Abstract. Real analysis is a course that is abstract and high difficulty level. Male students are
weak in understanding basic concepts, while women are always follow on examples of answers
from lecturers. Consequently, their abstraction abilities do not develop. To provide appropriate
treatment, the lecturer should know the rigour mathematical ability of the students. Therefore,
this study aims to identify students' rigour mathematical abilities in Real Analysis courses. The
research method is descriptive qualitative. The research instruments are test questions and
interview sheets. The sample was six students. The researcher divides the students into three
cognitive levels based on test results, i.e. two for low cognitive level, two for medium, and two
for a high cognitive level. This study concludes that there is a difference of mathematical
thinking of rigour of students based on gender-related to three levels of cognitive ability. Male
students have a simple way of thinking impacting on a short answer pattern. The way of thinking
of female students is systematic, and the pattern of the answer is long and sorted. The results of
this study can be the basis of the treatment of students based on the level of cognitive ability and
gender.