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Preprints of papers published in the online repository "arXiv"
“Manifold Structures in Regular Irreducible Algebraic Monoids”, a study of regular irreducible algebraic monoids over the field of complex numbers equipped with the euclidean topology (12 pages). Available HERE and in arXiv.org. (14 August 2011) Available in Internet Archive also.
“On Normed Semigroups”, a paper which presents a new definition of a normed semigroup (10 pages). Available HERE and in arXiv.org. (16 August 2015) Available in Internet Archive also.
“Geometry of the Set of Real Square Roots of the Matrices ± I_2”, a paper which shows that the set of real square roots of I_2 is a hyperboloid of one sheet and obtains several other similar results (32 pages). Available HERE and in arXiv.org. Available in Internet Archive also.
“Mystery of the 18th Elephant Solved,” a popular article that attempts to explain the mystery behind an 18th elephant that appears in many popular legends involving the division of a herd of 17 elephants into groups in the ratio 1/2:1/3:1/9 (4 pages). Available HERE and in arXiv.org. Available in Internet Archive also.
"Where Do the Terms of the Power Series Expansions of Sine and Cosine Functions Come from? Involutes!", an expository paper (13 pages, 7 figures). Available HERE and in arXiv.org. Available in Internet Archive also.
"Differential Equations: A Historical Refresher", a talk delivered in an ISTE sponsored Faculty Development Programme on Applications of Advanced Mathematics in Engineering held in Vidya Academy of Science & Technology during 27.11.2017 - 01.12.2017 (24 pages). Available HERE and in arXiv.org.
"Quadrics via Semigroups", National Seminar on Recent Trends in Analysis, held in Govt. Victoria College, Palakkad, during March 2007.Available HERE and in arXiv.org. Available in Internet Archive also.
"Ramanujan in Computing Technology", a paper presented in the National Conference on Advances in Computing Technology 2020 (NC-ACT 2020) organised by Department of Computer Applications, Vidya Academy of Science and Technology, Thrissur - 680501, Kerala, India during 4 - 5 December 2020 (32 pages). Available HERE and in arXiv.org.
"On Śankara Varman's (correct) and Mādhava's (incorrect) values for the circumferences of circles", a paper that examines what computational procedures Śankara Varman (1774-1839) and Sangamagrama Mādhava (c. 1340 - 1425), astronomer-mathematicians of the Kerala school, might have used to arrive at their respective values for the circumferences of certain special circles. Available in arXiv.org. (Uploaded on 18 May 2024)
"On Mādhava and his correction terms for the Mādhava-Leibniz series for π", a paper that reexamines the life of Sangamagrāma Mādhava, the founder of the Kerala school of astronomy and mathematics, in the light of modern historical scholarship and also presents a critical study of the three enigmatic correction terms, attributed to Mādhava, for obtaining more accurate values of π while computing its value using the Mādhava-Leibniz series. Available in arXiv.org. (Uploaded on 18 May 2024)
"Samgamagrāma Mādhava: An Updated Biography", a paper that presents an updated biography of Samgamagrāma Mādhava incorporating viewpoints expounded by scholars in the recent past and collecting together in one place more details about his works culled from recent researches into his contributions to mathematics and astronomy. Available in arXiv.org. (Uploaded on 22 August 2024)
"On the computation of the arcsin function in the Kerala school of astronomy and mathematics". This paper examines how the mathematicians and astronomers of the Kerala school tackled the problem of computing the values of the arcsin function. Four different approaches are discussed all of which are found in Nilakantha Somayaji's (1444 - 1545 CE) Tantrasangraha and the roots of all of which can be traced to ideas originally articulated by Sangamagrama Madhava (c. 1340 - 1425 CE): (i) a simple method when the argument is small; (ii) an iterative method when the argument is small; (iii) a method based on a lookup table; (iv) a method when the argument is large. Available HERE and in arXiv.org (Uploaded on 14 November 2024.)
Preprints of other papers
“An Overview of Optimisation Techniques”, an expository paper on some of the well known problems in optimization theory presented as a talk at Rajiv Gandhi Institute of Technology, Kottayam, on 03 March 2005, as part of a short-term course on “Decision Support Systems – Tools and Techniques” (25 pages). Available HERE.
