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After earning a PhD in Mathematics, graduates will possess the ability to: Utilize algebraic, analytical, and topological concepts to address both practical challenges and theoretical inquiries. Independently master core mathematical principles beyond formal coursework. Effectively communicate mathematical findings and logical arguments to fellow mathematicians. Navigate mathematical literature and databases to locate relevant theorems, constructions, or counterexamples. Produce well-structured, persuasive proofs for original mathematical discoveries. Requirements for the Mathematics PhD program include: Successfully complete (with a B grade or higher) a department-approved curriculum (transfer credits require approval from both the department and University Graduate Council) Pass qualifying examinations (details provided below) Demonstrate proficiency in one approved foreign language (French, German, or Russian) Develop an original dissertation approved by the department Pass a final oral defense of the dissertation. Typically, students earn an MA within one to two years post-BA, while the PhD requires four to five years of study.