnikov, Remeslennikov and Serbin, I have formed another class of groups, in which each group contains a subgroup isomorphic to one of Chiswell and M¨uller’s groups. After the introduction, the second chapter defines the set that contains the group and describes the multiplication for elements within the set. In chapter three I define exponentiation, which leads on to chapter four, in which I describe how it is used to find my groups. Then in chapter five I describe the structure of the centralisers of certain elements within the groups.
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Nicholson, Julia. "Otto Hölder and the development of group theory and Galois theory." Thesis, University of Oxford, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.333485.

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Hert, Theresa Marie. "An efficient presentation of PGL(2,p)." CSUSB ScholarWorks, 1993. https://scholarworks.lib.csusb.edu/etd-project/690.

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Bavuma, Yanga. "Some combinatorial aspects in algebraic topology and geometric group theory." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29763.

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The present Msc thesis deals with classical topics of topology and it has been written, referring to [C. Kosniowski, Introduction to Algebraic Topology, Cambridge University Press, 1980, Cambridge], which is a well known textbook of algebraic topology. It has been selected a list of main exercises from this reference, whose solutions were not directly available, or subject to differerent methods. In fact combinatorial methods have been preferred and the result is a self-contained dissertation on the theory of the fundamental group and of the coverings. Finally, there are some recent problems in geometric group theory which are related to the presence of finitely presented groups which appear naturally as fundamental groups.
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Books on the topic "Group theory – Mathematics"

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Karl, Strambach, ed. Loops in group theory and lie theory. Berlin: Walter de Gruyter, 2002.

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Smith, Geoff C. Topics in Group Theory. London: Springer London, 2000.

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H, Walton Paul. Beginning group theory for chemistry. Oxford: Oxford University Press, 1998.

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Davidson, George. Group theory for chemists. Basingstoke, Hampshire: Macmillan, 1991.

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Wielandt, Helmut. Mathematische Werke = Mathematical works. Berlin: Walter de Gruyter, 1994.

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Linear algebra and group theory. Mineola, N.Y: Dover Publications, 2011.

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Jean-Claude, Falmagne, and Ovchinnikov Sergeĭ, eds. Media theory: Interdisciplinary applied mathematics. Berlin: Springer, 2008.

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service), SpringerLink (Online, ed. Theory of Group Representations and Fourier Analysis. Berlin, Heidelberg: Springer-Verlag Berlin Heidelberg, 2011.

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Matrix groups: An introduction to Lie group theory. London: Springer, 2002.

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1946-, Kechris A. S., ed. The descriptive set theory of Polish group actions. New York: Cambridge University Press, 1996.

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Book chapters on the topic "Group theory – Mathematics"

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Mahan, Gerald Dennis. "Group Theory." In Applied Mathematics, 47–71. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4615-1315-5_3.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 275–91. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4899-0007-4_18.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 257–82. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-55193-3_14.

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Barbeau, Edward J. "Group Theory." In Problem Books in Mathematics, 149–51. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-28106-3_9.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 361–81. New York, NY: Springer New York, 2002. http://dx.doi.org/10.1007/978-1-4684-9281-1_19.

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Stillwell, John. "Group Theory." In Undergraduate Texts in Mathematics, 383–413. New York, NY: Springer New York, 2010. http://dx.doi.org/10.1007/978-1-4419-6053-5_19.

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Smith, Geoff. "Group Theory." In Springer Undergraduate Mathematics Series, 125–52. London: Springer London, 1998. http://dx.doi.org/10.1007/978-1-4471-0619-7_5.

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Bhattacharjee, Meenaxi, Dugald Macpherson, Rögnvaldur G. Möller, and Peter M. Neumann. "Some group theory." In Lecture Notes in Mathematics, 1–8. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0092551.

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Vinberg, E. "Elements of group theory." In Graduate Studies in Mathematics, 137–70. Providence, Rhode Island: American Mathematical Society, 2003. http://dx.doi.org/10.1090/gsm/056/04.

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Johnson, D. L. "Some Basic Group Theory." In Springer Undergraduate Mathematics Series, 27–43. London: Springer London, 2001. http://dx.doi.org/10.1007/978-1-4471-0243-4_3.

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Conference papers on the topic "Group theory – Mathematics"

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Léandre, Rémi. "Large Deviations Estimates in Semi‐Group Theory." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS: International Conference on Numerical Analysis and Applied Mathematics 2008. American Institute of Physics, 2008. http://dx.doi.org/10.1063/1.2990931.

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Léandre, Rémi, Theodore E. Simos, George Psihoyios, and Ch Tsitouras. "Girsanov Transformation for Poisson Processes in Semi-Group Theory." In Numerical Analysis and Applied Mathematics. AIP, 2007. http://dx.doi.org/10.1063/1.2790145.

