How important is memorization in high level math

Contribution series mathematics

Studies in Archeology, Studies in Biology, Studies in Chemistry, Studies in Geosciences, Studies in Mathematics, Studies in Medicine, Studies in Physics, Studies in Psychology, Studies in Technology
Prof. Dr. Burkhard Kümmerer

What does a mathematics degree look like? Like the math class at school? And what degree should I aim for? In a mathematics course you attend lectures and accompanying exercises on various topics, plus seminars, sometimes internships.
It's quite different from what it was at school. Above all: you need a lot of time to deal with mathematics independently. The more you use this time for intensive discussions with other students, the better it is. Shape the everyday life of our math students:

  • Lectures that you should attend and revise regularly,

  • Exercises for which you have to solve many exercises,

  • Seminars in which you prepare and give a mathematical lecture yourself.

There are also phases of exam preparation and the times in which a scientific thesis is written.

Working methods

Studying mathematics means working independently. Compared to other courses, especially engineering courses, the mathematics timetable provides for many "free" periods in the semester for independent work; During the lecture-free period, there are usually no events at all. Unlike at school, there is no compulsory attendance for the lectures. Nonetheless, the students work a lot, they can just organize their time more freely. You need self-discipline and staying power, because you don't understand mathematics "right away or never", but rather "a little better every time".

Mathematics is also a language, and languages ​​have to be spoken. It is not uncommon for a long sought solution to be found on the first attempt to explain to a fellow student what the problem is. In a group, it's not easy to give up, but neither is it easy to bite into it. The effort to find suitable partners and to learn teamwork is definitely worth it, also with regard to your later professional life.

It is useless to memorize definitions and sentences; only mathematics that you understand can be used again on its own; it is also easier to remember. In the course of the course you should become familiar with mathematical concepts, ways of thinking and methods and you should learn to apply your knowledge effectively and imaginatively to various problems. You have to practice regularly, but learn little by heart. Each element of mathematics study contributes in its own way to achieving these goals.


In a lecture, a lecturer, still too seldom a lecturer, explains the structure of a mathematical theory. Lectures are the backbone of a math course, unlike most humanities. In the introductory lectures of the basic course, which all students attend together, the two "main pillars" of mathematics, analysis and linear algebra are systematically built up from a few basic assumptions.
In the further course, the students first attend lectures that introduce different areas of mathematics, later further special lectures build on this and lead to a scientific thesis in one area. The material is discussed in less detail at university than at school. It is therefore all the more important to work on the lectures independently.


Exercises are offered for many lectures. The students work on (written or oral) exercises on the subject matter of the lecture and meet each week in smaller groups with their tutor. The completed tasks are discussed in these exercise groups, and smaller tasks are often also processed in the exercises.

The tasks can rarely be solved with routine, unlike with a lot of homework at school. It takes a lot of time and fills a considerable part of the gaps that the timetable allows. Editing the exercises are the training units of the mathematics study, without them nothing works. Often the students get together in small groups and spend whole afternoons over an exercise sheet.


In a seminar, a mathematical sub-area is dealt with much more deeply and independently than is possible in a lecture. Each participant receives a special topic to work on. Under supervision, you will familiarize yourself with this topic and prepare a one to one and a half hour lecture on it. This work usually takes place during the lecture-free period. The lectures will then be held during the lecture period. In the seminars you experience mathematics to a certain extent "at work", you learn how new theories are created and open questions are answered. Often this is where the first contact with the current mathematics that is still the subject of research takes place. In a seminar, the students should learn to familiarize themselves with an area independently and to pass on the newly acquired knowledge to others in an understandable form; two important skills you will need later in your career.

The scientific work

These aspects are intensified in the scientific work. Depending on the course of study, the course ends with a diploma or admission thesis (for the state examination), or a first, smaller scientific work is created for the bachelor's degree, and for the master’s degree the work is a bit more extensive and demanding, comparable to a diploma thesis.

Anyone who writes a scientific paper works, supervised by a lecturer, on the basis of scientific publications in a current issue. Understanding other people's thought processes and developing your own ideas can flow into one another. Sometimes a new mathematical theorem is proven in such a work.

Classic and new degrees

Until recently there were essentially two degrees for studying mathematics at a German university: the diploma and the state examination. The state examination qualifies you for a job as a teacher at a higher school and will remain in place until further notice. The classic diploma course is divided into an approximately two-year basic course and a three to four-year main course. It is currently being replaced in many universities by a Bachelor's and Master's degree in order to harmonize and make university studies in Europe more transparent as part of the so-called Bologna Process. A three-year course ends with a bachelor's degree and can then be continued with a two-year master's degree.


Based on 22 ratings.

December 23, 2010 by Josephine Nockel
The text was great;) really helpful!

Comments are currently disabled.