Bio-Data Name – Jai Pratap Singh Associate Professor, Department Of Mathematics B.S.N.V.P.G. College, Lucknow. Father’s Name – Raj Kishor Singh Date of Birth – 02-01-1970 Address – Dr. Jai Pratap Singh D – 3/1 , Vineet Khand Gomati Nagar, Lucknow. PIN 226010. Mobile No. – 9838622377. E-mail - Jaisinghjs@gmail.com Nationality : Indian Languages : English, Hindi, Sanskrit, Urdu, French. Ph. D. Thesis Title : A Study of Certain Structures and Integrability Conditions in a Differentiable Manifo ld. Educational Qualification : Ph. D., 1997 (Pure Mathematics, Lucknow University) Proficiency in French 1992 (Lucknow University) M.Sc. ,1989 (Mathematics, Lucknow University) B.Sc., 1987 (Physics , Statistics , Mathematics , Lucknow University) Intermediate, 1985 (Physics , Chemistry , Mathematics , Hindi , English) High School , 1983 ( Science , Mathematics , Hindi , English , Sanskrit ) Teaching Experience : 25 Years Taught undergraduate classes from July 1, 1991 to December 13, 91 at Lucknow Christian Degree College as a Lecturer (Leave Vacancy). Taught undergraduate classes during sessions 93-94, 94-95, 95-96, 96-97 at Lucknow University as JRF (Junior Research Fellow) and SRF (Senior Research Fellow). Taught B.Tech. Classes at UNSIET, Poorvanchal University , Jaunpur From 17-11-97 to 13-10-1999 as a Lecturer. Presently teaching undergraduate classes at B.S.N.V.P.G. College , Lucknow from 14-10-1999 as a Reader/Associate Professor. Research Experience: JRF (Junior Research Fellow) From 05-05-92 to 04-05-94 in Department of Mathematics, Lucknow University. SRF (Senior Research Fellow) From 05-05-94 to 04-05-97 in Department of Mathematics, Lucknow University. Published Research Papers / Articles: Total Published +Accepted = 15+1=16 On submanifolds of Riemannian Manifold with semi-symmetric non metric connection (1991) J.T.S.I., Vol. 10, pp. 31-38. Invariant submanifolds of a Manifold admitting Fλ(2ν+3 , -1) – structure manifold (1996) Demonstratio Mathematica Vol. XXIX (3), 479-484. An article on “Role of Mathematics in Advancement of Science & Techology : A Brief Note” published in Souvenir of National Conference organized by Department of Mathematics B.S.N.V.P.G. College , Lucknow on Oct. 18-20, 2013. Production to Control Quality: Important Tools of Operational Research, (2017) .International Journal of Pure and Applied Management Sciences. Vol. 1(1), pp. 44-60. ISSN: 2456-4516. PPAP Operational Research Approch Towards Quality Management, (2017) , International Journal of Pure and Applied Management Sciences. Vol.4 (1), pp. 48-56. ISSN: 2456-4516. ON F_a (K,(K-2) )-STRUCTURE MANIFOLD, (2018) International Journal of Pure and Applied Researches (IJOPAAR), pp. (104-109). ISSN: 2455-474X. UGC Serial No. 45204 . Generalized difference of biquadratic sequence space Γ4,(2018), International Journal of Creative Research Thoughts (IJCRT) . ISSN - 2320-2882 , UGC Serial No. 49023. Semi Invariant Submanifold of a manifold with framed Algebraic ϵ-Structure, (2019) Journal of Emerging Technologies and Innovative Research (JETIR),(pp. 656-659). ISSN-2349-5162, UGC Serial Number – 63975. Sasakian Manifold with generalized almost contact metric Structure, (2019) Journal of Emerging Technologies and Innovative Research (JETIR),(pp. 456-461). ISSN-2349-5162, UGC Serial Number – 63975. K¨othe- Toeplitz Duals of Generalized Difference Sequence Spaces, (2019) Journal of Emerging Technologies and Innovative Research (JETIR),(pp. 854-860). ISSN-2349-5162, UGC Serial Number – 63975. SUBMANIFOLDS IMMERSED IN A GENERALISED QUATERNION MANIFOLD.