Mathematical Analysis of the Present Status and Challenges of Higher Education in Nepal: A Case Study of Selected Universities

Higher education supports human capital formation, innovation, and socioeconomic development, yet Nepal’s tertiary education system faces persistent structural challenges amid expanding enrolment. This study aims to assess the status and challenges of higher education in Nepal through mathematical and statistical analysis of five universities: Tribhuvan University, Kathmandu University, Purbanchal University, Pokhara University, and Rajarshi Janak University. A quantitative case study approach was employed using secondary time-series data on enrolment, faculty numbers, and public funding for 2016/17–2023/24, obtained from the University Grants Commission’s Education Management Information System and related sources. Data were analyzed using compound annual growth rates, exponential growth projections, correlation, and regression analysis. A weighted Challenge Severity Index was also constructed to prioritize institutional constraints. The findings indicate that enrolment grew at a compound annual rate of 7.93%, compared with faculty growth of 3.81%, suggesting increasing pressure on teaching capacity. Growth projections indicated that the student–faculty ratio could rise from approximately 40:1 in 2016/17 toward 59:1. The gross enrolment ratio increased from 9% in 2008/09 to 20.05% in 2021/22, remaining below the reported comparison rates for India (26.9%), Malaysia (41.9%), and China (51%). Across the five universities, institutional size was negatively correlated with public funding per student (r = −.75). The severity index identified faculty shortages, underfunding, and gaps in quality assurance as the most pressing challenges. These findings highlight the need to align institutional expansion with staffing, funding, and quality assurance capacity. The study recommends faculty recruitment planning informed by enrolment projections, differentiated funding formulas, and quality assurance reform to support more balanced and sustainable development of Nepalese higher education.