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i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 12 Issue 2

Statistical Analysis on Job Satisfaction of Academic Staff at College of Natural Science in Jimma University, Ethiopia: A Cross-Sectional Study
Tolerance Based Rough Algebras Induced by Blocks
Significance of Thermal Boundary Layer Analysis of MHD Chemically Radiative Dissipative Casson Nanofluid Flow over a Stretching Sheet with Heat Source
Transient Analysis of M/M/1 Fractional Queue
A Novel Multi-Viewpoints Based Cosine Similarity Visual Technique for an Effective Assessment of Clustering Tendency

Most Cited

Volume 2 Issue 3 July - September 2013

Article

Pairing Figure Skating and Mathematics

Diana Cheng* , Tetyana Berezovski**

* Assistant Professor, Towson University, Maryland, USA.

** Associate Professor, St. Joseph's University, Pennsylvania, USA.

Cheng, D., and Berezovski, T. (2013). Pairing Figure Skating and Mathematics. i-manager’s Journal on Mathematics, 2(3), 1-6. https://doi.org/10.26634/jmat.2.3.2456

Abstract

In light of the Winter Olympic Games, a modeling problem is presented in the context of pair’s figure skating. Prospective and in-service high school teachers used related rates to solve the problem that involved differentiating the Pythagorean theorem and a trigonometric equation. Student work is analyzed and discussed.

References

[1]. Common Core State Standards Initiative (CCSSI). (2010). Common Core State Standards for Mathematics. Washington, DC: National Governors Association Center for Best Practices and the Council of Chief State School Officers. http://www.corestandards.org/assets/

[2]. Kerrigan, Nancy & Spencer, Mary. (2003). Artistry on Ice: Figure Skating Skills and Style, Human Kinetics: Champaign, IL.

[3]. United States Figure Skating Association. (1998). The official book of figure skating, Simon & Shuster Editions: New York, NY.

[4]. Martin, Tami. (2000). “Calculus Students' Ability to Solve Geometric Related-Rates Problems,”Mathematics Education Research Journal, 12:2, 74-91.

[5]. Teuscher, Dawn, and Robert E. Reys. (2010). “Slope, Rate of Change, and Steepness: Do Students Understand These Concepts?”, Mathematics Teacher, 103:7, 519-24.

[7]. Weber, Keith. (2005). “Students' Understanding of Trigonometric Functions,” Mathematics Education Research Journal, 17:3, 94–115.

[8]. White, Paul, and Michael Mitchelmore. (1996). “Conceptual Knowledge in Introductory Calculus,”Journal for Research in Mathematics Education, 27:1, 79-95.

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Article

Some Characterization of Curves of Constant Breadth According to Bishop Frame in E3 Space

Hülya Gün Bozok* , Handan Öztekin**

* Department of Mathematics, Osmaniye Korkut Ata University, Osmaniye, Turkey.

** Department of Mathematics, Firat University, Elazig, Turkey.

Bozok, H.G., and Öztekin, H. (2013). Some Characterization of Curves of Constant Breadth 3 According to Bishop Frame in E3 Space. i-manager’s Journal on Mathematics, 2(3), 7-11. https://doi.org/10.26634/jmat.2.3.2457

Abstract

In this paper, some characterizations of curves of constant breadth according to Bishop frame in E are presented.

References

[1]. A. Magden and Ö. Köse, (1997). On the curves of constant breadth in E space, Turkish J. Math. 21, No.3, 277-284.

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[3]. Bükcü B, Karacan MK (2009). "The Slant Helices According to Bishop Frame." Int. J. Comput. Math. Sci., 3(2): 67-70.

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[8]. H. H. Hacisalihoglu, (2000). Differential Geometry, Ankara University Faculty of Science.

[9]. H. H. Hacisalihoglu and R. Öztürk, On the Characterization of Inclined Curves in E I. Tensor, N.S. Vol. 64, pp.163-170.

[10]. H. Tanaka, (1976). Kinematics Design of Cam Follower Systems, Doctoral Thesis, Columbia Univ.

[11]. L.R. Bishop, (1975). There is More Than one way to Frame a Curve, Am. Math. Monthly, 82(3): 246-251.

