Mathematics Today Research Articles

Present day changes in Mathematical Research

Abstract In this work, various changes and developments in the field of mathematics were considered. To achieve this, trends generally and how they have affected the subject of mathematics were discussed, with consideration on some areas of trends in mathematics in the 1990s, identifying some notable developments in mathematics today, and some of the most current areas of developments in the field of mathematics and their effect between 2010 and today. In the course of these considerations, it was discovered that the subject of mathematics has experienced a lot of changes and evolutions over the years, and the application of mathematics today has grown beyond just physics and engineering but in many other fields. Computer has been identified as very important and useful in the current day mathematics, and mathematics also has been identified as very important and useful in computer science too. Also, it has been noticed that some concepts of hybridization as a result of the combination of mathematics and other fields now exist today, thereby promoting inter-field study. At the end of the work, the study revealed some changes which have occurred in the field of mathematics over the years, reiterated some applicable areas in mathematics today which occurred as a result of trends in mathematics in the 1990s, reiterated the importance and wide presence of computer in the current day mathematics and the importance and wide presence of mathematics in core areas of computer science and also identified some hybridized concepts which erupted as a result of the combination of mathematics and other fields.

Students’ mathematical critical thinking ability on cube and cuboid problems

The critical thinking ability becomes a prerequisite and purpose in learning Mathematics today. This study was aimed to analyze the mathematical critical thinking ability of students by using four indicators: identifying concept characteristics, selecting strategies for solving problems, providing complete and correct explanations, and evaluating the solution of problem. This was a descriptive research. Data collection was done by giving the test of mathematical thinking ability about cube and cuboid to 38 students in one of junior high schools in Lembang District. The results showed that the average ability of students in identifying the characteristics of the concept was about 43.7%, in choosing a strategy to solve the problem was about 17.9%, in providing a complete and correct explanation was about 26.8%, and in evaluating the solution of problem was about 21.1 % from the ideal score. According to the result, it showed the student need to enhance in critical thinking ability.

Use of Mnemonics for Teaching Mathematics at the Primary Level

A good understanding of mathematics is necessary not only for academics; rather it is also a fundamental skill which is required in a person’s personal, social, and work life. Mathematics today owes a huge debt to the outstanding contributions made by Indian mathematicians over many hundreds of years. However, nowadays Indian students underperform in mathematics. As per the Seventh Annual Survey of Education Report (ASER), 2012, of rural India, school enrolment has risen but there is a decline in attendance, over-reliance on private tuitions and decline in reading and mathematical ability of children in the age group between six and 14. In order to improve performance in mathematics and ensure that our students are equipped with the mathematical skills needed to succeed in a global marketplace, there is a need to start from the basics at primary level. The major reason for the difficulty in comprehending mathematical concepts is their abstract nature, inability to translate mathematical meaning to real -world entities and lack of multi-step problem solving skill. Thus, use of innovative techniques which make the mathematical concepts concrete and help in memorizing the basics along with inculcation of basic mathematical concepts and skills could be useful in improving the mathematical ability. The present paper considers some mnemonic techniques which could be easily incorporated in the regular classroom teaching methodology for enhancing mathematical skills and performance.

Leadership in Mathematics Education: Roles and Responsibilities

This article partitions leadership in mathematics education into two categories: leadership in defining and maintaining important principles in teaching mathematics, and leadership in informing the public about the importance of mathematics today and in the future. Examples of both types of leadership are given in the article. Teacher leaders in the field should be skilled in enriching instruction and linking best practice with research activities and results in the professional development of the teachers they lead.

