Dr. Meenakshi Rana

Associate Professor

Specialization

Partition Theory, Enumerative Combinatorics, Number Theory

Email

mrana@thapar.edu

Specialization

Partition Theory, Enumerative Combinatorics, Number Theory

Email

mrana@thapar.edu

Website

https://sites.google.com/thapar.edu/meenakshirana/home

 

Meenakshi Rana is working as Associate Professor with School of Mathematics, Thapar Institute of Engineering & Technology, Patiala. She begin her Job at Thapar Institute of Engineering & Technology in 2008. She has published many SCI/SCIE and refereed research articles. Dr Rana has completed two major research projects and is working on third project. She received the ‘Certificate in Academic Practice’ from CAPSL-Trinity College Dublin, Ireland and has been appointed as Thapar Trinity Academic Fellow. Apart from her research interest she is highly enthusiastic teacher and enjoys lecturing to her students.

 

Education

2010, Ph.D., Mathematics, Panjab University, Chandigarh

2003, M.Sc. (Hons.), Mathematics, Panjab University, Chandigarh

2001, B.Sc. (Hons.), Mathematics, Panjab University, Chandigarh

 

Experience

2017--onwards, Associate Professor, SOM, Thapar Institute of Engg. & Tech., Patiala, India

2008 -2017, Assistant Professor, SOM, Thapar University, Patiala, Punjab, India

2005–2008, Lecturer, Chitkara University, Banur, Punjab, India

2004–2005, Lecturer, SSIET, Dera Bassi, Punjab, India

 

Teaching Interest

               Number Theory, Discrete Math, Enumerative Combinatorics, Optimization Techniques, Linear Algebra, Complex Analysis, Graph Theory

 

Research Interest

Partition Theory, Enumerative Combinatorics, q-series, mock theta functions

 

Research Project

- Project Title: On Rogers-Ramanujan-Slater type identities and related topics in Partition Theory

Duration : From 2019 – (Ongoing)
Project No. MTR/2019/000123
Funding Agency:  Science and Engineering Research Board (SERB), MATRICS

 

- Project Title: on q-series, split n-color partitions and F-partitions

Duration : From 2016 –2019 (Completed)
Project No. 25(0256)/16/EMR-II
Funding Agency: Council for Scientific and Industrial Research (CSIR)

 

- Project Title: On Combinatorics of q-Series, Rogers- Ramanujan type identities and Split n-Color Partitions

Duration : From 2016 –2019 (Completed)
Project No. 2/48(18)/2016/NBHM(R.P.)/R&D II/14983
Funding Agency: National Board for Higher Mathematics (NBHM)

Abroad Visit (s)

  • University of Illinois, Urbana-Champaign Campus, USA, June 5 - 9, 2019 (Conference)
  • Trinity College, Dublin, Ireland  Jan 06 - Feb 24, 2018 (Teaching and Learning in Higher Education SPCert-Program)
  • Simon Fraser University, Burnaby Campus, Vancouver, Canada, June 15 - June 24, 2015 (Conference)

Thesis Supervision

Ph.D. Thesis

  • Ms. Vasudha (Pursuing)
  • Ms. PrabSimrat (Pursuing)
  • Ms. Harman Kaur (Pursuing)
  • Ms. Shruti Sharma, 2020 “ Combinatorics of Mock Theta Functions and q-series”.
  • Ms. Jasdeep Kaur, 2016 “Rogers-Ramanujan identities type identities and Combinatorics”.

 

M.Sc. Thesis

  • Watanjeet, 2019, “On Multiplicity of parts in n-colour compositions”
  • Amrinder Kaur, 2017, “On plane partitions and colored partitions”
  • Priyanka, 2016, ‘‘ A survey on colored partition and q-series”
  • Diksha Chawala, 2015, “Rogers-Ramanujan Identities and split (n+t) color Partition”
  • Nisha, 2015, “On Study of Lattice Paths”
  • Shelja Dutta, 2014, “On n-colour Compositions”
  • Avneet Kaur, 2013, “A Study of ordinary, colored and signed Gollnitz-Gordon identities”
  • Rajni Mittal, 2012, “A Study of Gollnitz-Gordon identities”
  • Richa Bansal, 2011, “A Study of Guassian polynomial”
  • Rajni Bansal, 2011, “Combinatorial interpretations of Rogers-Ramanujan identities and their analogues”
  • Inderpal Singh, 2010, “A Study of Coloured partitions”

 