“Nambooripad's Theory of Cross-connections”, an outline of the theory of cross-connections developed by K. S. S. Nambooripad as a generalisation to arbitrary regular semigroups of Grillet's theory of cross-connections (16 pages). Available HERE.
“Homotopy Properties of the Space of Idempotent Endomorphisms”, a paper which studies the homotopy properties of the space of idempotent endomorphisms of a finite dimensional real or complex vector space (18 pages). Available HERE.
“Yet Another Simple proof of FLT?”, a note exposing the error in a paper (T. Unnikrishnan, “Finding Numbers Satisfying The Condition A^n + B^n = C^n", IOSR Journal of Mathematics, Jul-Aug 2013) purportedly carrying a proof of the well known Fermat’s Last Theorem (FLT) and also the dubiousness of the journal in which the paper was published (5 pages). Available HERE.
“Basic Linux Commands”, lecture notes for giving a first introduction to the Linux operating system (17 pages). Available HERE.
“Google sites: Hands on!”, notes used for a presentation on Google Sites in a Two-day workshop (christened Chip-to-Net) organised by the Department of Computer Applications, Vidya Academy of Science & Technology, Thrissur – 680501, for the students of neighbouring arts and science colleges on 8 - 9 January 2015 (22 pages). Available HERE.
“A Catalogue of Elementary Statistical Tests”, a categorized catalogue of elementary statistical tests and relevant tables based on Probability and Statistics for Engineers (Third Edition) by Irwin Miller and John E Freund, Prentice Hall of India intended for the use of undergraduate engineering students and teachers, prepared in October 1992 (10 pages). Available HERE.
“A Ladder Problem”, a note giving a detailed analysis of the problem of determining the height to which a person can climb a ladder (7pages). Available HERE.
"Excelling in Errors", a compilation of some of the computational errors that lie hidden in the much popular Excel software (4 pages). Available HERE.
"Of a system in which doubling the cause doubles the effect!", a paper discussing the solutions of the functional equation f(2x) = 2f(x). (4 pages). Available HERE.
"Plausible Reasoning" (8 pages), a very concise summary of a two-volume book titled "Mathematics and Plausible Reasoning" authored by George Polya which presents plausible reasoning as a way of generating new mathematical conjectures. Available HERE.
"SVM computation: Pedagogical examples", a paper which illustrates the support vector machine (SVM) computations with actual numerical values using small data sets and hand computations (13 pages). Available HERE.
"GeoGebra commands for 2D geometrical constructions", a paper containing brief descriptions of GeoGebra commands for 2D geometrical constructions and illustrations of the applications of these commands in producing beautiful diagrams in triangle geometry (35 pages). Available HERE.
"Free software: An introduction" (10 pages). Available HERE.
"Determining Whether Meat Samples Come from Dead or Slaughtered Animals Using Machine Learning" (jointly with Dr V N Vasudevan, College of Veterinary and Animal Sciences, Mannuthy, Thrissur - 680651) (10 pages). Available HERE.
"An algorithm to find the largest rectangle in a union of rectangles" (7 pages). Available HERE.
"English translations of vākya-s in Madhava's sine table" (9 pages), uploaded on 8 Aug 2024. Available HERE.
"A note on Brahmagupta solution to Heronian triangle problem" (6 pages), uploaded on 26 August 2024. Available HERE.
"'കാൽക്കുലസിന്റെ കേരളീയ രീതിയും രാമാനുജന്റെ ഗണിത സംഭാവനകളും' എന്ന അബദ്ധപ്പഞ്ചാംഗം" (9 pages), uploaded on 11 January 2025. Comments on article by Dr. Unnikrishnan Thekkeppatt in the January 2025 issue of the Malayalam monthly Bhashaposhini. Available HERE. Submitted via email on 11 January 2025 to Bhashaposhini for publication in the journal. Covering note available HERE. The article as published in Bhashaposhini is available HERE.
"ഇനിയും മങ്ങാത്ത ഓർമകൾ" (2 pages), uploaded on 14 July 2025. Reminiscences about studying in L. P. School, Perincheri to be published in a Smaranika to be brought out by the school. Available HERE.
*Last update on 14 July 2025.
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