Recommendation for the design of the Bachelor's program (version 2021)

In principle, the course of study for the first three semesters of the Bachelor's program is prescribed by the curriculum. After that, students have the possibility to choose elective modules for further basic mathematical education as well as for "preparation for scientific work" and "mathematical career preparation".

The first year

The bachelor's program in mathematics is also required by law to have an study entrance- and orientation-phase (StEOP), the successful completion of which is a prerequisite for further study

The StEOP consists of the module "Einführung in das mathematische Arbeiten" (EMA, 16 ECTS), which consists of a lecture and an exercise class. The exercise class, in turn, is divided into two parts with separate content: exercises from the lecture and computational exercises. A positive completion of both parts is necessary to pass the exercise class. In order to avoid delays in studying, the entire StEOP module should be completed in the first semester. In addition, however, the VU Mathematisches Programmieren (MPR), the two basic lectures Analysis 1 and Linear Algebra 1 from the module "Einführung in die höhere Mathematik" (EHM) and the corresponding proseminar should be attended in the first semester. (It is no problem to take one of the two lecture exams during the second semester). In order to further studies, a positive completion of the VU Mathematisches Programmieren is especially important, since it is a prerequisite for the attendance of later courses.

The entire StEOP module as well as the VU Mathematisches Programmieren are also offered regularly in summer semesters.

As an introduction to studying, it is highly recommended to attend the information session for first-year students, which is usually held during the first unit of the lecture "Einführung in das mathematische Arbeiten" on the first day of the semester. Information on this can be found in the information for freshmen on the homepage of the Faculty of Mathematics

Already in the first semester, it is crucial to study regularly. Otherwise, the content of the courses will quickly become incomprehensible, and you will be lost in the course material. The tutorial and the proseminar in the EMA and EHM modules are of central importance for regular learning. Active participation and independent work on the exercises are the best way to "stay on the ball". Completing the exercises on time is also very useful from an organizational point of view, because making up for them in a later semester is rather time-consuming.

It is also important not to be discouraged by difficulties. Almost all beginners find it difficult to get used to the way of thinking and speaking in mathematics. But once you have overcome this hurdle, everything becomes much easier and less tedious.

In the second semester, the modules Analysis 2 and Lineare Algebra 2 (both VO+PS) continue the introductory courses. Together with the Diskrete Mathematik und Theoretische Informatik module (VO+PS), these three subjects form the focus of the second semester. Again, regular attendance of the proseminars and active participation helps to stay on the ball. In summary:

The second year

The third semester consists of the compulsory modules AlgebraNumerische Mathematik, and Integration und Stochastik (each 10 ECTS consisting of lecture and proseminar). From the fourth semester on, you have a lot of freedom to structure your studies yourself through the offered elective/compulsory subjects. We recommend students who have already developed an idea in which subject they want to write their bachelor thesis, to complete those necessary courses early.

The third year

In the third year, you will complete further elective/compulsory modules and finish your Bachelor's thesis during the Bachelor's seminar. All faculty members with a doctorate can be considered as supervisors for this work. It is advantageous to decide on a direction early on and to secure a commitment to supervision in the desired area.

Elective modules

In the 4th, 5th and 6th semesters, elective modules amounting to 80 ECTS must be completed. A distinction is made between the foundational-elective module group and the specialized-elective module group.

Foundational-elective module group

The foundational-elective module group consists of 7 modules of which, according to the standard study path, 3 should be completed in the 4th and 2 in the 5th semester. Each of these modules consists of a lecture and a proseminar for a total of 10 ECTS, which together are fundamental for further specializations in various fields.

Specialized-elective module group

The specialized-elective module group offers students a wide range of options, from mathematical specializations to very application-oriented ones: From this elective module group, elective modules amounting to a total of 30 ECTS are to be selected according to what is offered, whereby it is recommended to complete 10 of them in the 5th semester and the remaining 20 in the 6th semester. Please refer to the course catalog to find out which courses are offered in the respective semester. If no lecture or proseminar is listed under the module title, no course is offered in the respective semester.

Recommendation for the study plan in the Bachelor's program (Version 2014)

In principle, the course of study for large parts of the Bachelor's program is prescribed by the curriculum, although in the third year of study three modules may be chosen at will from the elective modules offered for "Vorbereitung auf die wissenschaftliche Arbeit" and from "Mathematischer Berufsvorbereitung".

