<![CDATA[Abstrak. The ability to prove is the essence in studying mathematics. And the ability to prove mathematics has not fully grown in students. This study specifically aims to analyze the ability of mathematical proof, to analyze learning difficulties in terms of student epistemology on the Limit Function material. The long-term benefit of this research is that the study of learning difficulties in terms of student epistemology related to mathematical proof in the Real Analysis course is expected to provide encouragement to other lecturers to further develop the learning process or teaching materials in an effort to develop mathematical proof skills for education students. mathematics. This study used a descriptive method, while the research subjects were 9 prospective mathematics teacher students at Pancasakti Tegal University who contracted the Real Analysis course. Data collection methods used include: (1) test of mathematical proof ability; (2) observation; (3) interview; and (4) documentation. The results obtained that there are 4 kinds of student difficulties in terms of epistemology related to Real Analysis courses, namely: a) learning difficulties related to difficulties in applying concepts; b) learning difficulties related to difficulties in determining principles; c) learning difficulties related to understanding the problem and d) related to difficulties in mathematical proof. Especially in mathematical proof, students experience difficulties, among others: not knowing how to start constructing proofs, not being able to use definitions (concepts) and principles that are already known, and tend to start constructing proofs with what has to be proven.]]>