Irrelevance of the fractal dimension term in the fractal attrition equation

The modified Fractal Attrition Equation (mFAE) models the casualties produced by Map Aware Non-uniform Automata (MANA), an agent based combat modelling distillation, at each MANA time step. The mFAE has three important differences from the simple early twentieth century models of casualties that used only the numbers on each side to make predictions. Firstly, only those agents within range of the enemy may inflict casualties. Secondly, the detection range is assumed to be greater than the range of weapons and a fitting factor assumed to represent the gap between these two ranges, is introduced. This builds in one of the assumptions of Network Centric Warfare, that you will be able to see your enemies before they can shoot at you. Thirdly, and novelly, a fractal dimension is introduced. We postulate that the important part of the information used in calculating the fractal dimension has already been incorporated into the model through the consideration of range. We test this hypothesis by comparing the outcomes of the mFAE with and without the fractal term on three scenarios: that used by the developers of the mFAE; best practice MANA tactics from the literature; and a rout scenario. When the two models are scaled to fit the MANA casualties there is no significant difference in fit. We conclude that the fractal term in the mFAE is redundant. References J. V. Chase, Sea fights, a mathematical investigation of the effect of superiority of force in. RG 8, Box 109, XTAV(1902), Naval War College Archives. F. W. Lanchester, Aircraft in warfare: the dawn of the fourth arm---No. V, The principle of concentration, Engineering 98: 422--423, (1914). http://www.archive.org/details/aircraftinwarfar00lancrich N. J. MacKay, Lanchester combat models, Mathematics Today, 42, pp.170--173, 2006. http://arXiv.org/abs/math/0606300v1 T. W. Lucas and T. Turkes Fitting Lanchester models to the battles of Kursk and Ardennes. Nav Res Log 51: 95--116 (2004). G. C. McIntosh and M. K. Lauren, Incorporating fractal concepts into equations of attrition for military conflicts, Journal of the Operational Research Society, 2(59): 703--713, (2008). doi:10.1057/palgrave.jors.2602383 M. K. Lauren Firepower concentration in cellular automaton combat models---an alternative to Lanchester, Journal of the Operational Research Society, 53: 672--679, (2002). doi:10.1057/palgrave.jors.2601355 M. K. Lauren, J. M. Smith, J. Moffat and N. D. Perry Using the fractal attrition equation to construct a metamodel of the MANA cellular automaton combat model, The Technical Cooperation Program, Joint Systems and Analysis Group, Technical Panel 3, November 2005. G. C. McIntosh, D. P. Galligan, M. A. Anderson and M. K. Lauren, MANA (Map Aware Non-uniform Automata) Version 4 User Manual, DTA Technical Note 2007/3 NR 1465. http://arxiv.org/abs/nlin/0607051v1 J. Moffat, J. Smith and S. Witty, Emergent behaviour: Theory and experimentation using the mana model, Journal of Applied Mathematics and Decision Sciences---JAMDS , 2006, pp.1--14, 2006. doi:10.1155/JAMDS/2006/54846 D. R. Shine, An Exploratory Study of the Army-as-a-System Core Skills: Comparing the Effectiveness of Warfighting Tactics Using MANA, DSTO-TR-1663, (2005), DSTO (Australia). P. Grassberger and I. Procaccia, Characterization of strange attractors, Phys Rev Lett 50(5): 346--349 (1983). doi:10.1103/PhysRevLett.50.346 J. G. Eisenhauer, Regression through the Origin, Teaching Statistics, 25(3): 76--80, (2003).

Detecting the phenomenon of strange non-chaotic attractors

I comment on how chaos might be defined. A sample of dynamical systems that have quasi-periodic forcing functions is then considered. The normal approach found in the literature is to start with an ordinary differential equation, change to a difference equation, and then plot a graph. The question of how to detect a strange non-chaotic attractor without the underlying ordinary differential equation is posed and some pointers are given as to a possible method of solution using statistical analysis. References Banks J., Brooks J., Cairns G., Davis G. and Stacey P., On Devaney's definition of chaos, American Mathematics Monthly . 99 (1992), 332--334. Box G. E. P, Jenkins G. M. and Reinsel G. C., Time series analysis John Wiley and Sons, New Jersy, 2008. Feitelson D. G., Workload modeling for performance evaluation, In: Lecture notes in computer science , vol. 2459, Springer, Berlin, 2002, 114--141. Glendinning P., The nonsmooth pitchfork bifurcation, Discrete and Continuous Dynamical Systems B . 4 (2004), 457--464. Glendinning P., T. H. Jager and G. Keller, How chaotic are strange non-chaotic attractors?, Nonlinearity . 19 (2006), 2005--2022. Glendinning P., View from the Pennines: strange nonchaotic attractors, Mathematics Today . 44 (2008), 119--120. Keller G., A note on strange nonchaotic attractors, Fundamenta Mathematicae . 151 (1996), 139--148. Li H., Workload dynamics on clusters and grids, Journal of Supercomputing . 47) (2009), 1--20. Lublin U., Feitelson D. G., The workload of parallel supercomputers: modeling the characteristics of rigid jobs, J. Parallel Distrib Comput . 63(11) (2003), 1105--1122. Squillante M. S., Yao D. D and Zhang L. The impact of job arrival patterns on parallel scheduling, ACM SIGMETRICS Perform Eval Rev. 26(4) (1999), 52--59.

