Mini School on Philosophy of Mathematics

21.12.2019 3p.m. to 5 p.m. First Lecture    Click here for the Video               Click Here for the Presentation

28.12.2019 3 p.m. to 5 p.m. Second Lecture  Click here for the Video         Click Here for the Presentation

4.1.2020 3 p.m. to 5 p.m. Third Lecture       Click here for the Video            Click Here for the Presentation

11.01.2020 3 p.m. to 5 p.m. Fourth Lecture  Click here for the Video            Click Here for the Presentation

Lecture on the History of Astronomy and Mathematics in Kerala (Malayalam)   Click here for Video

Lecture on Life and Work of Ramanujan

on 22.12.2019 at 10 a.m Life and Work of Ramanunjan ( Malayalam), National Mathematics Week Celebrations, RSC and Planetarium, Kozhikode     Click here for Video

You Tube Channel: Ramachandran P.T.    Link

WhatsApp Groups run by me:

GANITHAM,  GANITHAM2 & GANITHAM3 : For University Level Mathematics     Click here for details

GANITHAM DEGREE : For UG level mathematics                 Click here for details

APPLIED MATHEMATICS : For Applied and Engineering Mathematics   Click here for details

GANITHA KAIRALI : For School Level mathematics                  Click here for details

GANITHA CHARITHRAM: For History of Mathematics      Click here for details

GANITHA DARSANAM: For the Philosophy of Mathematics      Click here for details

GANITHA SOUHRUDAM: For all lovers of Mathematics              Click here for details

FB Groups:

Ganitham        FB Link

Ganitha Charithram  FB Link

Telegram Groups :


Ganitha Charithram

Discord Group:


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28     53     08     41     24     57     12     37

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Regional Mathematical  Olympiad  2019



Topology I   2014

 2013 Second and Fourth Semester Full


1.Why 0! is taken as 1?

2. What are the positive integers which cannot be written as a sum of two or more consecutive positive integers?

Post Graduate Level


Question 1. Determine all topologies on a set { a,b,c} with 3 elements   Click here for Answer

Question 2. Give an example of a connected topological space which is totally disconnected?

Question3. Prove or disprove: The closure of an open ball in any metric space  is the corresponding closed ball.

Question 4. Prove or disprove: :Let f be a real valued continuous function on the real line. Then the image of any connected set under f is connected

Question 5. Prove or disprove: The intersection of any two dense subsets of a topological space is dense.

Question 6. Prove or disprove: The set of all rational numbers with the subspace topology (from the real line with the usual topology) is locally compact.

Question 7. Prove or disprove: The set of all rational numbers with the subspace topology (from the real line with the usual topology) is totally disconnected.

Question 8. Give an example of a first countable space which is not second countable.

Question 9. Give an example of a countable topological space which is not first countable.

Question 10. Give an example of a connected space which is not locally connected

Question 11. Give an example of a locally connected space which is not connected

Question 12. Prove that the complex plane cannot be made disconnected by deleting a countable number of points.

Question 13. Prove that any open subset of the real line is a countable disjoint union of open intervals.

Question 14.Give an example of a continuous function which is not open

Question 15.Prove that a bijection is open if and only if it is closed.

Question 16. Prove or disprove: A function is open if and only if it is closed

Question 17.Prove or disprove:A quotient map is open and closed

Question 18.Prove or disprove:A quotient map is open or closed.

Question 19. Does there exist an uncountable discrete subspace of the real line? Substantiate your claim?


Question 1. Give an example of an infinite  group in which every element is of finite order?

Question 2. Prove or disprove: A normal subgroup of a normal subgroup is a normal subgroup

Question3. Give an example of a commutative ring with an identity having  a sub ring with a different identity?

Question 4. Given an arbitrary nonempty set G, can you make it a group?

Question 5. Does there exist a field with 4 elements? If the answer is yes, give an example? If the answer is no, prove your claim?


Question 1. Give an example of a real valued discontinuous function on the real line which maps connected sets to connected sets?

Question 2. Which is bigger: e to the power of pi or pi to the power of e?

Question 3. Give an example of an uncountable subset of the real line with measure 0 ?