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Research Paper

Applied Mathematical Statistical Modeling to Determine the Validity and Reliability of Independent Instructional Measures

James Edward Osler II* , Mahmud A. Mansaray**

* North Carolina Central University.

** Research Analyst, Department of Research, Evaluation and Planning, North Carolina Central University.

Osler, J. E., II. and Mansaray, M.A. (2013). Applied Mathematical Statistical Modeling to Determine The Validity And Reliability of Independent Instructional Measures. i-manager’s Journal on Mathematics, 2(3), 12-31. https://doi.org/10.26634/jmat.2.3.2458

Abstract

Most universities and colleges in United States and elsewhere use student ratings of instruction for summative (e.g. faculty promotion, etc.) and formative (e.g. instructional improvement, etc.) evaluation purposes. This research examines the reliability and validity of the rating instrument used to evaluate teaching effectiveness and student learning outcomes. The sample consisted of 7,919 students of Historic Black College and University [HBCU] who completed the 2012 spring semester. Student Ratings of Instruction [SRI] survey (a measurement instrument used by students to assess instruction in courses in which they are currently enrolled) was used. The application of the Cronbach's Alpha Reliability Model, in the study helps to find strong internal reliability [consistency] of the rating instrument used to comprehensively assess teaching quality. At the same time, the application of Principal Component Factor Analysis with Varimax Rotation also finds strong construct validity of the assessment tool used to evaluate faculty.

References

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[14]. El Hassan, K. (2009). Investigating substantive and consequential validity of student ratings of instruction. Higher Education Research & Development, 28(3), 319-333. doi:10.1080/07294360902839917.

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[17]. Frick, T., Chadha, R., Watson, C., Wang, Y., & Green, P. (2009). College student perceptions of teaching and learning quality. Educational Technology Research & Development, 57(5), 705-720. doi:10.1007/s11423-007-9079-9.

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[26]. Ibrahim, A. (2011). Using generalizability theory to estimate the relative effect of class size and number of items on the dependability of student ratings of instruction. Psychological Reports, 109(1), 252-258. doi:10.2466/03.07.11.PR0.109.4.252-258.

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[32]. Lüdtke, O., Trautwein, U., Kunter, M., & Baumert, J. (2006). Reliability and agreement of student ratings of the classroom environment: A reanalysis of TIMSS data. Learning Environments Research, 9(3), 215-230. doi:10.1007/s10984-006-9014-8.

[33]. Madden, T. J., Dillon, W. R., & Leak, R. L. (2010). Students' evaluation of teaching: Concerns of item diagnosticity. Journal of Marketing Education, 32(3), 264-274. doi:10.1177/0273475310377759.

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[35]. Marsh, H. W. (2007). Students' evaluations of university teaching: Dimensionality, reliability, validity, potential biases, and usefulness. In R. Perry & J. C. Smart (Eds.), The scholarship of teaching and learning in higher education: An evidence-based perspective (pp. 319-383). Netherlands: Springer.

[36]. Marsh, H. W., Ginns, P., Morin, A. S., Nagengast, B., & Martin, A. J. (2011). Use of student ratings to benchmark universities: Multilevel modeling of responses to the Australian Course Experience Questionnaire (CEQ). Journal of Educational Psychology, 103(3), 733-748. doi:10.1037/a0024221.

[37]. McKeachie, W. J. (2007). Good teaching makes a difference—And we know what it is. In R. Perry & J. C. Smart (Eds.), The scholarship of teaching and learning in higher education: An evidence-based perspective (pp. 457-474). Netherlands: Springer.

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[40]. Roche, L. A., & Marsh, H. W. (2000). Multiple dimensions of university teacher selfconcept. Instructional Science, 28(5), 439-468.

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[51]. Zerbini, T., & Abbad, G. (2009). Reação aos procedimentos instrucionais de um curso via internet: Validação de uma escala. Estudos De Psicologia, 26(3), 363-371. doi:10.1590/S0103-166X2009000300009.

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Research Paper

Another Locus Property of the Thomson Cubic

Mikhail Goldenberg* **

* Department of Mathematics, The Ingenuity Project Baltimore Polytechnic Institute 1400 W, Cold Spring Lane Baltimore.

