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Region Mathematics-a New Direction in Mathematics: Part-2
Pure and Applied Mathematics Journal
Volume 5, Issue 3, June 2016, Pages: 60-76
Received: Mar. 23, 2016; Accepted: Apr. 13, 2016; Published: May 3, 2016
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Ranjit Biswas, Department of Computer Science & Engineering, Faculty of Engineering & Technology, Jamia Hamdard University, Hamdard Nagar, New Delhi, India
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This is sequel to our earlier work [11] in which we introduced a new direction in Mathematics called by “Region Mathematics”. The ‘Region Mathematics’ is a newly discovered mathematics to be viewed as a universal mathematics of super giant volume containing the existing rich volume of mathematics developed so far since the stone age of earth. To introduce the ‘Region Mathematics’, we began in [11] by introducing three of its initial giant family members: Region Algebra, Region Calculus and Multi-dimensional Region Calculus. In this paper we introduce three more new topics of Region Mathematics which are : Theory of Objects, Theory of A-numbers and Region Geometry. Several new kind of Numbers are discovered, and consequently the existing ‘Theory of Numbers’ needs to be updated, extended and viewed in a new style.
Onteger, Prime Object, Imaginary Object, Complex Object, Compound Number, Region Geometry
To cite this article
Ranjit Biswas, Region Mathematics-a New Direction in Mathematics: Part-2, Pure and Applied Mathematics Journal. Vol. 5, No. 3, 2016, pp. 60-76. doi: 10.11648/j.pamj.20160503.12
Copyright © 2016 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Althoen, S. C. and Kugler, L. D.: When Is R2 a Division Algebra? American Math. Monthly. Vol. 90. 625-635 (1983)
Artin, Michael.: Algebra. Prentice Hall, New York. (1991)
Biswas, Ranjit.: Birth of Compound Numbers. Turkish Journal of Analysis and Number Theory. Vol. 2(6). 208-219 (2014)
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.: Is ‘Fuzzy Theory’ An Appropriate Tool For Large Size Problems?. in the book-series of Springer Briefs 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)
Biswas, Ranjit.: Introducing ‘NR-Statistics’: A New Direction in “Statistics”. Chapter-23 in "Generalized and Hybrid Set Structures and Applications for Soft Computing". IGI Global. USA. (2016)
Biswas, Ranjit.: Region Mathematics ̶ A New Direction In Mathematics: Part-1. Pure and Applied Mathematics Journal (to appear).
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)
Herstein, I. N.: Topics in Algebra. Wiley Eastern Limited. New Delhi. (2001)
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)
Loney, S. L.: The Elements of Coordinate Geometry. Part-I, Macmillan Student Edition, Macmillan India Limited, Madras. (1975)
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, Walter.: 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)
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