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Pukhnachev, V. V., Michail D. Todorov, and Christo I. Christov. "Group-theoretical Methods in Convection Theory." In APPLICATION OF MATHEMATICS IN TECHNICAL AND NATURAL SCIENCES: 3rd International Conference—AMiTaNS'11. AIP, 2011. http://dx.doi.org/10.1063/1.3659901.

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Piatek-Jimenez, Katrina, Brent Jackson, Ana Dias, Weverton Ataide Pinheiro, Harryson Gonçalves, Jennifer Hall, Elizabeth Kersey, and Angela Hodge-Zickerman. "Working group on gender and sexuality in mathematics education: Informing methodology with theory." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-15.

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Nolan, Kathleen. "A theory-methodology framework for conceptualizing a culturally responsive mathematics/teacher education." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-397.

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Bowers, David Matthew, and Brian R. Lawler. "Reconciling tensions in equity discourse through an anti-hierarchical (anarchist) theory of action." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-68.

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Zhuang, Yuling, and AnnaMarie Conner. "Teacher questioning strategies in supporting validity of collective argumentation: explanation adapted from habermas' communicative theory." In 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. PMENA, 2020. http://dx.doi.org/10.51272/pmena.42.2020-387.

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Zixiang, Zou, and Yuan Ding. "A New Method of Calculating Optimum Velocity Distribution Along the Blade Surface on Arbitrary Stream Surface of Revolution in Turbomachines." In ASME 1987 International Gas Turbine Conference and Exhibition. American Society of Mechanical Engineers, 1987. http://dx.doi.org/10.1115/87-gt-30.

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This paper presents a physical model and its mathematical expressions (partial differential equation group), which are to be used to calculate the optimum velocity distribution on blade surface. The method is based on the theory of boundary layer and the calculation of cascade loss, and to employ the Pontijagin maximum principle as well as the new optimum techniques in applied mathematics. In this paper, a computing method of optimum velocity distribution along the blade surface in 2-D incompressible flow is presented by analysing and solving the equation group, and then by using the method which is presented by Zou Zixiang (1976), and through a logical analysis, a new method has been offered, which can converted from an optimum velocity distribution along the plane stream surface of incompressible fluid flow into that of an arbitrary stream surface of revolution in compressible fluid flow.
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Sarmin, Nor Haniza, Mustafa Anis El-sanfaz, and Sanaa Mohamed Saleh Omer. "Groups and graphs in probability theory." In ADVANCES IN INDUSTRIAL AND APPLIED MATHEMATICS: Proceedings of 23rd Malaysian National Symposium of Mathematical Sciences (SKSM23). Author(s), 2016. http://dx.doi.org/10.1063/1.4954600.

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Boz, Selma. "TRANSFER EFFECT OF N-BACK TRAINING: MATHEMATICAL IMPLICATIONS IN SCHOOL-AGE CHILDREN." In International Conference on Education and New Developments. inScience Press, 2021. http://dx.doi.org/10.36315/2021end121.

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Working memory (WM) is the system which is used for short-term storage and where information about cognitive tasks is manipulated. One of the most important characteristics of WM is its limited capacity, which restricts cognitive performance. Despite of this limit in WM capacity, the efficiency of WM can be improved with WM training and this training effect can be transferred to performance on complex tasks, such as mathematical operations. Such training tasks are complex and necessarily include core processes and these measures, therefore, contribute to difficulty to design tasks and interpret the outcomes for specific changes gained from the training. For example, n-back tasks which are used in a wide range of research are based on core training. Since core trainings address the executive functions of WM and enhance the domain-general aspects, increasing performance on domain-general factors may promote both near and far transfer effects of training. In the current study, WM training will be constructed on the basis of the interference framework that characterizes individual differences in WM performance. The aim of this study is to explore individual differences in training and the way transfer effects occur, evaluating gains from Mathematics proficiency. An adaptive version of n-back tasks will be implemented for the proposed study, within WM load and interference lures. The study will be carried out with 40 school-age children between the ages of 9 and 12, and Solomon four group design method will be used to group them. d’ (D-Prime) theory will be conducted in order to obtain detailed comparison between groups as well as interpretation of individual differences in processing of information.
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Reports on the topic "Group theory – Mathematics"

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Hyman, J., W. Beyer, J. Louck, and N. Metropolis. Development of the applied mathematics originating from the group theory of physical and mathematical problems. Office of Scientific and Technical Information (OSTI), July 1996. http://dx.doi.org/10.2172/257450.

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Álvarez Marinelli, Horacio, Samuel Berlinski, and Matías Busso. Research Insights: Can Struggling Primary School Readers Improve Their Reading through Targeted Remedial Interventions? Inter-American Development Bank, November 2020. http://dx.doi.org/10.18235/0002863.

