Publications of Dr V N Krishnachandran
The details of publications and other works are organised as follows
A. Thesis
1. "The Topology and Geometry of the Biordered Set of Idempotent Matrices", thesis submitted to University of Kerala for
the award of PhD degree.
The full text of the thesis is available at Shodhganga@INFLIBNET Centre and can be viewed or downloaded from here.
Shodhganga is a repository of PhD theses submitted to various universities in India and is maintained by Information and Library Network
(INFLIBNET) Centre, Gandhinagar which is an Autonomous Inter-University Centre (IUC) of University Grants Commission.
B. Books
1. Lecture Notes in Engineering Mathematics III, Calicut University Central Cooperative Stores Ltd., 2005 (330 pages)
2. Lecture Notes in Probability and Statistics for MCA students of Calicut University.
Available as an electronic file in the PDF format, January 2015 (207 pages).
3. A First Introduction to Number Theory and Cryptography, available as an electronic file in the PDF format, June 2014 (275 pages).
Available at https://sites.google.com/site/vidyaacademymcaextension02e/home/016-First%20Introduction%20to%20Cryptograpy.pdf
4. First Lessons in TeX, available as an electronic file in the PDF format, January 2011 (65 pages).,
Available at https://sites.google.com/site/vidyaacademymca/Home/attachments-i/FirstLessonsinLaTeX.pdf
5. Lecture Notes in Machine Learning, available as an electronic file in the PDF format, July 2018 (226 pages).
6. Manual for RLMCA133/Applied Statistics Lab, available as an e-file in the PDF format here (168 pages) (item added on 26 September 2018).
C. Coursepacks
1. Advanced Engineering Mathematics for M Tech (Embedded Systems) (Calicut University), July 2014.
Available as an electronic file in the PDF format here.
2. MCA103 Discrete Mathematics of APJ Abdul Kalam Technological University, Version 01, August 2016.
Available as an electronic file in the PDF format here.
Note:
A course pack is a compilation of course materials put into one easy-to-access place for students.
Course packs can act as a supplement to a textbook or as a replacement. The Delhi High Court has ruled in
September 2016 that photocopying portions of academic publications to make course packs for
students does not amount to copyright infringement and hence is not illegal in India.
D. Journal papers
1. “Topology of the Semigroup of Singular Endomorphisms” (with K. S. S. Nambooripad), Semigroup Forum, pp. 224-248, 2000.
2. “Geometry of the Biordered Set of Idempotent Endomorphisms” (with K.S.S. Nambooripad), Southeast Asian Bulletin of Mathematics,
Vol. 27, pp. 95-112, 2003.
3. “Strongly Unit Regular Subemigroups of T_X”, Southeast Asian Bulletin of Mathematics, Vol. 31, pp. 269-274, 2007.
4. "Bundle Structure of the Green Classes in M_n(K)", Semigroup Forum (DOI: 10.1007/s00233-011-9314-x), 24 June 2011.
5. "A Pedagogically Significant Approach to Inputting Mathematical Expressions at Runtime in C"
(jointly with Jisha Jose Panackal and Salkala K S), International Journal of Computer Applications (online journal).
A preliminary version of the paper was presented in the International Conference on
Information Systems and Technology, held in MES College of Engineering, Kuttippuram, during 16-17 May 2011.
Available at http://www.ijcaonline.org/proceedings/icist/number1/3256icist011.
E. Conference papers
1. “Bessel Functions via CAS’s” (jointly with P Smitha), International Conference on Mathematical Modelling and Applied Computing (MMASC 2012)
held in Coimbatore Institute of Technology (CIT), Coimbatore, during 11 - 13 July 2012.
2. "More CAS's in Maths Classrooms: An Urgent Imperative” (jointly with Reji C Joy, and Siji K B),
International Conference on Technology Enhanced Education
held in Amrita Viswa Vidyapeethom, Amritapuri Campus, Kollam, Kerala, during 3 - 5 January 2012.
3. "On Sangamagrama Madhava's (c.1350 - c.1425) Algorithms for the Computation of Sine and Cosine Functions"
(jointly with Reji C Joy and Siji K B), International Conference on Computational Engineering Practices and Techniques
held in MES College of Engineering, Kuttippuram - 679573, India, during 25 - 26 November 2010.
4. "On Finite Differences, Interpolation Methods and Power Series Expansions in Indian Mathematics”,
International Conference on Mathematical Modelling and Applications to Industrial Problems (MMIP 2011),
held in National Institute of Technology Calicut, Kerala, India, during 28 – 31 March 2011.
5. "A Note on the Integral Operator" (jointly with Vijitha Mukundan), International Seminar on New Trends in Applications of Mathematics
held at Bharata Mata College, Thrikkakara, during 31 January - 02 February 2011.
