A Journey Through Learning and Problem Solving
My professional journey has developed across mathematics, engineering, research, software development, teaching, and entrepreneurship. Although these fields may appear different, each stage has built naturally on the experiences and skills developed in the ones before it.
Mathematical problem solving provided an early foundation, while university introduced both theoretical mathematics and practical engineering. Graduate research added scientific exploration and computational modeling, eventually leading to deeper work in programming and software engineering. Teaching then provided an opportunity to bring many of these experiences together while helping others develop their own knowledge and problem-solving skills.
Throughout these different chapters, one principle has remained constant: continuing to learn, explore challenging problems, and build on what each experience has taught me.
Mathematics Olympiad
Mathematical olympiads were one of the earliest defining stages of my academic journey. Preparing for challenging problems in geometry, number theory, combinatorics, and algebra developed my interest in mathematics while strengthening the creativity, persistence, and logical reasoning required to approach unfamiliar problems.
Earning a silver medal in the Mathematical Olympiad became an important milestone, but the experience had a much longer-lasting influence. It established a problem-solving mindset that would continue through university mathematics, research, programming, and many of the professional paths that followed.
University
University expanded my academic journey in two complementary directions through bachelor’s degrees in Mechanical Engineering and Pure Mathematics. Engineering introduced me to physical systems, mathematical modeling, and practical problem solving, while pure mathematics developed a deeper appreciation for abstraction, rigorous reasoning, and proof.
Studying both disciplines gave me the opportunity to approach complex problems from theoretical and applied perspectives. This combination became an important foundation for what followed, eventually allowing mathematics, engineering, and computation to come together in my graduate research.
Master’s Degree
My master’s studies at the University of British Columbia (UBC) marked my transition from learning established mathematics to experiencing mathematical research firsthand. I initially continued in pure mathematics through research related to Harmonic Analysis and Banach Space Theory, building on the interests I had developed during my undergraduate studies.
As my research interests evolved, I moved toward Applied Mathematics, Fluid Dynamics, and Chaotic Advection. My master’s research brought together mathematical theory, numerical methods, and physical modeling to investigate how geometry can influence the behavior of fluid flow.
This transition broadened my perspective on mathematics and introduced a new way of connecting theoretical ideas with computational problems—an experience that eventually led me toward doctoral research in Computational Fluid Dynamics.
PhD
My doctoral studies at the University of Toronto (U of T) took my research further into Computational Fluid Dynamics (CFD), where mathematics, engineering, numerical methods, and computer programming came together to solve complex fluid-flow problems.
As part of my research, I worked extensively with C++ and high-performance computing to solve the Navier–Stokes equations computationally. My work also explored extending the Volume of Fluid (VOF) method from two to three dimensions, requiring a combination of mathematical modeling, numerical techniques, and computational problem solving.
This experience significantly strengthened my interest in programming and scientific computing. As computation became an increasingly important part of my work, it eventually opened the door to a broader exploration of software engineering.
Software Engineering
My experience with scientific computing gradually developed into a broader interest in Software Engineering. The programming skills I had built through computational research expanded into software development, where I gained experience with implementation, debugging, testing, documentation, and building reliable software solutions.
Algorithmic problem solving became a particularly important part of this journey. I worked extensively with data structures and algorithms, LeetCode-style problems, and time and space complexity analysis, strengthening my ability to develop and evaluate efficient computational solutions.
This expertise also became part of my teaching work through technical interview preparation, where I helped others develop their algorithmic problem-solving skills and prepare for coding interviews. In this way, software engineering eventually connected two important parts of my professional journey: solving challenging technical problems and teaching others how to approach them.
Lifetime Learner
Lifetime Learner brought together many of the different threads of my professional journey. My background in mathematics, research, programming, and technical problem solving became the foundation for an educational business centered on helping others understand challenging ideas and develop stronger problem-solving skills.
While mathematics has remained at the core of my teaching, my work has expanded across programming, computer science, technical interview preparation, and other technical subjects. Building Lifetime Learner has also allowed me to grow beyond the role of an instructor, developing my experience in entrepreneurship while continuing to learn through teaching.
More than simply another professional chapter, Lifetime Learner represents a place where many of my previous experiences have come together—combining learning, problem solving, teaching, technology, and building something of my own.
The Journey Continues
My professional journey has never followed a single predefined path. Each stage has built on what came before while opening opportunities to explore new fields, develop new skills, and approach problems from different perspectives.
What connects these experiences is a commitment to continuous learning. Mathematics, engineering, research, software development, teaching, and entrepreneurship have each contributed something different to the way I think and work today.
The journey continues as I keep learning, building, teaching, and exploring where these experiences may lead next.