**MATHEMATICS**

**LECTURE SERIES ON THE PHILOSOPHY OF MATHEMATICS AT RSC& PLANETARIUM CALICUT**

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

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 :**

Ganitham

Ganitha Charithram

Discord Group:

Ganitham

( With various subgroups)

MAGIC
SQUARE FOR KNIGHT BY EULER

1
48 31
50 33
16 63 18

30
51 46
03 62
19 14 35

47
02 49
32 15
34 17 64

52
29 04
45 20
61 36 13

05
44 25
56 09
40 21 60

28
53 08
41 24
57 12 37

43
06 55
26 39
10 59 22

54 27 42 07 58 23 38 11

QUESTION PAPERS

Regional Mathematical Olympiad 2019

UNIVERSITY OF CALICUT

CCSS

2013 Second and Fourth Semester Full

Questions

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

T**OPOLOGY**

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?

**ALGEBRA**

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?

**ANALYSIS**

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?

**SET
THEORY**

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**

Mine

Ramachandran P.T.,

**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

Others

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 Companyâ€™s Civil
Service on the Madras Establishment.(Communicated by the MADRAS LITERARY
SOCIETY AND AUXILIARY ROYAL ASIATIC SOCIETY).Read the 15^{th} 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 â€“ 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 â€“ Vyakhya by Sankaranarayana Ed. by P.K. Narayana
Pillai,Trivandrum1949.

Observational Astronomy inIndiaâ€“ 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-BhÄá¹£Ä (Rationales in Mathematical Astronomy) of Jyeá¹£á¹hadeva: 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

**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 â€“
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 Govindaâ€™s Muhurta ratna
and Sripathiâ€™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

3.

**DEPARTMENT OF MATHEMATICS, UNIVERSITY OF CALICUT **

Faculty
Members

Dr. Preethi Kuttipulackal (pretikut@rediffmail.com, Mob: 9562475245) Head

Dr.
Raji Pilakkat (rajipilakkat@gmail.com, Mob: 9947513828 )

Dr.
Anil Kumar V. ( E-mail: anil@uoc.ac.in, Mob:9605494831)

Dr.
Sini P. (sinimecheri@gmail.com, Mob: 9744717571 )

Courses:

M.Sc.
Mathematics (20 Seats)

M.Phil
Mathematics

Ph.D.
Mathematics

Contact
Details

Phone:

Head:

Land:
0494 2407418

Office
:

Land:
0494-2407428

Office: Praveen ( Mob: 8547668852)

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

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

Email:

Head:

mathshod@uoc.ac.in