By Immaculate Bazira

Dr. Olivia Nabawanda, is the youngest female to graduate with a PhD in Mathematics at the age of 31 from Makerere University. This was in 2022. She shared her story, and talks about how Makerere has been a gateway to a world of possibilities for her.

Tell us about your education background. How did you join Makerere University?

I am from Kanjuki village, Kayunga District and it is where I began my education at Kanjuki C/U Primary School. I later transferred to St. Bruno Kanjuki R/C Primary School, where I completed my Primary Leaving Examinations with a First Grade — the only First Grade in my school that year.

For my secondary education, I attended Kanjuki Senior Secondary School for both O’Level and A’Level. In O’Level, I performed well, earning a First Grade and emerging as the best female student. In A Level, I pursued Physics, Chemistry, Biology, and Mathematics, initially aspiring to study Pharmacy at university. However, destiny had a different plan for me.

Olivia with her PhD supervisor Dr Alex Samuel Bamunoba

I was awarded a government scholarship to study a Bachelor of Science with Education (Mathematics and Physics) at Mbarara University of Science and Technology (MUST). During my final year, I specialised in Mathematics, which further ignited my passion for the subject.

After my undergraduate studies, I received a scholarship from the African Institute for Mathematical Sciences (AIMS - Ghana) to pursue a master’s degree in mathematics. Upon completing my master’s, I returned to Uganda and started lecturing part-time at Mbarara University.

While at MUST, an opportunity arose for staff in public universities to pursue PhDs in mathematics under a capacity-building initiative aimed at strengthening mathematics education in Uganda. I applied and was awarded a scholarship to pursue my PhD in Mathematics at Makerere University in 2017. In May, 2022, I graduated as the youngest female to earn a PhD in Mathematics at Makerere University.

What was your most memorable experience at Makerere?

My most memorable experience was the day I defended my PhD thesis. After years of intense research, sleepless nights, and overcoming challenges, standing before the panel to present my work was both nerve-wracking and fulfilling. When the panel acknowledged my research contributions and announced that I had passed, I felt a deep sense of accomplishment. That moment was testament to my hard work and resilience, and it became even more special knowing I had made history as the youngest female to earn a PhD in Mathematics at Makerere.

Another unforgettable experience was the vibrant mathematical community I joined at Makerere. I was privileged to connect with brilliant mathematicians, both local and international, many of whom have become lifelong colleagues and research collaborators. Through these networks, I was granted incredible opportunities to travel for research visits to Sweden, France, Madagascar, and Ethiopia. These doors opened at Makerere, and the collaborations that began there have birthed more global research partnerships. Makerere was a gateway to a world of possibilities for me.

Were there other activities you were involved in at Makerere?

I had the opportunity to connect with other women in mathematics, which led me to join The Association of Women Mathematicians Uganda (AWoM), founded by Prof. Betty Nannyonga. The association aims to mentor, encourage, and support more women and girls in STEM, especially mathematics. Through AWoM, I actively participated in school outreach programmes across Uganda, engaging in career guidance, counselling, and mentorship for primary and secondary students. I found great fulfillment in inspiring young learners, sharing my journey, and encouraging them to embrace mathematics. This passion for mentorship has continued beyond my time at Makerere, and to this day, I remain actively involved in such initiatives — starting with my alma mater in Kayunga District, where I strive to give back and uplift the next generation of scholars.

Who are some of the lecturers or fellow students you give credit for helping you complete your PhD?

I am deeply grateful to Prof. John Mango Magero, the Principal Investigator of my PhD project, for his vision in initiating the programme that has benefited many mathematics lecturers in public universities and for his excellent coordination of the project.

I also extend my appreciation to my PhD supervisors: Dr. Alex Samuel Bamunoba (Makerere University), Prof. Paul Vaderlind (Stockholm University), Prof. Fanja Rakotondrajao (University of Antananarivo), and Prof. Per Alexandersson (Stockholm University), whose guidance and mentorship were invaluable throughout my research journey. Additionally, I acknowledge the staff of the Mathematics Department at Makerere University for providing a conducive academic environment, as well as fellow PhD students, with whom I faced the challenges of the journey, overcoming obstacles together.

So what does one do with a PhD in math?

A PhD in mathematics is a journey of continuous learning, and what I do with it is far-reaching. As a researcher, I collaborate with mathematicians globally, and our research results are published as stepping stones for even bigger discoveries. While the discoveries might not always be groundbreaking in the traditional sense, they have potential to influence other fields and solve real-world problems. For instance, my research in combinatorics can contribute to areas such as data analysis, or cryptography: this deals with developing secure encryption algorithms and systems to protect digital information, and network theory, where small mathematical advancements can improve technological innovations. In addition, I am passionate about teaching and mentoring the next generation of mathematicians. A PhD is not just for individual achievement — it is a tool for community development. As a lecturer, I guide students, helping them navigate complexities of mathematics. In general, a PhD in mathematics equips researchers with advanced skills needed to solve complex problems that drive national progress. Through mathematical research, innovations emerge that revolutionize key sectors such as technology, finance, healthcare, and infrastructure.

What was your research topic and findings?