Predicting university performance

University admissions in Australia are dictated primarily by entrance ranking scores (TER) based on all courses taken in secondary school. However, these are unreliable indicators of ability to do mathematically based university courses. Differences in mathematical curricula between Australian states also complicates admissions for students moving interstate, especially with 19 or more different mathematical courses being offered in high schools across Australia. This article compares student TER and performance in a diagnostic test, against their university grade at the end of one semester to find a better predictor than simple TER measures. References E. A. Catchpole and B. R. Anderson, Comparing the performances of NSW and Victorian students in a first-year mathematics course. Austr. New Zealand J. Statist. 40(4), 1998, 389--406. doi:10.1111/1467-842X.00044 A. C. Croft, S. Hibberd, D. A. Lawson, L. R. Mustoe and C. T. Shaw, Engineering mathematics in the UK: SARTOR---a timely opportunity for reform. Engineering Science and education Journal. 2000, 77--87. doi:10.1049/esej:20000205 Engineering Council (UK), Measuring the Mathematics problem, Engineering Council, June 2000. http://www.engc.org.uk/publications/pdf/mathsreport.pdf M. S. Fadali, N. Velasquez--Bryant and M. Robinson, Work in progress---Is attitude toward mathematics an obstacle to engineering education? 4th ASEE/IEEE Frontiers in Education Conference, 19--24, 2004. http://fie.engrng.pitt.edu/fie2004/papers/1090.pdf B. Hassler, R. Atkinson, D. Quinney and M. Barry, The Experience of Fresher Students in Mathematics Diagnostic Testing, MSOR connections, Aug 2004, 4. http://www.atm.damtp.cam.ac.uk/people/bh213/ARDTS/DiagnosticTesting_MSOR_aug04.pdf D. Lawson, Changes in student entry competencies, 1991--2001. Teaching Mathematics and its applications, 22(4), 171--175. doi:10.1093/teamat/22.4.171 Ltsn, MathsTEAM Project, Diagnostic testing for mathematics, http://mathstore.ac.uk/mathsteam/packs/diagnostic_test.pdf MDTP, Mathematics Diagnostic Testing Project, California State University, http://www.math.csusb.edu/mdtp/Home.htm A. Miller, J. Bradbury and D. Middleman, Diagnostic testing, Mount Allison University, USA. http://mathcs.mta.ca/demo1.htm I. E. Otung, Reassessing the mathematics content of engineering education. Engineering Science and education journal, 2001, 130--138. doi:10.1049/esej:20010401 F. Barrington and P. Brown, Comparison of Year 12 pre-tertiary mathematics subjects in Australia 2004--2005. Australian Mathematics Science Institute, 2005. http://www.ice-em.org.au/images/stories/FileDownloads/Comparison_of_Year_12_Pre-tertiary_Mathematics_Subjects_in_Australia_2004-2005.pdf J. Ridd, Participation in Physics and rigorous mathematics and a consideration of educational, economic and political influences. PhD Thesis, James Cook University, 2003. J. Ridd, Year 9 and 10 structures in Queensland and possible implications for subsequent studies in Mathematics and Physics. The Physicist, 37(3), 94--98, 2000. P. Ridd, Physics will add up only with maths. The Australian, July 19, 2006. p.32. K. L. Todd, An historical study of the correlation between GCE Advanced level grades and the subsequent academic performance of well qualified students in a university engineering department. Mathematics Today, 37(5), 2001. F. Barrington, Participation in Year 12 mathematics across Australia 1994--2005. ICE-EM Publications in Education No 2, Australian Mathematics Science Institute, 2006. http://www.ice-em.com.au/pdfs/Participation_in_Yr12_Maths.pdf S. I. Barry and S. Davis, Essential mathematical skills for undergraduate students. Int. J. of Math. Education in Science and Technology, 30, 499--512, 1999. S. I. Barry and S. Davis, Essential Mathematics Skills, UNSW Press, Australia, 2002,