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This paper assesses the effectiveness of an intervention aimed at improving the reading skills of struggling third-grade students in Colombia. In a series of randomized experiments, students participated in remedial tutorials conducted in small groups during school hours. Trained instructors used structured pedagogical materials that can be easily scaled up. Informed by the outcomes of each cohort, the intervention tools are fine-tuned for each subsequent cohort. The paper finds positive and persistent impacts on literacy scores and positive spillovers on some mathematics scores. The effectiveness of the program grew over time, likely because of higher dosage and the fine-tuning of materials.
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Tucker-Blackmon, Angelicque. Engagement in Engineering Pathways “E-PATH” An Initiative to Retain Non-Traditional Students in Engineering Year Three Summative External Evaluation Report. Innovative Learning Center, LLC, July 2020. http://dx.doi.org/10.52012/tyob9090.

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The summative external evaluation report described the program's impact on faculty and students participating in recitation sessions and active teaching professional development sessions over two years. Student persistence and retention in engineering courses continue to be a challenge in undergraduate education, especially for students underrepresented in engineering disciplines. The program's goal was to use peer-facilitated instruction in core engineering courses known to have high attrition rates to retain underrepresented students, especially women, in engineering to diversify and broaden engineering participation. Knowledge generated around using peer-facilitated instruction at two-year colleges can improve underrepresented students' success and participation in engineering across a broad range of institutions. Students in the program participated in peer-facilitated recitation sessions linked to fundamental engineering courses, such as engineering analysis, statics, and dynamics. These courses have the highest failure rate among women and underrepresented minority students. As a mixed-methods evaluation study, student engagement was measured as students' comfort with asking questions, collaboration with peers, and applying mathematics concepts. SPSS was used to analyze pre-and post-surveys for statistical significance. Qualitative data were collected through classroom observations and focus group sessions with recitation leaders. Semi-structured interviews were conducted with faculty members and students to understand their experiences in the program. Findings revealed that women students had marginalization and intimidation perceptions primarily from courses with significantly more men than women. However, they shared numerous strategies that could support them towards success through the engineering pathway. Women and underrepresented students perceived that they did not have a network of peers and faculty as role models to identify within engineering disciplines. The recitation sessions had a positive social impact on Hispanic women. As opportunities to collaborate increased, Hispanic womens' social engagement was expected to increase. This social engagement level has already been predicted to increase women students' persistence and retention in engineering and result in them not leaving the engineering pathway. An analysis of quantitative survey data from students in the three engineering courses revealed a significant effect of race and ethnicity for comfort in asking questions in class, collaborating with peers outside the classroom, and applying mathematical concepts. Further examination of this effect for comfort with asking questions in class revealed that comfort asking questions was driven by one or two extreme post-test scores of Asian students. A follow-up ANOVA for this item revealed that Asian women reported feeling excluded in the classroom. However, it was difficult to determine whether these differences are stable given the small sample size for students identifying as Asian. Furthermore, gender differences were significant for comfort in communicating with professors and peers. Overall, women reported less comfort communicating with their professors than men. Results from student metrics will inform faculty professional development efforts to increase faculty support and maximize student engagement, persistence, and retention in engineering courses at community colleges. Summative results from this project could inform the national STEM community about recitation support to further improve undergraduate engineering learning and educational research.
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Incongruity between biological and chronologic age among the pupils of sports schools and the problem of group lessons effectiveness at the initial stage of training in Greco-Roman wrestling. Aleksandr S. Kuznetsov, March 2021. http://dx.doi.org/10.14526/2070-4798-2021-16-1-19-23.

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Considerable influence and compulsory dropout among those, who go in for GrecoRoman wrestling at the age of 10-13, does not take into account the level of individual biological development and integral demands domination claimed on too high general physical training (GPT) (4) normatives fulfillment. It corresponds with general situation in the system of education (6, 9). In spite of uneven speed of biological development (1, 8, 9), there are general demands claimed on physical training at school for age groups (5) in accordance with chronologic age. The same situation is at sports schools. Technical and physical training lessons at Greco-Roman wrestling school at the stage of initial training are organized according to general group principle. Research methods. Information sources analysis and summarizing, questionnaire survey, coaches’ experience summarizing, methods of mathematical statistics. Results. The received research results led to the following conclusion: it is possible to solve the problem of dropping out of Greco-Roman wrestling sports schools in terms of minimal loss in the quality of sports training by means of dividing the training groups into subgroups. There different normatives of material mastering and set by standard physical qualities development are used. For this purpose we created the training groups and subgroups of the set objectives realization at Greco-Roman wrestling sports schools.
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