Practice for Math PhD Prelims - TCU

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The Mathematics PhD program requires substantial training in algebra, real analysis, topology, and complex analysis. The student must pass 3 of the following 4 preliminary written exams:

• Real Analysis Exam - based on MATH 50503 and 60513
• Algebra Exam - based on MATH 50253 and 60263
• Topology Exam - based on MATH 60313and 60323
• Complex Analysis Exam - based on MATH 50403 and 60413

The student must pass the Real Analysis Exam, the Algebra Exam, and either the Topology Exam or the Complex Analysis Exam. These exams are administered twice each year and must be passed by the end of the first semester of the third year. The exams will be given at the beginning of each semester.

Below are more detailed syllabi for the Preliminary Examinations, and practice problems are also available.

Syllabi for the four Prelim Exams:

• Click here.

Practice Problems:

• Practice problems for the Algebra Prelim
• Practice problems for the Real Analysis Prelim
• Practice problems for the Complex Analysis Prelim
• Practice problems for the Topology Prelim

Actual Prelim Exams:

• Algebra
  • August, 2010
  • January, 2011
  • August, 2011
• Real Analysis
  • August, 2010
  • January, 2011
  • August, 2011
  • January, 2012
• Complex Analysis
  • August, 2010
  • June, 2011
  • January, 2012
• Topology
  • January, 2011
  • August, 2011