Pure and Applied Mathematics Journal
Volume 5, Issue 3, June 2016, Pages: 39-59
Received: Mar. 23, 2016;
Accepted: Apr. 13, 2016;
Published: Apr. 25, 2016
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Ranjit Biswas, Department of Computer Science & Engineering, Faculty of Engineering & Technology, Jamia Hamdard University, Hamdard Nagar, New Delhi, India
In this paper the author introduces a new direction in Mathematics called by “Region Mathematics” to the world mathematicians, academicians, scientists and engineers. The purpose of developing ‘Region Mathematics’ is not just for doing a generalization of the existing rich volume of classical Mathematics, but it has automatically happened so by this work. To introduce the ‘Region Mathematics’, we begin here with introducing three of its initial giant family members: Region Algebra, Region Calculus and Multi-dimensional Region Calculus. Three more of its initial giant family members: Theory of Objects, Theory of A-numbers (Number Theory) and Region Geometry will follow in the sequel work. The development of the subject ‘Region Mathematics’ is initiated from its zero level for all its initial giant family members. The subject is expected to grow very fast with time to take its own shape, and it will surely cater to all branches of Science, Engineering, and others wherever an element of mathematics needs to be done. With the introduction of Region Mathematics, all existing branches of mathematics will get wide horizontal shifts in the academic universe of science, mathematics, engineering, social science, statistics, etc. with many more alternative new approaches and new thoughts.
Region Mathematics-a New Direction in Mathematics: Part-1, Pure and Applied Mathematics Journal.
Vol. 5, No. 3,
2016, pp. 39-59.
Althoen, S. C. and Kugler, L. D.: When Is R2a Division Algebra?. American Math. Monthly. Vol. 90. 625-635 (1983).
Artin, Michael.: Algebra. Prentice Hall, New York. (1991)
Biswas, Ranjit.: Region Algebra, Theory of Objects & Theory of Numbers. International Journal of Algebra. Vol. 6(8). 1371–1417 (2012).
Biswas, Ranjit.: Calculus Space. International Journal of Algebra. Vol. 7(16). 791–801 (2013).
Biswas, Ranjit.: Region Algebra. Information. Vol. 15(8). 3195-3228 (2012).
Biswas, Ranjit.: “Theory of Numbers” of a Complete Region. Notes on Number Theory and Discrete Mathematics. Vol. 21(3) 1-21 (2015).
Biswas, Ranjit.: Region Mathematics ̶ A New Direction In Mathematics: Part-2. Pure and Applied Mathematics Journal (communicated).
Biswas, Ranjit.: Is ‘Fuzzy Theory’ An Appropriate Tool For Large Size Problems ?. in the book-series of SpringerBriefs in Computational Intelligence. Springer. Heidelberg. (2016)
Biswas, Ranjit.: Is ‘Fuzzy Theory’ An Appropriate Tool For Large Size Decision Problems ?, Chapter-8 in Imprecision and Uncertainty in Information Representation and Processing, in the series of STUDFUZZ. Springer. Heidelberg. (2016)
Beachy, J. A., and Blair, W. D.: Abstract Algebra. 2nd Ed., Waveland Press, Prospect Heights, Ill. (1996)
Bourbaki, Nicolas.:Elements of Mathematics: Algebra I.New York: Springer-Verlag. (1998)
Copson, E. T.: Metric Spaces. Cambridge University Press (1968)
Dixon, G. M.: Division Algebras: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics. Kluwer Academic Publishers, Dordrecht. (2010)
Ellis, G.: Rings and Fields. Oxford University Press. (1993)
Herstein, I. N.: Topics in Algebra. Wiley Eastern Limited. New Delhi. (2001)
Hungerford, T., Algebra, Graduate Texts in Mathematics, Vol. 73, Springer-Verlag, New York, 1974.
Jacobson, N.: Basic Algebra I. 2nd Ed., W. H. Freeman & Company Publishers, San Francisco. (1985)
Jacobson, N.: Basic Algebra II. 2nd Ed., W. H. Freeman & Company Publishers, San Francisco. (1989)
Jacobson, N.: The Theory of Rings. American Mathematical Society Mathematical Surveys. Vol. I. American Mathematical Society. New York. (1943)
Lam, T. Y.: Exercises in Classical Ring Theory, Problem Books in Mathematics, Springer-Verlag, New York. (1995)
Lang, Serge.: Undergraduate Algebra. (3rd ed.). Berlin, New York: Springer-Verlag. (2005)
Matsumura, Hideyuki.: Commutative Ring Theory. Cambridge University Press, Cambridge. (1986)
Pierce, Richard S.: Associative algebras. Graduate Texts in Mathematics. Studies in the History of Modern Science. Springer-Verlag. Berlin. (1982)
Reyes, Mitchell.: The Rhetoric in Mathematics: Newton, Leibniz, the Calculus, and the Rhetorical Force of the Infinitesimal. Quarterly Journal of Speech. Vol. 90. 159-184 (2004).
Rudin, W alter.: Real and Complex Analysis. McGraw Hills Education, India. (2006)
Saltman, D. D.: Lectures on Division Algebras. Providence, RI: Amer. Math. Society. (1999)
Simmons, G. F.: Introduction to Topology and Modern Analysis. McGraw Hill, New York. (1963)
Van der Waerden and Bartel Leendert.: Algebra. Springer-Verlag, New York. (1991)