Question 4. Give an example of a continuous function which is not differentiable?


1. Prove that the cardinality of the real line and the cardinality of the complex plane are equal?

2. Prove that the set of all algebraic numbers is countable.

3. Give an example of two well ordered sets having the same cardinality which are not order isomorphic?

4. How many symmetric relations are there on a set with n elements?

5. Give an example of a function from a set to itself which is one to one but not onto?

5. Give an example of a function from a set to itself which is onto but not one to one?


Kerala School of Mathematics and Related Works


            Ramachandran P.T., Jyothisasthra Nireekshanathinte Keraleeya Parambaryam ., Sasthrakeralam, December 2019, 65-67

  • Ramachandran P.T.Pi and the Kerala School of Mathematics , Kerala School of Mathematics: Trajectories and Impact, N.K. Sundaresan (Ed.), Ganga Books, Calicut (2014) 112-125 ISBN 978-81-931168-0-7
  • Ramachandran P.T., Ariyapedaatha Ganithasastra Parambaryam,(Malayalam) 47 th Sate Conference Souvenir, Kerala Sastra Sahithya Parishad,  2010, 38-39
  • Ramachandran P.T.,Ganitam Malaylathil,( Malayalam) Kavana Koumudi, Vol.16. Issue. 2 November- January 2014, 53-62
  • Ramachandran P.T., Madhavanum Sishyarum, Sasthrakeralam, December 2016


XXXIII  on the Hindu Quadrature of the circle and the infinite series of the proportion of the circumference to the diameter exhibited in the four Sastras, the Tantra Sangraham, Yucti Bhasha, Carona Padhati and Sadratnamala By CHARLES M. WHISH, Esq., of the Hon. East-India Company’s Civil Service on the Madras Establishment.(Communicated by the MADRAS LITERARY SOCIETY AND AUXILIARY ROYAL ASIATIC SOCIETY).Read the 15th of December 1832.

Sarma, K.V. :  History of the Kerala School of Hindu Astronomy,  Vishvesharanand Institute, Hoshiarpur 1972.

Sphutachandrapthi (Computation of True Moon) of Sangamagrama Madhava: (Ed.) K.V. Sarma, Vishvesharanand Institute, Hoshiarpur 1973

Venvaroha of Sangamagrama Madhavan with Commentary in Malayalam by Achyutha Pisharody : (Ed.) K.V. Sarma, Sanskrit College, Thrippunithura (1956)

Iyotirmimasa by Nilakantha Somayaji Ed. By K.V. Sarma V. Inst. Hoshiarpur 1977.

Aryabhatiya – Bhashya by Nilakanta Somayaji Ed. by K. Samasiva Sastri & S. Kunjan Pillai, Kerala University 3.Vols. 1930, 1931, 1957.

Aryabhatiya by Aryabhata : Cr. Edn with Translation and notes by K.S. Shukla and K.V. Sarma, Indian National Science Academy, New Delhi, 1976.

Goladipika by Paramesvara Ed. with autocom. And Tr. by K.V. Sarma, Adayar LibraryMadras1957.

Laghubhaskariya – Vyakhya by Sankaranarayana Ed. by P.K. Narayana Pillai,Trivandrum1949.

Observational Astronomy inIndia– K.V. Sarma,CalicutUniversitySanskrit Series No.5, Dept. of Sanskrit,UniversityofCalicut1990.

Mathematics in India: Kim Plofker,Princeton University Press, Princeton 2009

Geometry in Ancient and Medieval India:    T.A. Sarasvati Amma,Motilal Banarsidass Pub. Pvt Ltd. Delhi 1979

Ganitayukthibhasha:Jyeshtadeva, ( K.V. Sarma Ed.)

