Naïve Set Theory & its applications
Venue:  University of Kashmir, Hazratbal, Srinagar 190006 
Dates:  13^{th} April to 2^{nd} May, 2015 
Convener(s)  Speakers, Syllabus and Time table  Applicants/Participants 
Name  Amin Sofi 
S. M. Srivastava 
Mailing Address  University of Kashmir, Srinagar, 190006  Indian Statistical Institute, Kolkata 
Programme Schedule
Day  Date  LectureI 9.3011.00 
Tea 1111.30 
LectureII 11.301.00 
Lunch 1.002.30 
TutorialI 2.303.30 
Tea 3.304.00 
TutorialII 4.305.30 
Mon  13.04.2015  BVR  MAS  SMS 

SMS  
Tue  14.04.2015  BVR  MAS  BVR  MAS  
Wed  15.04.2015  BVR  MGN  MAS  BVR  
Thu  16.04.2015  MGN  MAS  MGN  MAS  
Fri  17.04.2015  MGN  MAS  MGN  MAS  
Sat  18.04.2015  BVR  MAS  MGN  BVR  
Mon  20.04.2015  BVR  MGN  MAS  BVR  
Tue  21.04.2015  MGN  HS  MGN  BVR  
Wed  22.04.2015  HS  SMS  MGN  HS  
Thu  23.04.2015  SG  RB  SG  RB  
Fri  24.04.2015  RB  SG  RB  SG  
Sat  25.04.2015  SMS  HS  SMS  HS  
Mon  27.04.2015  HS  SMS  HS  SMS  
Tue  28.04.2015  SG  HS  SG  HS  
Wed  29.04.2015  RB  SG  RB  SG  
Thu  30.04.2015  SMS  RB  SMS  RB  
Fri  01.05.2015  RB  SMS  SG  RB  
Sat  02.05.2015  SG  SMS  Distribution of certificates & valedictory 
 RB Rana Barua
 SGSreela Ganopadhyay
 MGNM.G.Nadkarni (Measure Theory)
 BVRB.V.Rao(Measure Theory)
 HSH.Sarbadhikari (Set Theory)
 MASM.A.Sofi (Metric Topology)
 SMSS.M.Srivastava (Set Theory)
3. Resource Persons:
 Rana Baura, ISI Kolkatab.
 Sreela Ganopadhyay, ISI Kolkatad.
 M.G.Nadkarni (Measure Theory), CBS, Mumbaif.
 B.V.Rao(Measure Theory), CMI, Chennai
 Sarbadhikari (Set Theory), ISI Kolkataf
 M.A.Sofi (Metric Topology), Kashmir University, Srinagar
 S.M.Srivastava (Set Theory), ISI Kolkata
 S.M.Srivastava: An overview of how Cantor discovered set theory.
 H.Sarbadhikari: Finite and infinite sets, countable and uncountable sets and standard results on them, definition of X = Y and X ≤ Y, X, Y sets and standard results on them, naïve definition of cardinal numbers and cardinal arithmetic. Applications.
 S. Ganopadhyay: Well ordered sets, proofs and definitions by transfinite induction, comparability of well ordered sets, naïve definition of ordinal numbers, trichotomy theorem of well ordered sets, well ordering sets of ordinal numbers, limit and successor ordinal numbers, countable ordinals, the first uncountable ordinal 1 , alephs, continuum hypothesis and generalized continuum hypothesis. Applications.
 M.A.Sofi: Metric spaces and their topology, complete and separable metric spaces, continuous and uniformly continuous functions, Pasting lemma, compact metric spaces, compactness in R , continuous maps on compact metric spaces, extension of (a) continuous functions from subsets of metric/normal spaces (b) homeomorphisms from compact subsets of R.
 Rana Barua: partially ordered sets, axiom of choice, well ordering principle and Zorn’s lemma, equivalence of three axioms, Applications.
 M.G.Nadkarni: Poincare recurrence theorem, BanachTarski paradox, GlimmEffros dichotomy.
 B.V.Rao: Measurable spaces and measures, Lebesgue measure, Vitali partition, example of a non measurable sets, Polish spaces, Baire category theorem and applications, standard Borel spaces.
 S.M.Srivastava: CantorBendixon derivatives, characterization of countable closed subsets, Cantor theorem on sets of uniqueness (an application in Fourier series), Polish groups.
Actual Participants 
S.No  Name  Gender  Institution  State  Degree/ Position 
1  Ratan Kumar Giri  M  NIT, Rourkela  Odisha  Ph.D 
2  Anand Pratap Singh  M  ISM,Dhanbad  Jharkhand  Ph.D 
3  Bulusu Naga Vekatesh Satish  M  ICAS, Kakinada  Karnataka  Asst.Prof. 
4  Firdous Ahmed Shah  M  Kashmir Univ, S. Campus  J&K  Asst.Prof. 
5  Ravi Kumar  M  C. Univ of Hyderabad  Telengana  Ph.D 
6  T. Kalimani  M  Govt.Arts College, Thiruvalluvar  T.N.  Ph.D 
7  Dilip Kumat Pradhan  M  Rourkela Univ.  Odisha  Ph.D 
8  S. Arunagirinathan  M  Govt.Arts College, Thiruvalluvar  T.N.  Ph.D 
9  Mohd Saleem Lone  M  CUK, Srinagar  J&K  M.Phil 
10  Shameek Paul  M  CBS, Mumbai  Maharashtra  Ph.D 
11  Pratush Kumar  M  ISM,Dhanbad  Jharkhand  Ph.D 
12  Sushil Sangli  M  Shiv Nadir Univ.,Noida  U.P.  M.Sc 
13  Mushtaq Ahmed Bhat  M  Kashmir Univ, Srinagar  J&K  Ph.D 
14  Mujeeb Ahmed Kawoosa  M  A.S. College, Srinagar  J&K  Asst. Prof. 
15  Khalid Nazir  M  Kashmir Univ, S. Campus  J&K  Ph.D 
16  Nisar Ahmed Lone  M  Govt. Degree Col, Pulwama  J&K  Asst. Prof. 
17  Bisma Zahoor M  F  Kashmir Univ, Srinagar  J&K  M.Phil 
18  Sumaira Shafi  F  Kashmir Univ, S. Campus  J&K  M.Phil 
19  Shaista Bashir  F  Kashmir Univ, S. Campus  J&K  M.Phil 
20  Asma Rafiq Sofi  F  Kashmir Univ, S. Campus  J&K  M.Phil 
21  Fida Hussain  M  Kashmir Univ, S. Campus  J&K  M.Phil 
22  Manzoor Ahmed Zargar  M  Kashmir Univ, S. Campus  J&K  M.Phil 
23  Sameer Ahmed Gupkari  M  A.S.College, Srinagar  J&K  Asst. Prof. 
How to reach
Depending upon the modes of travel from other parts of the country to Srinagar, one has the following
options:
1. By Air: From the airport to the university campus situated in Hazratbal, one can hire a cab/radio taxi which would charge something like Rs.700800/. There are several university campuses in Srinagar & the taxi driver shall have to be told to take him/her to the Kashmir University campus at Hazratbal(Dargah, as it is popularly known locally).
2. Those coming by train/air upto Jammu & plannig to travel to Srinagar by road (Taxi/bus/private car) usually end up at the TRC (Tourism Reception Centre) in Srinagar from where one can take an autorickshaw to the Kashmir university campus as explained above. Since the charges as quoted by the driver can in general be negotiated, the normal charges should not exceed Rs.250/.