Math Problem Collection

This collection contains a selection from the body of exercises that have been used in problem session classes at ELTE TTK in the past few decades. These classes include the current analysis courses in the Mathematics Bsc programs as well as previous offerings of Analysis I-IV and Complex Functions --- many of them are already published in our previous problem book,, but we plan to add problems from other courses also.

We recommend these exercises for the participants and teachers of the Mathematician, Applied Mathematician programs and for the more experienced participants of the Teacher of Mathematics program.

All exercises are labelled by a number referring to its difficulty. This number roughly means the possible position of the problem in an exam. For the Teacher program the range is 1-7, for the Applied Mathematician program 2-8, and for the Mathematician program 3-9. (Usually the students need to solve five problems correctly for maximum grade, the sixth and seventh problems are to challange the best students.) Problems with difficulty 10 are not expected to appear on an exam, they are recommended for students aspiring to become researchers.

For many exercises we are not aware of the exact origin. They are passed on by "word of mouth" form teacher to teacher, or many times form the teacher of the teacher to the teacher. Many exercises may have been created several generations before.

We provide you random problems in order to polish your problem solving skills. After signing in, you can assemble problem sheets for practice or tests.

Feed-backs and error reports are welcome at


Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government