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The Mathematical Sciences department at Leicester offers a supportive learning atmosphere for both undergraduate and graduate students. Our mathematics research group ranks among the UK's most dynamic, with particular expertise across several specialized fields. The actuarial science faculty brings substantial professional experience from diverse sectors. Doctoral candidates undertake self-directed research projects with supervision, typically spanning 3.0-3.5 years for full-time students or 6.0-6.5 years for part-time students. An additional year (or remaining portion) may be allocated for thesis preparation. The final dissertation, limited to 50,000 words, must demonstrate novel scholarly insights and include publishable material. Candidates must successfully defend their thesis in an oral examination to earn their degree.