** Adjunct Professor, Department of Mathematics, Towson University, York Road Towson.

Goldenberg, M., and Kaplan, M. (2013). Another Locus Property of The Thomson Cubic. i-manager’s Journal on Mathematics, 2(3), 32-37. https://doi.org/10.26634/jmat.2.3.2459

Abstract

Generalizing the concept of the symmedian point of a triangle we introduce the point called quasi-symmedian point and prove that the locus of quasi-symmedian points is the Thomson cubic.

References

[1]. Coxeter, H. S. M. (1993). The Real Projective Plane (3rd ed.). Cambridge, England: Cambridge University Press, p. 103.

[2]. Cundy, H. M., Parry, C. F. (1995). Some Cubic Curves Associated with a Triangle. Journals of Geom. 53, 41-66.

[3]. Gibert, B. (2012, June 25). Thomson Cubic. St Etienne, France: Cubics in the Triangle Plane. Retrieved from http://perso.wanadoo.fr/bernard.gibert/Exemples/k002.html

[4]. Honsberger, R. (1995). Episodes in Nineteenth and Twentieth Century Euclidean Geometry. Washington, DC: Math. Assoc. Amer, pp. 98-124.

[5]. Kimberling, C. (1994). Central Points and Central Lines in the Plane of a Triangle. Math. Mag., 67, 163-187.

[6]. Kimberling, C. (1998). Triangle Centers and Central Triangles. Congr. Numer., 129, 1-295.

[7]. Rubio, P. (1989). Cubic Lines Relative to a Triangle. Journals of Geom. 34, 152-171.

[8]. Sigur, S. (2005). Where are the Conjugates? Forum Geom. 5, 1-15.

[9]. Wells, D. (1991). The Penguin Dictionary of Curious and Interesting Geometry. London, England: Penguin, pp. 190-191.

[10]. Yiu, P. (2000). The uses of homogeneous barycentric coordinates in plane euclidean geometry. Int. Journals of Math. Educ. Sci. Technol., 31, 569 – 578.

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Article

Collections Of Statements Related To Point-Set Domination Numbers In Graphs

D. R. Robert Joan*

Assistant Professor, M.Ed. Department, M.E.T. College of Education, Chenbagaramanputhoor, Tamilnadu, India.

Joan, D.R.R. (2013). Collections of Statements Related to Pointset Domination Numbers in Graphs. i-manager’s Journal on Mathematics, 2(3), 38-49. https://doi.org/10.26634/jmat.2.3.2460

Abstract

Let G be a connected graph. A set D V(G) is a point-set dominating set (psd-set) of G if for every set S V – D, there exists a vertex v D such that the subgraph induced by S {v} is connected. The point-set domination number γ (G) p of G is the minimum cardinality of a psd-set. This paper provides a comprehensive treatment of point set domination in graphs. First introduce the point-set domination number of a graph G, and determine this number for various known graphs. The relationship between set domination number with r point set domination number, point-set domination number and also few results regarding point-set are given as statements. Also In this paper the investigator say about global set-domination number γ and global point-set domination number γ of a graph G and determine these sg pg numbers for various known graphs and obtain some bounds for the graph G of diameters 3 and 4 in terms of γ. Finally the concept of the strong point-set domination number of a graph G is introduced, and its exact value is determined for some known graphs.

References

[1]. Acharya, B. D., and Gupta, P. (2005). On Point-Set Domination in Graphs II: Minimum PSD-Sets. 2(2), 87 - 98.

[2]. Garey., Michael, R., Johnson., & David, S. (1979). Computers and Intractability: A Guide to the Theory of NP-Completeness. ISBN 0-7167-1045-5, 190.

[3]. Sampathkumar, E., and Latha, L.P. (1993). Point-Set Domination Number of a graph, Indian Journal of pure applied Mathematics, 24(4), 225 - 229.

[4]. Sampathkumar, E., and Latha, L.P. (1994). The Global Set-Domination Number of a Graph, Indian Journal of pure applied Mathematics, 25(10), 1053-1057.

[5]. Sampathkumar, E. (1989). The Global Domination Number of a Graph, The Journal of mathematics, 23(5), 377 - 385.

[6]. Swaminathan., and Poovazhaki, R. (2003). Global Strong Point-Set Domination Number of a Graph. Proceedings of the KMA, National Seminar on Discrete Mathematics and Applications, St. Thomas College, Kozhencherry, 107 - 112.