(2020) Journal of Emerging Technologies and Innovative Research (JETIR),(pp. 1920-1925). ISSN-2349-5162, UGC Serial Number – 63975. On integrability conditions of a framed algebraic (ε,r ) – structure manifold, (2021) International Journal of Science and Research (IJSR), (pp. 1693-1695). ISSN : 2319-7064. The Nörlund space and Nörlund Orlicz space of Biquadratic entire sequences, (2021) ,Journal of Emerging Technologies and Innovative Research (JETIR), (pp. e250-256). ISSN-2349-5162, UGC Serial Number – 63975. Study of some properties on almost para contact metric manifolds with certain connection, (2021) ,Journal of Applied Science and Education (JASE), (pp. 1-5). ISSN : 2583-1372(E). On certain submaifolds of an H-structure manifold, (2021) International Journal of Pure and Applied Researches (IJOPAAR), pp. (1-5). ISSN: 2455-474X. UGC Serial No. 45204 . "Comparison of Present Cosmological Principles with Cosmology of Hindu Dharm Granth" Accepted for publication in vol. 10, 2022 of Anusandhan Vigyan Shodh Patrika. Published Books: No. of Books – 19 Objective Differential Calculus for B.Sc. and Competitive Exams. 2021 with Dr. Rama Jain. Krishna Prakashan Media (P) Ltd. Objective Linear Programming for B.Sc. and Competitive Exams. 2021 with Dr. Rama Jain. Krishna Prakashan Media (P) Ltd. Objective Integral Calculus for B.Sc. and Competitive Exams. 2021 with Dr. Rama Jain. Krishna Prakashan Media (P) Ltd. Objective Algebra for B.Sc. and Competitive Exams. 2021 with Dr. Rama Jain. Krishna Prakashan Media (P) Ltd. Objective Numerical Analysis & Programming in C for B.Sc. and Competitive Exams. 2021 with Dr. Rama Jain. Krishna Prakashan Media (P) Ltd Objective Linear Algebra for B.Sc. and Competitive Exams. 2021 with Dr. Rama Jain. Krishna Prakashan Media (P) Ltd. Advanced Calculus, (2016), Krishna Prakashan Media (P) Ltd. ISBN : 81-8283-361-2 Analysis (2014), Krishna Prakashan Media (P) Ltd. ISBN : 81-8283-591-7 Differential Geometry & Tensor Analysis (2014) with Dr. Preeti Pandey and others., Krishna Prakashan Media (P) Ltd. Book Code No. : 850-01, ISBN : 978-81-8283-312-4. Geometry & Trigonometry (2013) with A.R.Vasishtha and othrs. Krishna Prakashan Media (P) Ltd. ISBN : 978-81-8283-180-3. Mathematical Methods (2013) with A.R.Vasishtha and othrs. Krishna Prakashan Media (P) Ltd. ISBN : 978-81-8283-362-3. Differential Equations (2013) with A.R.Vasishtha and othrs. Krishna Prakashan Media (P) Ltd. ISBN : 978-81-8283-363-0. Calculus (2012) with A.R.Vasishtha and othrs. Krishna Prakashan Media (P) Ltd. , Book Code No. : 734-21, ISBN : 978-81-8283-214-5. Matrices, Vectors & Differential Equations (2012) with A.R.Vasishtha and othrs. Krishna Prakashan Media (P) Ltd. ISBN : 978-81-8283-254-1. Numerical Analysis (2005) with Dr. Mohd. Mian , Prakashan Kendra, Lucknow Abstract Algebra (2005) with Dr. Deepak Kumar Srivastava, Alok Prakashan , Lucknow , ISBN : 978-81-89599-95-9. Differential Calculus & Vector Analysis (2004), Unitech House, Aminabad, Lucknow. Mathematical Methods (2004) with Dr. M.K.Shukla and others., Unitech House, Aminabad, Lucknow. Differential Equations (2004) with Dr. U.B.Singh and others Alok Prakashan , Lucknow. Award/ Fellowship/Merit /Competitive Exams : First Rank in general Category in the list of selected candidates for Lectureship, Mathematics by Utter Pradesh Higher Education Service Commission. Junior Research Fellow (JRF) From 05-05-92 to 04-05-94 in Department of Mathematics, Lucknow University. Senior Research Fellow ( SRF) From 05-05-94 to 04-05-97 in Department of Mathematics, Lucknow University.