By Thi Tam Dang
The pursuit of a PhD can be a significant chapter in one’s life, with its various challenges and triumphs. Reflecting on my own journey, I still remember a pivotal moment that took place during my pursuit of a Master’s degree in France at the age of 21. Although my passion for Mathematics was present, it was not yet fully developed. My primary motivation for embarking on this academic journey was to prove my independence to my parents and to explore the world on my own. During my studies, I faced numerous academic hurdles, including struggling with courses that involved numerical experiments and coding. These challenges, coupled with a lack of confidence in my mathematical abilities, caused me to question my potential as a successful mathematician. However, I persevered, seeking guidance from mentors and taking the time to develop my skills in coding and numerical experiments. Over time, I began to regain my confidence and appreciation for mathematics, which led me to pursue a PhD.
Upon submitting my PhD application in mathematics, I was privileged to receive an offer to join the DP DOCC program as one of 15 PhD students at the University of Innsbruck. My jour- ney as a PhD student was met with several challenges, beginning with my inability to register on time for the PhD program at the university due to the lack of an original master’s diploma from Italy. The pandemic also posed a significant challenge, leading me to face depression due to my pre-existing health condition, coupled with the lack of social support from family and friends. The isolation and loneliness I experienced were overwhelming, making it difficult for me to cope and find motivation to continue my studies. Despite the difficulties, I persevered and continued to work towards my academic goals, seeking support from my peers and men- tors. Over time, I was able to register for my PhD program. Nevertheless, I remain grateful for the opportunity to pursue my academic aspirations and have learned valuable lessons about perseverance and seeking help during challenging times.
During the summer in Innsbruck, I engaged in hiking activities with my colleagues and friends, which provided a source of respite from the demands of academic work. Initially, having no prior experience in the activity, I found hiking to be a challenging activity. However, as I persevered and became more adept at it, I was able to conquer the mountains and behold the breathtaking vistas from their peaks. The experience of hiking to the mountaintop and gazing out over the surrounding landscape was a breathtaking and awe-inspiring sensation. It instilled a sense of wonder and gratitude within me, evoking an appreciation for the natural beauty of our world.
Refecting on my PhD journey, I am reminded of the analogy with hiking. The early stages of the journey may challenging, but with persistence and dedication, one can overcome obstacles and experience the pleasure and beauty of the journey. In a similar manner to the sense of awe and gratitude instilled by the landscapes during hiking, the pursuit of a PhD can instill a sense of fulfillment and purpose, evoking a deep appreciation for the pursuit of knowledge and the opportunities for personal growth and development that it presents. Conducting research work in the field of mathematics often require a substantial amount of reading to look for interesting problems. During the early phase of my research, I dedicated several months to reading var- ious papers and books to gain a comprehensive understanding of numerical methods, such as exponential integrators and splitting methods, for solving semilinear partial differential equa- tions. The selection process must take into consideration factors such as practical applicability and solvability. In the context of my own research, I am interested in splitting methods when applied to diffusion-reaction problems, which have broad practical applications in fields such as chemistry, biology, physics, and climate change. However, splitting methods encountered obstacles in the presence of nontrivial boundary conditions.
The primary objective of my research work is to develop a modified splitting method that can effectively overcome the problem of order reduction. This task was exceedingly arduous, requiring extensive numerical analysis to identify the source of errors and determine an ap- propriate solution. Unfortunately, due to the complexity of the calculations involved, I made several mistakes that led to numerous failed attempts. Consequently, I experienced heightened levels of stress and self-doubt, with negative thoughts of inadequacy occasionally creeping in. Despite these setbacks, I persevered in my efforts, repeating the analysis multiple times until a viable solution was obtained. In order to check the effectiveness of my proposed approach, I conducted numerous numerical experiments. I faced significant challenges with implementing the code for my research work due to my limited coding experience. My efforts were hindered by numerous bugs and errors, which demanded extensive debugging. I had to spend considerable time and effort in correcting my errors. Despite encountering difficulties due to a lack of coding experience, consistent practice and perseverance allowed for the gradual improvement of coding skills and a more efficient testing process. After a year of arduous work, I successfully resolved the problem and discovered that our solution can be applied to more general problems, which was a significant breakthrough in my research. Throughout this process, I accumulated exten- sive knowledge and invaluable experience, bolstering my confidence and passion for research. The research journey is often fraught with obstacles and setbacks; however, with determination, perseverance, and an unwavering belief in oneself, one can ultimately achieve success.
To prepare for the presentation, I invested considerable effort in designing the slides and practicing rehearsal. I was struggling with insomnia on the night before the presentation, and the nerves were palpable when the time finally arrived. Despite the initial difficulties, I even- tually managed to complete the presentation successfully, thanks to the support of supervisors and colleagues who were present to offer encouragement. I also gained valuable insights on managing fear and anxiety in public speaking.
As the journey of mine as a Phd student draws to an end, I am filled with a sense of personal growth and development. The challenges and triumphs that I have encountered throughout this journey have contributed to my enhanced self-confident, social adeptness, and heightened level of activity. The knowledge and insights that I have gained during this period will remain a lasting influence, continuing to shape my future endeavors. As I move beyond this stage, I aspire to further advance my research aspirations with unwavering determination. Though I will soon leave Innsbruck, the memories of this experience will endure within me, alongside the invaluable lessons and acts of kindness imparted by those who have crossed my path. I hold the time spent as a PhD student in the highest regard and remain deeply appreciative of the sense of fulfillment it has provided me.