6. "Fractional Calculus and Applications", International Seminar on Recent Trends in Topology and Its Applications,
held in St Joseph’s College, Irinjalakuda, Kerala, India, during 19 -21 March 2009.
7. “On the Revival of Triangle Geometry”, National Seminar on Topology, Category Theory, and Their Applications to Computer Science,
held in St. Joseph’s College, Irinjalakuda, during 11 – 13 March 2004.
8. “Topological Regular Semigroups”, National Conference on Algebra & Discrete Mathematics,
held in University of Kerala, Thiruvananthapuram, during 12-14 January 2005.
9. "Quadrics via Semigroups", National Seminar on Recent Trends in Analysis, held in Govt. Victoria College, Palakkad, during March 2007.
Available at https://arxiv.org/abs/0902.4288
10. “Geometry of the Biordered set of Idempotent Endomorphisms : A Preliminary Report”,
15th Annual Conference of Ramanujan Mathematical Society,
held in Ramanujan Institute for Advanced Study in Mathematics, University of Madras, during 5-7 June 2000.
11. “Harnessing Google Sites To Enhance Native And Vernacular Content In The Web: An Experiential Report”
(jointly with Ms. Reji C Joy (Associate Professor), Ms. Siji K B (Assistant Professor) and Ms Salkala K S (Assistant Professor))
Proceedings of the 28th Kerala Science Congress, held at Calicut University Campus during 28 – 30 January 2016, pp. 2225 - 2229.
The complete text of the Proceedings is available here (119 MB).
F. Preprints and unpublished manuscripts
1. “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).
2. “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.
Available at https://arxiv.org/abs/1108.2878 (12 pages).
3. “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).
4. “On Normed Semigroups”, a paper which presents a new definition of a normed semigroup.
Available at https://arxiv.org/abs/1508.03844 (10 pages).
5. “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).
6. “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.
Available at https://arxiv.org/abs/1406.7452 (32 pages).
7. “Yet Another Simple proof of FLT?”, a note exposing the error in a paper (T. Unnikrishnan, “Finding Numbers Satisfying The Condition An + Bn = Cn",
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) .
8. “Basic Linux Commands”, lecture notes for giving a first introduction to the Linux operating system (17 pages).
9. “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).
10. “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 at http://arxiv.org/pdf/1508.05828.pdf
11. “A Catalogue of Elementary Statistical Tests”, a categorised 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).
12. “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).
13. "Where Do the Terms of the Power Series Expansions of Sine and Cosine Functions Come from? Involutes!", an expository paper
(13 pages, 7 figures). Posted in arXiv on 16 October 2016 and available at http://arxiv.org/abs/1610.04825.
G. Slide shows
1. “Almost All about Google Drive”, slides prepared in November 2013 as part of the Internal Faculty Development Programme
of the Department of Computer Applications, Vidya Academy of Science & Technology, Thrissur-680501 (86 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/almost-all-about-google-drive
2. “Why I Love Fractals”, slides used during an invited talk delivered at Ansar Women’s College, Perumpilavu, Thrissur, on 02 December 2014 (70 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/first-introduction-to-fractals
3. “An Introduction to TeX and LaTeX”, a first introduction to TeX and LaTeX providing a flavour of the TeXnical typesetting environment (35 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/an-introduction-to-tex-and-latex.
4. “Technical Writing: Some Guidelines”, slides used during a talk delivered to First Semester M Tech students of
Vidya Academy of Science and Technology, Thrissur - 680501, on 27 July 2015 as part of a Bridge Course of Kerala technological University.
Available at http://www.slideshare.net/PlusOrMinusZero/technical-writing-some-guidelines
5. “Linear Algebra Behind Google Search”, slides used during an invited talk in a National Conference on Recent Trends in Advanced Mathematics at
Vidya Academy of Science & Technology, Thrissur – 680501, held during 02‐04 February 2012 (80 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/linear-algebra-behind-google-search
6. “Free Software: An Introduction”, prepared in December 2009 as part of the Internal Faculty Development Programme of
the Department of Computer Applications, Vidya Academy of Science & Technology, Thrissur-680501 (74 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/an-introduction-to-free-software
7. “Computer Algebra Systems”, slides used during an invited talk in the National Seminar on Applications of Mathematics in Engineering and Technology
held at Rajagiri School of Engineering & Technology on 11-13 March 2005 (88 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/introduction-to-computer-algebra-systems
8. “Pi to a Trillion Digits: How and why”, prepared in October 2009 as part of the Internal Faculty Development Programme of
the Department of Computer Applications, Vidya Academy of Science & Technology, Thrissur-680501 (46 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/pi-to-a-trillion-digits-how-and-why
9. “Slide Presentation Guidelines”, (39 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/slide-presentation-guidelines
(Published on 12 June 2009 and attracted 21,978 views as on 03 September 2015.)