My PhD research focused on Pattern Avoidance and Behavior of Statistics on Permutations, specifically examining run-sorted permutations and their combinatorial properties. A run in a permutation is a maximal increasing subsequence where the next element after the last one forms a descent. I derived recursive formulas for counting run-sorted permutations of [n] with k runs and provided a combinatorial proof for these relations. I also established the generating function and explored properties that linked this class of permutations to real-rooted polynomials.

Notably, I proved that run-sorted permutations, when analyzed through the run-statistic, lead to a special class of polynomials called real-rooted polynomials, contributing to the well-known Eulerian polynomials. Additionally, I defined a bijection between partitions of [n] and run-sorted permutations, leading to a new interpretation of the OEIS sequence A124324. This bijection has since sparked further research, with new discoveries made by several scholars, and one of my articles in this area has gained nearly 20 citations within three years.

Olivia with the Principal Investigator of her PhD project, Prof. John Mango Magero

Furthermore, I investigated pattern avoidance in run-sorted permutations, particularly for patterns of length three, and uncovered links to fundamental combinatorial sequences such as Catalan and Motzkin numbers, offering new insights into bijective proofs and connections between various combinatorial structures.

The combinatorial structures I studied have implications for cryptography, quantum computing, and artificial intelligence, where structured permutations and recurrence relations are fundamental. While these applications may not be realized immediately, they highlight the importance of continued research and government support for mathematics, as many theoretical discoveries eventually lead to significant breakthroughs in science and technology.

Statistically, 27% of females are able to pursue fields in STEM. How have you managed to pursue math in a field that is male dominated?

I pursued mathematics because I genuinely love the subject. When you are passionate about something, nothing can stop you. Throughout my journey, I received incredible support from my parents, teachers, and peers, which helped me stay confident in myself. I also believe deeply in the power of faith, as I can do all things through Christ who strengthens me. When it comes to breaking barriers in STEM, it's all about perception. There is no rule or truth that says math is only for men. These stereotypes are human-made and can be broken. As women, we have every right to pursue and excel in STEM fields.

What are some of the highlights of your professional journey?

Coming from a humble village background and attending schools with limited resources, I was not exposed to the best learning conditions, but my determination and love for mathematics kept me focused. My journey took a significant turn when I joined Mbarara University for my undergraduate studies. Despite facing financial and personal hardships, I excelled academically, which opened doors for further opportunities. After completing my PhD, I joined Mbarara University of Science and Technology as a lecturer, where I have been actively engaged in teaching, research, and mentoring students. One of the highlights of my career has been the opportunity to inspire young people in Uganda and Africa as well as mentoring many people irrespective of age.

Being appointed to the Board of Governors of my former high school and serving as the Chairperson of the Academic Committee has also been a significant milestone, allowing me to give back to my community by working to improve education standards in underprivileged schools.

Another of my proudest achievements was organising the "Women in Sage - Uganda" workshop in 2023. The workshop brought together female researchers for mentorship and skill-building in programming, which is crucial for research. The event attracted both local and international participants. It was a collaborative effort with colleagues from Makerere, Busitema University, and Kabale University.

Dr. Nabawanda with her mother at her PhD graduation party

What are some of the lessons you’ve learned while studying at Makerere University that have helped your career?

First and foremost, I learned patience. Research, especially in mathematics, can be tricky and sometimes requires slowing down to analyse problems and explore different angles. I also learned the importance of hard work and persistence, as the journey toward completing a PhD is filled with challenges that demand dedication.

Another significant lesson was the importance of marketing myself. Through public speaking, I was able to share my work ideas, which in turn has opened doors for opportunities to teach at various mathematical activities organised at universities across Africa. This experience has improved my communication skills and boosted my confidence.

I also learned the value of collaboration, which has been crucial in my academic career. Working with colleagues from different parts of the world has broadened my perspective and enriched my research.

Time management was another crucial lesson, as balancing my research and other responsibilities required efficient planning. Finally, I learned the importance of seeking mentorship and building a strong network. The guidance and support I received from mentors and colleagues have been pivotal in helping me achieve my goals as a researcher and educator.

What advice would you give to students at Makerere University preparing to enter the career world of STEM?

Success in STEM is achievable with dedication, hard work, and self-belief. Stay committed to your goals, embrace challenges as opportunities for growth, and develop both technical and soft skills like communication, collaboration, and time management. Join university clubs and associations to build your network and gain valuable experience. Continuously learn, seek guidance, and always maintain your passion for your field — it will keep you motivated during tough times.

How do you see the university evolving to meet needs in STEM?

To address the challenges faced by STEM students, Makerere University can evolve by improving online resources, such as subscribing to high-quality databases like MathSciNet etc, which will enhance access to current research articles and papers. Providing access to specialized software like Mathematica etc, which are crucial for research but often not freely available, would benefit both students and staff. Upgrading libraries would also facilitate learning and research. Furthermore, increasing funding support for research and creating scholarship opportunities would ensure that talented students are not held back by financial limitations. Additionally, introducing promotions and recognition programmes for faculty who excel in research would increase morale and productivity. Strengthening collaborations with global institutions, expanding online learning platforms, and establishing mentorship programmes would also offer students the tools, networks, and resources to succeed in the rapidly changing world of STEM.