Membership of Professional Institutions, Associations, Societies

  • Life member of Ramanujan Mathematical Society (644)
  • Life member of Indian Mathematical Society (R-10- 131)
  • Life member of Society for Special function and their Applications (804)
  • Life member of Indian Science Congress (L-16404)
  • Life member of Punjab Academy of Sciences (L-1406)

 

List of Publications

 

Published (SCI/SCIE)

  1. S. Sharma and M Rana, ‘A Simple Combinatorial Treatment for the q–Series Interpreted by Agarwal’, Utilitas Mathematica (Accepted)
  2. M Rana, S Sharma, n-Color Compositions and Lattice Paths of Agarwal-Bressoud, Indian Journal of Pure and Applied Mathematics (SCI), Indian J Pure Appl Math., https://doi.org/10.1007/s13226-021-00120-w, (2021) 52:87–95. (July 2021)
  3. M Rana and N Saikia, Combinatorial interpretations of q-series using n-color partitions, J. Ramanujan Math. Soc. 36, No. 2 (2021) 123–127. (June 2021)
  4. M Rana and S Sharma, “Combinatorics of some fifth and sixth order mock theta functions, Electronic Research Archive, 29(1): 1803-1818 (doi: 10.3934/era.2020092), March 2021.
  5. K. Singla and M Rana, Exact Solutions and Conservation Laws of Multi Kaup-Boussinesq System with Fractional Order, Analysis and Mathematical Physics (2021) 11:30, https://doi.org/10.1007/s13324-020-00467-z (Jan 2021)
  6. A Kumar, M Rana, “On the treatment of partitions as factorization and further analysis”, J. Ramanujan Math. Soc., 35, No. 3 (2020) 263-27
  7. Komal Singla and M Rana, Symmetries, Explicit Solutions and Conservation Laws for Some Time Space Fractional Nonlinear Systems, Reports in Math. Physics, Vol 86, NO. 2, 2020.
  8. V. Gupta, M Rana and S Sharma, “On Weighted Signed Color Partitions”, Proc. Indian Acad. Sci. (Math. Sci.) (2020) 130:10 Https://Doi.Org/10.1007/S12044-019-0545-1 (0.341) 09, January 2020
  9. S Sharma, M Rana, On Mock Theta Functions and Weight-Attached Frobenius Partitions, Ramanujan Journal, 50: 289-303, https://doi.org/10.1007/s11139-018-0054-3 , September 2018
  10. S.  Sharma, M. Rana, “Interpreting some fifth and sixth order mock theta functions by attaching weights,” J. Ramanujan Math. Soc. 34, No.4 (2019) 401–410, Dec 2019
  11. S Sharma, M Rana, “A new approach in interpreting some mock theta functions” International journal of Number Theory, Vol. 15, No. 7 (2019) 1369–1383, 2019. (IF: 0.462) March 2019
  12. M Goyal and M Rana, “Combinatorial Identities for Tenth Order Mock Theta Functions”, Proc. Indian Academy of Sciences, (2019) 129:39 https://doi.org/10.1007/s12044-019-0475-y, (2019) (0.341), JUNE 2019
  13. M Rana, J. K. Sareen and D. Chawala, “On Generalized q-Series and Split (n+t)-Color Partitions”, Utilitas Mathematica, 108(2018), Page No. 3-19. (IMPACT FACTOR-0.228)
  14. M Goyal and M Rana, “On Central Tendencies of the Parts in Certain Restricted Partitions”, Mathematical Reports, Vol. 20(70)3, Page No. 291-300, (2018) (IMPACT Factor-0.341)
  15. S Sharma, M Rana, “Combinatorial interpretations of mock theta functions by attaching weights”, Discrete Mathematics Vol. 341 (2018) PP 1903–1914. (Impact Factor-0.728)
  16. M Rana and M Goyal, “On Combinatorics of Modified Lattice Paths and Generalized q-series”, Contributions to Discrete Math., Vol. 13, No. 1, pp 136-149, ISSN 1715-0868, (2018). (Impact Factor-0.419)
  17. M Rana and J K Sareen, “Split (n+t)-Color Partitions and 2-Color F-Partitions”, Contributions to Discrete Math., Vol. 12, No. 2, pp 115-145, ISSN 1715-0868, 20 (Impact Factor-0.28)
  18. J K Sareen and M Rana, “Four-way combinatorial interpretations of some Rogers-Ramanujan type identities”, ARS-Combinatoria, 133(2017), pp 17-35. (Impact Factor-0.268)
  19. M Rana, “Partition Theoretic Interpretations of The A2 Rogers-Ramanujan Identities”, ARS -Combinatoria, 130 (2017), pp 119-129. (Impact Factor-0.268)
  20. J K Sareen and M Rana, “Combinatorics of Tenth Order Mock Theta functions”, Proc. Indian Acad. Sci. (Math. Sci), Vol. 126, No. 4, November 2016, pp. 549-556. (Impact Factor-0.371)
  21. A K Agarwal and M Rana, New combinatorial versions of Gollnitz- Gordon identities, Utilitas Mathematica, Vol. 79 (2009), pp. 145-155. (Impact Factor-0.28)
  22. M Rana and A K Agarwal, On an extension of a combinatorial identities, Proc. Indian Acad. Sci. (Math. Sci), Vol. 119, No. 1, (2009), pp. 1-7. (Impact Factor-0.371)

