Dr. Amritanshu Rai

Dr. Amritanshu Rai is a mathematician specializing in algebra, finite fields, and permutation polynomials. He completed his Ph.D. at BITS Pilani, Hyderabad Campus in 2025, where his doctoral research focused on constructing and analyzing new classes of permutation polynomials. He has published multiple articles in SCI-indexed journals, contributing to the theoretical development of polynomial mappings over finite fields. 

He has cleared multiple national examinations, including UGC NET JRF, GATE, IIT JAM, and various State Eligibility Tests. He has also received international travel grants supporting his academic participation abroad. 

Beyond teaching and research, he remains active in the mathematical community through conference presentations, workshops, and review work for reputed journals. 

Before joining UPES, Dr. Rai worked as a Graduate Teaching Assistant at BITS Pilani, Hyderabad Campus (2021–2024) during his Ph.D., where he conducted lectures and tutorials for several core mathematics courses. His roles included classroom teaching, academic mentoring, and supporting course administration. 

Algebraic structures over finite fields | Permutation polynomials and their applications | Construction of new polynomial families | Algebraic properties of polynomial mappings | Field extensions | Polynomial functions | Algebraic combinatorics. 

Dr. Rai believes in building mathematical understanding through conceptual clarity, structured reasoning, and engagement with problem-solving. He encourages students to develop intuition by connecting abstract ideas with clear examples. 

His teaching emphasizes step-by-step learning, active participation, and regular feedback, aiming to create a positive and motivating environment that supports both advanced and struggling learners. 

At BITS Pilani, he has taught Mathematics-I, Mathematics-II, and Algebra-I, covering topics such as calculus, linear algebra, and introductory abstract algebra. His experience includes conducting lectures, tutorials, assessments, and student support sessions across several semesters. 

Dr. Rai has cleared UGC NET JRF 2022 (AIR 118), UGC NET 2020 (AIR 54), GATE 2019 (AIR 354), IIT JAM 2015, CGSET 2020, and MPSET 2018. 

He received the BITS Pilani Institute Fellowship during his Ph.D. and earned two international travel awards from DST-SERB and another from BITS Pilani supporting participation in academic events abroad. 

Dr. Rai has authored several research papers in peer-reviewed journals such as Finite Fields and Their Applications, Communications in Algebra, Cryptography and Communications, and Journal of Algebra and Its Applications. His work contributes to the theory of permutation polynomials, including trinomial, quadrinomial, and pentanomial constructions, as well as polynomial functions over finite field extensions. 

He has served as a reviewer for Cryptography and Communications, demonstrating his involvement in scholarly evaluation. He has participated in various academic events, including the ICDEP Conference at ISI Delhi, the Advanced Instructional School on Finite Fields at IMSc Chennai, workshops at IIT Patna and IIIT Allahabad, and the IST School on Polynomials at Manipur University. He has also presented his research at the Indian Mathematical Society Conference. 

amritanshu.rai@ddn.upes.ac.in