Pure and Applied Mathematics Journal

| Peer-Reviewed |

Region Mathematics-a New Direction in Mathematics: Part-2

Received: 23 March 2016    Accepted: 13 April 2016    Published: 03 May 2016
Views:       Downloads:

Share This Article

Abstract

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.

DOI 10.11648/j.pamj.20160503.12
Published in Pure and Applied Mathematics Journal (Volume 5, Issue 3, June 2016)
Page(s) 60-76
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Onteger, Prime Object, Imaginary Object, Complex Object, Compound Number, Region Geometry

References
[1] Althoen, S. C. and Kugler, L. D.: When Is R2 a Division Algebra? American Math. Monthly. Vol. 90. 625-635 (1983)
[2] Artin, Michael.: Algebra. Prentice Hall, New York. (1991)
[3] Biswas, Ranjit.: Birth of Compound Numbers. Turkish Journal of Analysis and Number Theory. Vol. 2(6). 208-219 (2014)
[4] Biswas, Ranjit.: Region Algebra, Theory of Objects & Theory of Numbers. International Journal of Algebra. Vol. 6(8). 1371–1417 (2012)
[5] Biswas, Ranjit.: Calculus Space. International Journal of Algebra. Vol. 7(16). 791–801 (2013)
[6] Biswas, Ranjit.: Region Algebra. Information. Vol. 15(8). 3195-3228 (2012)
[7] Biswas, Ranjit.: “Theory of Numbers” of a Complete Region. Notes on Number Theory and Discrete Mathematics. Vol. 21(3) 1-21 (2015)
[8] 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)
[9] 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)
[10] 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)
[11] Biswas, Ranjit.: Region Mathematics ̶ A New Direction In Mathematics: Part-1. Pure and Applied Mathematics Journal (to appear).
[12] Copson, E. T.: Metric Spaces. Cambridge University Press (1968)
[13] Dixon, G. M.: Division Algebras: Octonions Quaternions Complex Numbers and the Algebraic Design of Physics. Kluwer Academic Publishers, Dordrecht. (2010)
[14] Herstein, I. N.: Topics in Algebra. Wiley Eastern Limited. New Delhi. (2001)
[15] Jacobson, N.: Basic Algebra I. 2nd Ed., W. H. Freeman & Company Publishers, San Francisco. (1985)
[16] Jacobson, N.: Basic Algebra II. 2nd Ed., W. H. Freeman & Company Publishers, San Francisco. (1989)
[17] Jacobson, N.: The Theory of Rings. American Mathematical Society Mathematical Surveys. Vol. I. American Mathematical Society. New York. (1943)
[18] Loney, S. L.: The Elements of Coordinate Geometry. Part-I, Macmillan Student Edition, Macmillan India Limited, Madras. (1975)
[19] 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)
[20] Rudin, Walter.: Real and Complex Analysis. McGraw Hills Education, India. (2006)
[21] Saltman, D. D.: Lectures on Division Algebras. Providence, RI: Amer. Math. Society. (1999)
[22] Simmons, G. F.: Introduction to Topology and Modern Analysis. McGraw Hill, New York. (1963)
[23] Van der Waerden and Bartel Leendert.: Algebra. Springer-Verlag, New York. (1991)
Author Information
  • Department of Computer Science & Engineering, Faculty of Engineering & Technology, Jamia Hamdard University, Hamdard Nagar, New Delhi, India

Cite This Article
  • APA Style

    Ranjit Biswas. (2016). Region Mathematics-a New Direction in Mathematics: Part-2. Pure and Applied Mathematics Journal, 5(3), 60-76. https://doi.org/10.11648/j.pamj.20160503.12

    Copy | Download

    ACS Style

    Ranjit Biswas. Region Mathematics-a New Direction in Mathematics: Part-2. Pure Appl. Math. J. 2016, 5(3), 60-76. doi: 10.11648/j.pamj.20160503.12

    Copy | Download

    AMA Style

    Ranjit Biswas. Region Mathematics-a New Direction in Mathematics: Part-2. Pure Appl Math J. 2016;5(3):60-76. doi: 10.11648/j.pamj.20160503.12

    Copy | Download

  • @article{10.11648/j.pamj.20160503.12,
      author = {Ranjit Biswas},
      title = {Region Mathematics-a New Direction in Mathematics: Part-2},
      journal = {Pure and Applied Mathematics Journal},
      volume = {5},
      number = {3},
      pages = {60-76},
      doi = {10.11648/j.pamj.20160503.12},
      url = {https://doi.org/10.11648/j.pamj.20160503.12},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.pamj.20160503.12},
      abstract = {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.},
     year = {2016}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Region Mathematics-a New Direction in Mathematics: Part-2
    AU  - Ranjit Biswas
    Y1  - 2016/05/03
    PY  - 2016
    N1  - https://doi.org/10.11648/j.pamj.20160503.12
    DO  - 10.11648/j.pamj.20160503.12
    T2  - Pure and Applied Mathematics Journal
    JF  - Pure and Applied Mathematics Journal
    JO  - Pure and Applied Mathematics Journal
    SP  - 60
    EP  - 76
    PB  - Science Publishing Group
    SN  - 2326-9812
    UR  - https://doi.org/10.11648/j.pamj.20160503.12
    AB  - 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.
    VL  - 5
    IS  - 3
    ER  - 

    Copy | Download

  • Sections