Yukthibhasha Part I ( Malyalam):  Rama Varma (Maru) Tampuran and A.R. Akilesvara Ayyar Mangalodayam, Trichur (1948)

Ganita Yukthibhasha of Jyeshtadeva : K.V. Sarma ( Ed.), Hindustan Book Agency, New Delhi, 2008


Ganita-Yukti-Bhāṣā (Rationales in Mathematical Astronomy) of Jyeṣṭhadeva: Volume I: Mathematics Volume II: Astronomy: K.V. Sarma,K. Ramasubramanian,M. D. Srinivas&M. S. Sriram, Springer-Verlag London 2008 Hardcover ISBN 978-1-84882-072-2


Proceedings of the International Seminar and Colloquim on 1500 Years of Aryabhateeyam, Kerala Sastra Parishad, Kochi( 2002) ISBN  81-88033-29-4


Studies in the History of Indian Mathematics: Ed. C.S. Seshadri, Hindustan Book Agency, New Delhi (2010) ISBN  978-93-80250-06-9


The History of Ancient Indian Mathematics: C.N. Srinivasiengar, The World Press Private Ltd Calcutta (1967)


The First Textbook of Calculus: Yuktibhasa, P.P. Divakaran, Jour.Ind.Phil. 35,417-443,2007


The Crest of the Peacock: Non-European Roots of Mathematics, George Gheeverghese Joseph, Princeton University Press, Princeton and London (2000)


Kerala Mathematics: Its History and Possible Transmission to Europe, (Ed.) George Gheeverghese Joseph, B.R. Publishing Co. Delhi (2009)


A Passage to Infinity: Medieval Indian Mathematics from Kerala and its Impact, George Gheeverghese Joseph, Sage, New Delhi (2009) ISBN  978-81-321-0168-0 (HB)


Ganitakeralam (Malayalam), Indological Trust, Calicut-673005 (2011)


A Commentary of Tantrasangraha in Keralabhasha: Kriyakalapa- Engish Translation with Notes, Venkateswara Pai R, K. Mahesh & K Ramasubrahmanian, Indian National Science Academy, New Delhi 2010

The Mathematics of  India, Concepts, Methods, Connections, P.P.Divakaran, Hindustan Book Agency ISBN 978-93-86279-69-9

Works of Madhava of Sangamagrama

1. Golavada

2. Madhyajyanayanaprakara

3 Mahajyanayanaprakara

4. Lagnaprakarana

5. Venvaroha (Published)

6. Sphutacandrapti (c.1400 C.E.) (Published)

7. Aganita-grahacara

8. Chandravakyani


Works of Paramesvara


1. Gokdipika (I), Trivandrum Sanskrit series,

2. Gokdipika (II) Ed. K.V. Sarma,

3. Grahanamandana – in two versions,

4.  Grahanyayadipika,

5.  Vakyakarana,

6. Bhatadipika (Commentary on Aryabhatiya Ed. Kern, Leyden in 1874.

7. Karmadipika (Commentary a Mahabhaskariya),

8.  Laghumanasa Vyakhya,

9. Vivarana on Suryasiddhanta,

10. Vivarana on Lilavati,

11. Vritti on his own Gokdipika, (l)

Also several works on Astrology like Acharasamgraha, commentaries on Govinda’s Muhurta ratna and  Sripathi’s Jatakapaddhati.


Works of Neelakanta


1. Aryabhateeya Bhashya

2. Tantrasangraha

3. Jyotirmimamsa


Works of Jyeshtadeva


1. Yukthibhasha (Malayalam)


Works of  Trikudaveli Sankara Variyar


1. Kriyakramakari

2. Kriyakalapa




The Department is a constituent of the School of Mathematical and Computational Sciences. Presently it is on the top floor of the Physics-Mathematics Building in The Science Block. The new building for the School of Mathematical and Computational Sciences is under construction in the Science Block.

Faculty Members

Dr. Preethi  Kuttipulackal (, Mob: 9562475245)  Head

Dr. Raji Pilakkat (, Mob: 9947513828 )

Dr. Anil Kumar V. ( E-mail:,    Mob:9605494831)

Dr. Sini P.  (, Mob: 9744717571 )



M.Sc. Mathematics     (20 Seats)

M.Phil Mathematics

Ph.D. Mathematics

Contact Details



Land: 0494 2407418

Office :

Land: 0494-2407428

Office: Praveen ( Mob: 8547668852)

Librarian: Mr. Manu C. ( Mob: 9846146320)

Office Attendant: Ms. Beena P.T. ( 9495282060)