 

Published (NON-SCI /Refereed  Journals)

 

  1. S Sharma and M Rana, ‘Three-way Combinatorial Interpretations of Rogers–Ramanujan Identities’, Journal of Indian Math. Soc. (Accepted).
  2. V Gupta, M Rana, “Rogers–Ramanujan type identities for (n + t)–color over-partitions’, J. of Ramanujan Society of Mathematics and Mathematical Sciences, Vol. 8, No. 2 (2021), pp. 01-16
  3. S. Sharma and M. Rana, “Combinatorics Of Third Order Mock Theta Function f(q) and Sixth Order Mock Theta Functions φ(q), ψ(q)”, J. of Ramanujan Society of Mathematics and Mathematical Sciences , Vol. 7, No. 1 (2019), pp. 31-36.
  4. V. Gupta, M Rana, “On Some Combinatorics of Rogers–Ramanujan Type Identities Using Signed Color PartitionsCurrent Trends in Mathematical Analysis and Its
    Interdisciplinary Applications, https://doi.org/10.1007/978-3-030-15242-0_3.
  5. M Rana and J K Sareen, “On Combinatorial Extensions of Some Mock Theta Functions Using Signed Partitions”, Advances in Theoretical and Applied Mathematics, Vol. 10, No.1, pp 15-25 (2015)
  6. A K Agarwal and M Rana, “Combinatorial interpretation of a generalized basic series”, Analytic Number Theory, approximation Theory, and special functions, DOI 10.1007/978-1-4939-0258-3_7 HMS-Volume, Springer, 215-225 (2013).
  7. A K Agarwal and M Rana, Two new combinatorial interpretations of a fifth order mock theta function, Journal of The Indian Mathematical Society, Special Centenary Volume (1907-2007), (2009), pp 11-24.
  8. M Rana and A K Agarwal, Frobenius partition theoretic interpretation of a fifth order mock theta function, Canadian Journal of Pure & Applied Sciences, Vol. 3, No.2, (2009), pp. 859-863.

Conferences/Workshops

Abroad

  • M. Rana,“ Analytics and Combinatorial Number Theory-A legacy of Ramanujan, University of Illinois, June 5-9, 2019, USA
  • Trinity College, Dublin, Ireland  Jan 06 - Feb 24, 2018 (Teaching and Learning in Higher Education SPCert-Program)
  • M. Rana, “Split (n+t)-Color Partitions and 2-Color F- Partitions”, Connections in Discrete Mathematics, 15-19 June, 2015, Simon Fraser University, Burnaby, Canada.

