The PG and Research Department of Mathematics organized the five-day virtual FDP on Research in Mathematics: Present Trends and Future Prospects between 18^th and 22^nd November, 2024. On the first day Dr. A. George Maria Selvam, Head (PG), welcomed the faculty members of both Sacred Heart College and Patrician College, and also the participants from various institutions. He continued to explain the importance and dynamics of the entire FDP. Dr. D. Ajay, Assistant Professor, introduced the resource person Dr. R. Sivaraj. He elaborated on thermal conductivity of a fluid, atomic view of electronic vibrations, nanofluids, nanoparticles, heat transfer applications of nanofluids and heat transfer cavities.. On the second day Dr. D. Ajay, Assistant Professor welcomed everyone the introduced the resource person Dr. J. Ravisankar. Then the resource person went on to explain his new findings. In this session he explained the basic concepts of Graph Theory, Important types of Graphs, Applications, Connectivity between Graphs and Zero Divisors, Topological Indices and also their applications. On the third day Rev. Dr. John Borg, Controller of Examinations and Assistant Professor, greeted everyone for the session and introduced the Resource Person Dr. Rajkumar with his delightful words. He demonstrated his findings and concepts such as bicomplex space, zero divisors, Euclidean Norm, sequence and some sequence spaces, holomorphic functions, bicomplex integration, differential and integral calculus, Fractional Maxwell’s type equations in source free domains and applications to an LCR – circuits.  On the fourth day Dr. Merceline Anita, Assistant Professor welcomed the gathering and introduced the resource Person Dr. Suvankar Biswas. The session began with the introduction of fuzzy theory. He explained the origin of fuzzy, the necessity of fuzzy, and the following topics: fuzzy sets, interval number, fuzzy number, collection method, differential transformation method, mathematics of fuzzy sets and fuzzy logic and uncertainty characterized by non – random process. The fifth and final day began with the warm words of Dr. F. Silviya, Assistant Professor. She welcomed everybody and introduced the resource person Dr. G. Britto Antony Xavier. He explained the topics such as displacement, velocity, acceleration and in a beautiful way. Then he asked the participants about 0.25^th derivative, 0.5^th derivative, 0.75^th derivative, 1.25^th derivative of displacement and alpha times derivative of displacement and he explained them very clearly. Finally, he concluded his lecture with fractional order integration of acceleration computing the value of Gamma function. In the end Rev. Dr. John Borg, Controller of Examinations and Assistant Professor expressed his words of gratitude to Rev. Fr. Rector, Rev. Fr. Principal, Resource Persons, Dr. A. George Maria Selvam, Head (PG), Dr. R. Murali, Head (UG), Faculty members of both Sacred Heart College and Patrician College, and also the participants from various institutions.