Practice for Math PhD Prelims  TCU
The Mathematics PhD program requires substantial training in algebra, real analysis, topology, and complex analysis. The student must pass three of the following four preliminary written exams:
Real Analysis Exam (based on MATH 50503 and 60513)
Algebra Exam (based on MATH 30224, 50253 and 60263)
Topology Exam (based on MATH 60313 and 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 sixth 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 (v 2.0)
 Practice problems for the Real Analysis Prelim (v 2.0)
 Practice problems for the Complex Analysis Prelim (v 2.0)
 Practice problems for the Topology Prelim
Actual Prelim Exams:
 Algebra
 Real Analysis
 Complex Analysis
 Topology
 Exam Solutions
 Sample Practice Problem Solutions

Fields and Galois Theory 2013 notes (George Gilbert)
Fields and Galois Theory 2015 notes (George Gilbert)