India

  1. National Center for Mathematics (NCM) Workshop on Modular Forms (2020), IIT Guwahati, Assam, December 14-19, 2020.
  2. M. Rana, “On Combinatorics of Mock Theta Functions with Attached Weights,” at Amal Jyoti Engineering  College, Kanjirapalli, Kottayam, Kerala, India, November 22-24, 2018.
  3. M.  Rana “On Split (n+t)–Color Partitions and 2–color F–partitions,” at Fractional Calculus, Special Functions and their Applications in Computer Science, November 10-12, 2018, Deptt of Mathematics, TDPG College, Jaunpur, UP, India
  4. M. Rana, “q-Series and Split (n+t)-Color Partitions”, International Conference on Special Functions and their Applications, 9-11 September 2016, Jamia Millia Islamia, New Delhi
  5. M. Rana, “On Split (n+t)-Color Partitions, 2-Color F- Partitions and Mock Theta Functions”, South Asian Mathematics Research Scholars Meet , 8-9 May, 2015, South Asian University, New Delhi.
  6. M.  Rana, “On Combinatorics of RRI”, 18 th Punjab Science Academy Annual Conference, 7-9 February, 2015, DeshBhagat University, Mandi Gobindgarh, Punjab, India.
  7. M. Rana, “On some extension of Tenth order mock theta functions”, International Conference of Special Functions and Their Applications, 16-18 October, 2014, Thapar Institute of Engineering & Technology, Patiala, India.
  8. M. Rana, “Three way combinatorial interpretations of some RRI”, International Conference of Special Functions and Their Applications, 13-15 December, 2013, MVNIT, Jaipur, India.
  9. M. Rana and H. Kaur, “Combinatorial interpretations of some tenth order mock theta functions”, National Conference on Advances in Mathematics & its Applications in Mathematics & its Applications, 25-27 June, 2013, NIT, Hamirpur, India.
  10. M. Rana, “Partition theoretic interpretations of Some double series q- identities”, International Conference of Special Functions and Their Applications, 27-29 June, 2012, SVNIT, Surat, India.
  11. M. Rana, “Partition theoretic interpretations of RR type identities”, Twenty first International conference of forum for Interdisciplinary Mathematics, 15-17 Dec, 2012, P.U., Chandigarh, India.
  12. M. Rana, “On a fifth order mock theta function”, 98th Indian Science Congress, 3-7 Jan, 2011, SRM University, Chennai, India.
  13. M. Rana and A. K. Agarwal, “New combinatorial versions of Gollnitz-Gordon identities” 11th Punjab Science congress, 7-9 Feb, 2008, T. U., Patiala, India.
  14. M. Rana and A. K. Agarwal, “Partition theoretic interpretation of a fifth order mock theta function” 74th annual conference of IMS, 27-30 Dec, 2008, University of Allahabad, Allahabad, India.
  15. M. Rana and A. K. Agarwal, “On a Combinatorial identity”, 73th annual conference of IMS, 27-30 Dec, 2007, University of Pune, Pune, India.

INVITED TALKS

  1. “On Combinatorics of Mock Theta Functions with Attached Weights,” at Amal Jyoti Engineering  College, Kanjirapalli, Kottayam, Kerala, India, November 22-24, 2018.
  2. “On Split (n+t)–Color Partitions and 2–color F–partitions,” at Fractional Calculus, Special Functions and their Applications in Computer Science, November 10-12, 2018 and a National Workshop on “Science fare creating awareness, interest, motivation in Science and Mathematics for school students and teachers” , November 10-13, 2018, Deptt of Mathematics, TDPG College, Jaunpur, UP, India
  3. “q-Series and Split (n+t)-Color Partitions” at International Conference on Special Functions and their Applications, 9-11 September 2016, JamiaMilliaIslamia, New Delhi
  4. “On Multiple Integrals and its applications in engineering”, October 20, 2015, at Chandigarh Engineering College, Landran, Mohali, Punjab, India.
  5. “On some extension of Tenth order mock theta functions”,  at International Conference of Special Functions and Their Applications, 16-18 October, 2014, Thapar Institute of Engineering & Technology, Patiala, India.
  6. “Applications of Mathematics in Engineering,” at Rayat and Behra Institute for Women, Khrar, Mohali, February 07, 2014.
  7. “Three way combinatorial interpretations of some RRI” at International Conference of Special Functions and Their Applications, 13-15 Dec, 2013, MVNIT, Jaipur, India.

Awards and Honours

  1. Awarded $750 Funding by Simon Fraser University, Burnaby during participating in conference “Connections to Discrete Mathematics”
  2. Awarded Cash Prize for the best paper presentation in Number Theory/Algebra in Indian Mathematical Society Annual Conference (IMS), 2007
  3. 2nd Rank in M.Sc. (Hons.) Mathematics, Panjab University, Chandigarh 2003
  4. 4th Rank in B.Sc.(Hons.) Mathematics, Panjab University, Chandigarh 2001

 

Conferences & Workshops Organized

  1. Organized various workshop under Thapar Mathematical Society since 2016.
  2. Convener: “International Conference of Special Functions and Their Applications”, 16-18 October 2014, Thapar University, Patiala, India
  3. Convener “Conference on Number Theory, Combinatorics & Special Function (NTCSF-2019)., Thapar Institute of Engineering & Technology, Patiala

 

Administrative/Additional Responsibilities

  • President (2015 onwards till date) Thapar Mathematical Society
  • Warden-PG hostel (2015-19), Thapar Institute of Engineering & Technology
  • Vice President – Kalam (2017 onwards) (Under privileged children society)
  • Faculty Advisor  (2018 onwards)- Gender Champions Society for students at TIET
  • School Profile Coordinator (2010-2013), School of Mathematics.

Message to Students & Community

Learn a skill that enable you to learn new skills, built up and work upon for building your learning capabilities. Perfection is hard to achieve, but learning allows to improve, even from best of your form.