He was taught applied mathematics at University College by Arthur Conway who held the chair of Mathematical Physics there. Murnaghan was awarded a National University of Ireland Travelling Scholarship to study abroad but, with the outbreak of World War I, his initial idea of studying in Germany became a non-starter.
Siya ay tinuturuan-apply na sa matematika at University College sa pamamagitan ng Arthur Conway na gaganapin sa silya ng matematika Physics doon. Murnaghan ay iginawad ng National University of Ireland paglalakbay Scholarship sa pag-aaral sa ibang bansa ngunit, sa pag-aalsa ng World War I, ang kanyang unang ideya ng pag-aaral sa Alemanya ay naging isang non-starter.