JOHAN VAN BENTHEM, GERHARD HEINZMANN, MANUEL REBUSCHI, and HENK VISSER, eds. The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Logic, Epistemology, and the Unity of Science; 3

Johan van Benthem, Gerhard Heinzmann, Manuel Rebuschi, and Henk Visser, eds. The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Logic, Epistemology, and the Unity of Science; 3 Get access van Benthem Johan Heinzmann Gerhard Rebuschi Manuel Visser Henk. The Age of Alternative Logics: Assessing Philosophy of Logic and Mathematics Today. Logic, Epistemology, and the Unity of Science; 3. Dordrecht: Springer, 2006. ISBN-13 978-1-4020-5011-4 (hbk); 978-1-4020-5012-7 (e-book). Pp. ix + 348. Philosophia Mathematica, Volume 16, Issue 2, June 2008, Page 284, https://doi.org/10.1093/philmat/nkn005 Published: 01 April 2008

Philip Gerald Drazin

Philip Gerald Drazin

Lightweight tension structures – an aesthetic integration of geometry and mechanics. Part 1. The role of minimal surfaces and soap films. Part 2. Finding the form of a minimal surface, by W. J. Lewis, Mathematics Today 35 (1) pp. 10–16, (3) pp. 80–84, 1999. - Magic squares indeed!, by Arthur T. Benjamin and Kan Yasuda, American Mathematical Monthly 106 (2),

Lightweight tension structures – an aesthetic integration of geometry and mechanics. Part 1. The role of minimal surfaces and soap films. Part 2. Finding the form of a minimal surface, by W. J. Lewis, Mathematics Today 35 (1) pp. 10–16, (3) pp. 80–84, 1999. - Magic squares indeed!, by Arthur T. Benjamin and Kan Yasuda, American Mathematical Monthly 106 (2), pp. 152–156, 1999. - Pierre-Simon de Laplace: 1749–1827, by Roger Cook, Mathematical Spectrum 31 (3), pp. 49–51, 1998/9. - Unifying threads in Alfred Tarski’s work, by Steven Givant, The Mathematical Intelligencer 21 (1), pp. 47–58, 1999. - André Weil and algebraic topology, by Armand Borel, pp. 422–427. - André Weil as I knew him, by Goro Shimura, pp. 428–433. - André Weil: A prologue, by Anthony W. Knapp, pp. 434–439. - André Weil (1906-1998), by Armand Borel, Pierre Carrier, Komaravolu Chandrasekharan, Shiing-Shen Chern and Shokichi Iyanaga, pp. 440–447. - The apprenticeship of a mathematician – autobiography of André Weil, reviewed by V. S. Varadarajan, pp. 448–456. - Introduction to metric preserving functions, by Paul Corazza, The American Mathematical Monthly 106 (4) pp. 309–323, 1999. - Visual aspects of understanding group theory, by D. F. Almeida, Int. J. of Mathematical Education in Science and Technology 30 (2) pp. 159–166, 1999 - Marriage, Magic, and Solitaire, by David B. Leep and Gerry Myerson, The American Mathematical Monthly 106 (5) pp. 419–429, 1999. - Professional Development of Mathematics Teachers, by H. Wu, Notices of the American Mathematical Society 46 (5) pp. 535–541, 1999. - Mathematics Today 35 (4) pp. 118–122, 1999 contains three short articles under the heading Mathematics and Dyslexia. - Difficulties in Knowledge Integration: Revisiting Zeno’s Paradox with Irrational Numbers, by Irit Peled and Sara Hershkovitz, International Journal of Mathematical Education in Science and Technology 30 (1) pp. 39–46, 1999. - Volume 83 Issue 498