[7]. Swaminathan., and Poovazhaki, R. (2002). Strong point-set domination number of graphs, Proceedings of the KMA, National Seminar on Graph Theory, St. Mary's College, Thrissur, 131 - 143.

[8]. Kulli, V.R., and Janakiram, B. (2005). Global non split domination in graphs. Proceedings of the National Academy of Sciences, India, 11-12.

[9]. Haynes., Teresa, W., Hedetniemi., Stephen., Slater., and Peter. (1998). Fundamentals of Domination in Graphs. Marcel Dekker, Madison Avenue, New York , 10016 ISBN 0-8247-0033-3, OCLC 37903553 INC., 270.

i-manager's Journal on Mathematics (JMAT)

Current Issue Vol. 12 Issue 2

Most Read

Most Cited

Volume 2 Issue 3 July - September 2013

Pairing Figure Skating and Mathematics

Diana Cheng* , Tetyana Berezovski**

* Assistant Professor, Towson University, Maryland, USA. ** Associate Professor, St. Joseph's University, Pennsylvania, USA.

Cheng, D., and Berezovski, T. (2013). Pairing Figure Skating and Mathematics. i-manager’s Journal on Mathematics, 2(3), 1-6. https://doi.org/10.26634/jmat.2.3.2456

Abstract

References

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Some Characterization of Curves of Constant Breadth According to Bishop Frame in E3 Space

Hülya Gün Bozok* , Handan Öztekin**

* Department of Mathematics, Osmaniye Korkut Ata University, Osmaniye, Turkey. ** Department of Mathematics, Firat University, Elazig, Turkey.

Bozok, H.G., and Öztekin, H. (2013). Some Characterization of Curves of Constant Breadth 3 According to Bishop Frame in E3 Space. i-manager’s Journal on Mathematics, 2(3), 7-11. https://doi.org/10.26634/jmat.2.3.2457

Abstract

References

Full Article (HTML)

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Applied Mathematical Statistical Modeling to Determine the Validity and Reliability of Independent Instructional Measures

James Edward Osler II* , Mahmud A. Mansaray**

* North Carolina Central University. ** Research Analyst, Department of Research, Evaluation and Planning, North Carolina Central University.

Osler, J. E., II. and Mansaray, M.A. (2013). Applied Mathematical Statistical Modeling to Determine The Validity And Reliability of Independent Instructional Measures. i-manager’s Journal on Mathematics, 2(3), 12-31. https://doi.org/10.26634/jmat.2.3.2458

Abstract

References

Full Article (HTML)

Pdf

Another Locus Property of the Thomson Cubic

Mikhail Goldenberg* **

* Department of Mathematics, The Ingenuity Project Baltimore Polytechnic Institute 1400 W, Cold Spring Lane Baltimore. ** Adjunct Professor, Department of Mathematics, Towson University, York Road Towson.

Goldenberg, M., and Kaplan, M. (2013). Another Locus Property of The Thomson Cubic. i-manager’s Journal on Mathematics, 2(3), 32-37. https://doi.org/10.26634/jmat.2.3.2459

Abstract

References

Full Article (HTML)

Pdf

Collections Of Statements Related To Point-Set Domination Numbers In Graphs

D. R. Robert Joan*

Assistant Professor, M.Ed. Department, M.E.T. College of Education, Chenbagaramanputhoor, Tamilnadu, India.

Joan, D.R.R. (2013). Collections of Statements Related to Pointset Domination Numbers in Graphs. i-manager’s Journal on Mathematics, 2(3), 38-49. https://doi.org/10.26634/jmat.2.3.2460

Abstract

References

Full Article (HTML)

Pdf

* Assistant Professor, Towson University, Maryland, USA.

** Associate Professor, St. Joseph's University, Pennsylvania, USA.

* Department of Mathematics, Osmaniye Korkut Ata University, Osmaniye, Turkey.

** Department of Mathematics, Firat University, Elazig, Turkey.

* North Carolina Central University.

** Research Analyst, Department of Research, Evaluation and Planning, North Carolina Central University.

* Department of Mathematics, The Ingenuity Project Baltimore Polytechnic Institute 1400 W, Cold Spring Lane Baltimore.

** Adjunct Professor, Department of Mathematics, Towson University, York Road Towson.