Dr. Ram Krishna Verma

I believe that an innovative and effective learning environment is created through the active involvement of both teachers and students. In my teaching, I integrate a variety of online learning platforms and technology-enabled pedagogical tools, including well-structured PowerPoint presentations enriched with relevant graphics, illustrations, and visual examples, to make mathematical concepts clear, engaging, and easier to understand. For undergraduate students, I also incorporate research-based learning through projects and technical reports, which encourages independent thinking, develops analytical and problem-solving skills, and connects theoretical knowledge with practical applications. My research primarily focuses on algebraic coding theory, particularly skew polynomial rings, codes over finite rings, and classical and quantum error-correcting codes. Since skew polynomial rings involve non-commutative algebraic structures, working with them requires advanced algebraic techniques and careful mathematical analysis. In my research, I have investigated codes over various finite rings and studied their Gray images, which provide corresponding codes over finite fields and facilitate the development of efficient encoding and decoding methods for classical information systems. I have also constructed new quantum error-correcting codes from classical linear codes over non-chain rings. Several of these constructions offer improved parameters, including code rates and minimum distances, or provide parameters that have not previously been reported in the literature. Through this research, I aim to contribute to the development of algebraic methods for reliable and efficient information transmission. In the coming years, I will continue to maintain high standards of teaching by communicating course expectations, learning outcomes, and assessment criteria clearly to students. I will provide appropriate grading rubrics for extensive assignments and projects, return evaluated work promptly, and provide answer keys or feedback wherever appropriate. These practices help students understand their progress, manage their time effectively, and take greater responsibility for their learning. In research, I plan to continue and expand my work in algebraic coding theory, with particular emphasis on skew codes, codes over finite rings, classical and quantum error-correcting codes, and related algebraic structures. I also intend to strengthen research-based learning by involving students in mathematical research, computational experimentation, thereby fostering a culture of innovation, critical thinking, and continuous learning.