10 "Perfectly Legal Illegal Resources in the Web : catching slumdogs using the net", prepared in March 2009 as part of
the Internal Faculty Development Programme of the Department of Computer Applications,
Vidya Academy of Science & Technology, Thrissur-680501 (68 slides).
11 “On Sangamagrama Madhava's (c.1350 - c.1425) Algorithms for the Computation of Sine and Cosine Functions” (80 slides).
Available at
12 “Fractional Calculus and Applications” (79 slides).
Available at http://www.slideshare.net/PlusOrMinusZero/fractional-calculus-and-applications.
13 “On Finite Differences, Interpolation Methods and Power Series Expansions in Indian Mathematics” (46 slides).
Available at
14. "Presenting Vidya Mobile (An Android app for VAST)", the slideshow presented during the launching of Vidya Mobile,
an Android app for Vidya Academy of Science & Technology, on 20 January 2017 (43 slides).
Available at: http://www.slideshare.net/PlusOrMinusZero/preseenting-vidya-mobile
(Entry added on 02 February 2017)
H. Editorial work
1. Edited the Souvenir of the 22nd Annual ISTE State Convention held on 19 November 2011 at Vidya Academy of Science and Technology,
Thrissur – 680501.
2. Compiled, edited and typeset in LaTeX the “Compendium of Abstracts EPSICON 2010”, a compilation of the abstracts of papers presented in the
International Conference on Power, Control, Signals and Computation organised by the Department of Electrical and Electronics Engineering,
Vidya Academy of Science & Technology, Thrissur – 680501, during 4 – 6 January 2010.
Available here: EPSCICON 2010 Compendium of Abstracts
3. Helped (jointly with Ms. Reji C. Joy and Ms Jyothy P. R.) to compile, design and typeset the College Calendar and Diary for 2015-16 and for 2016-17.
Available here: College Calendar and Diary 2015 - 16, College Calendar and Diary 2016 - 17
I. Popular writing
Have created more than 270 articles in Wikipedia on a variety of topics. Many of them are in the form of short notes, however there are a few longer ones.
a) The following are some of the recently created articles:
b) The following is a list of the titles of some of the longer articles. Since their creations, many Wikipedians might have contributed to develop these
articles to their present forms.
1. Aryabhata’s sine table
2. Bhargava cube
3. Crank of a partition
4. Dr. A P J Abdul Kalam Technological University
5. Geometric cryptography
6. K. S. S. Nambooripad
7. Madhava series
8. Mulabhadra
9. Napoleon points
10. Plausible reasoning
11. Pulijanmam
12. Ramanujan's ternary quadratic form
13. Ramavarmapuram
14. Special classes of semigroups
15. Spline wavelet
16. Sriramachakra
17. Transcomputational problem
18. Vararuchi
19. Weyr canonical form
20. Zak transform
c) The full list of articles can be viewed in the Wikipedia page here
Note:
Have been using the user id Krishnachandranvn to sign in to Wikipedia and to edit and create articles. Wikipedia has a page titled "Wikipedia:List of Wikipedians by article count". As on 02 February 2017, the user id Krishnachandranvn appears at Serial Number 1965 in that list. The list is valiable here.
J. Websites created
1. Designed, created and developed the website of the Department of Computer Applications, Vidya Academy of Science & Technology, Thrissur – 680501.
The website is now collectively maintained by the staff and faculty of the Department.
The URL of the website is https://sites.google.com/site/vidyaacademymca/ .
2. Designed, created and developed a website titled “Lingering Shadows” which presents a collection of 55 poems by Mr T K Jayanthan,
an occasional poet of the older generation.
The URL of the site is https://sites.google.com/site/tkjayanthan.
3. Designed, created and developed a website titled “Malayalam in computers” explaining some of the methods for
preparing documents in Malayalam using a computer.
The URL of the site is https://sites.google.com/site/malayalamincomputer/.
K. Mobile app
1. Designed, created and developed a comprehensive mobile app christened "Vidya Mobile" as a mobile platform for Vidya Academy of Science & Technology.
The app is available for download and installation in Google Play Store at the following URL:
https://play.google.com/store/apps/details?id=com.vidyamobile.latha.vidyaacademy01&hl=en
(Entry added on 02 Feb 2017.)
L. Work in progress
1. “From Brahmagupata to Bhargava via Gauss”, an expository paper on the mathematics of Manjul Bhargava (completed 35 pages)
2. “A lowbrow introduction to Hyperelliptic Cryptography”, a paper attempting to present an elementary introduction to
hyperelliptic cryptography (completed 21 pages)
3. “A Collection of Wavelets” (completed 31 pages)
Last updated on 26 September 2018