Take the qual in the semester before you start your thesis. For the usual fall/spring thesis, this means taking the qual in the spring of your junior year. For a spring/fall thesis, you may take the test in January. Make-up exams and in other rare cases, you may need to take the exam in August.
Junior Qual FAQ
For general information on the math/stats qual, see the Requirements page. For college-wide requirements for the junior qual, see Section IV.I of the Faculty Code.