The aim of this course is to test the knowledge of the student in the basic areas of mathematics. For this purpose, a written exam is given in the following topics and subtopics: Algebra (A. Groups and Rings B. Modules and Fields). Analysis (A. Real Analysis B. Complex Analysis). Differential Equations (A. Ordinary DE B. Partial DE). Geometry-Topology (A. Geometry B. Topology). Numerical Analysis (A. Numerical Analysis I B. Numerical Analysis II). Each student is expected to pass the exam in 3 subtopics chosen from 3 distinct topics.