An update of the four-color problem, by Robin Thomas, Notices of the American Mathematical Society 45 (7) pp. 848–859, 1998. - Reflections on reflection in a spherical mirror, by Peter M. Neumann, American Mathematical Monthly 105(6) pp. 523–28, 1998. - Most-perfect pandiagonal magic squares, by Kathleen Ollerenshaw and David S. Bree, Mathematics Today 34 (5) pp. 139–143, 1998. - Aspects

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Soundoff: A Case against Computer Symbolic Manipulation in School Mathematics Today

The National Council of Teachers of Mathematics and leaders in mathematics education must move vigorously to build a consensus for acceptance of the Curriculum and Evaluation Standards (NCTM 1989). One important assumption of the Curriculum and Evaluation Standards is that all students should use computers and graphing calculators on a regular basis in school mathematics. The symbol-manipulating ability of such computer algebra systems (CAS) as the IBM Math Exploration Tool Kit, Mathematics™, and Derive™ can be used today in school mathematics to do algebra. However, we take exception to the use of computer symbol manipulation in school mathematics today for two important reasons.

Primary Mathematics Today. By E.M. Williams and Hilary Shuard. Pp. x, 462. £5. 1970. (Longman.)

Primary Mathematics Today. By E.M. Williams and Hilary Shuard. Pp. x, 462. £5. 1970. (Longman.)

Mathematics Today, the Dartmouth Conference: New Directions in Mathematics . A conference, arranged by John G. Kemeny and Robin Robinson, and held at Dartmouth College in November 1961. Robert W. Ritchie, Ed. Prentice-Hall, Englewood Cliffs, N. J., 1963. iv + 124 pp. Illus. $6.60.

Mathematics Today, the Dartmouth Conference: <i>New Directions in Mathematics</i> . A conference, arranged by John G. Kemeny and Robin Robinson, and held at Dartmouth College in November 1961. Robert W. Ritchie, Ed. Prentice-Hall, Englewood Cliffs, N. J., 1963. iv + 124 pp. Illus. $6.60.

Mathematics Today, the Dartmouth Conference: New Directions in Mathematics . A conference, arranged by John G. Kemeny and Robin Robinson, and held at Dartmouth College in November 1961. Robert W. Ritchie, Ed. Prentice-Hall, Englewood Cliffs, N. J., 1963. iv + 124 pp. Illus. $6.60.

Mathematics Today, the Dartmouth Conference: <i>New Directions in Mathematics</i> . A conference, arranged by John G. Kemeny and Robin Robinson, and held at Dartmouth College in November 1961. Robert W. Ritchie, Ed. Prentice-Hall, Englewood Cliffs, N. J., 1963. iv + 124 pp. Illus. $6.60.

Mathematics Today. By E. E. Biggs and H. E. Vidal. Introductory Course: Part 1, The Tools of Mathematics. Pp. 336, 7s. 6d. Part 2, Mathematics in Action. Pp. 288. 6s. 6d. Answers to each part 1s. 6d. 1955. (Ginn)

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Mathematics Today. III. Largest and Smallest. By E. E. Biggs and H. E. Vidal. Pp. 193. 5s. 6d. 1952. (Ginn)

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Mathematics To-day. II. By E.E. Biggs and H.E. Vidal. Pp. 358. 8s. 6d. 1952. (Ginn)

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School Mathematics Today and Tomorrow: Presidential Address to the Mathematical Association, April 9, 1953

School Mathematics Today and Tomorrow: Presidential Address to the Mathematical Association, April 9, 1953

The Teaching of College Mathematics Today

The Teaching of College Mathematics Today