The first year

The bachelor's program in mathematics is also required by law to have an study entrance- and orientation-phase (StEOP), the successful completion of which is a prerequisite for further study

The StEOP consists of the module "Einführung in das mathematische Arbeiten" (EMA, 16 ECTS), which consists of a lecture and an exercise class. The exercise class, in turn, is divided into two parts with separate content: exercises from the lecture and computational exercises. A positive completion of both parts is necessary to pass the exercise class. In order to avoid delays in studying, the entire StEOP module should be completed in the first semester. In addition, however, the VU Mathematisches Programmieren (MPR), the two basic lectures Analysis 1 and Linear Algebra 1 from the module "Einführung in die höhere Mathematik" (EHM) and the corresponding proseminar should be attended in the first semester. (It is no problem to take one of the two lecture exams during the second semester). In order to further studies, a positive completion of the VU Mathematisches Programmieren is especially important, since it is a prerequisite for the attendance of later courses.

The entire StEOP module as well as the VU Mathematisches Programmieren are also offered regularly in summer semesters.

As an introduction to studying, it is highly recommended to attend the information session for first-year students, which is usually held during the first unit of the lecture "Einführung in das mathematische Arbeiten" on the first day of the semester. Information on this can be found in the information for freshmen on the homepage of the Faculty of Mathematics

Already in the first semester, it is crucial to study regularly. Otherwise, the content of the courses will quickly become incomprehensible, and you will be lost in the course material. The tutorial and the proseminar in the EMA and EHM modules are of central importance for regular learning. Active participation and independent work on the exercises are the best way to "stay on the ball". Completing the exercises on time is also very useful from an organizational point of view, because making up for them in a later semester is rather time-consuming.

It is also important not to be discouraged by difficulties. Almost all beginners find it difficult to get used to the way of thinking and speaking in mathematics. But once you have overcome this hurdle, everything becomes much easier and less tedious.

In the second semester, the modules Analysis 2 and Lineare Algebra 2 (both VO+PS) continue the introductory courses. Together with the Diskrete Mathematik und Theoretische Informatik module (VO+PS), these three subjects form the focus of the second semester. Again, regular attendance of the proseminars and active participation helps to stay on the ball.

Im zweiten Semester setzen die Lehrveranstaltungen Analysis und Lineare Algebra und Geometrie 1 (both VO+UE) continue the introductory courses. Together with the Zahlentheorie (VO+UE), these three subjects form the focus of the second semester. Again, regular attendance of the proseminars and active participation helps to stay on the ball. The course sequence on Analysis und Lineare Algebra will be completed by the end of the third semester.  Alongside in the second semester, there is also the module Programmieren (PRO) to be completed.  In summary: 

First semester (33 ECTS)

  • StEOP: module GHM (VO "Einführung in das mathematische Arbeiten", UE "Hilfsmittel aus der EDV") 15 ECTS
  • module EHM (VO+UE "Einführung in die Analysis", VO+UE "Einführung in die Lineare Algebra und Geometrie") 18 ECTS

Second semester (30 ECTS)

  • module ANA (VO+UE "Analysis") 11 ECTS
  • from the module LAG: VO+UE "Lineare Algebra und Geometrie 1" 9 ECTS
  • module ZTH (VO+UE "Zahlentheorie") 5 ECTS
  • module PRO (PR "Programmierpraktikum") 5 ECTS

The second year

In general, in the second and third year you have a little freedom (through the offered electives) to structure your studies yourself. We recommend students who have already developed an idea in which subject they want to write their bachelor thesis, to complete the necessary courses early. The standard study path has the following courses:

Third Semester (28 ECTS)

  • from the module LAG: VO "Lineare Algebra und Geometrie 2“ 3 ECTS
  • module HAN (VO+UE "Höhere Analysis und elementare Differentialgeometrie“) 10 ECTS
  • module NUM (VO+UE "Numerische Mathematik 1“) 10 ECTS
  • module KAN (VO+UE "Komplexe Analysis“) 5 ECTS

Fourth Semester (29 ECTS)

  • module PTS (VO+UE "Wahrscheinlichkeitstheorie und Statistik“) 10 ECTS
  • module DMA (VO+UE "Diskrete Mathematik“) 5 ECTS
  • from the module DGL: VO+UE "Gewöhnliche Differentialgleichungen“ 7 ECTS
  • from the module ALG: VO+UE "Algebra 1“ 7 ECTS

The third year

In the third year, the Bachelor's thesis is presented as part of the Bachelor's seminar. All faculty members with a doctorate can be considered as supervisors for this work. It is advantageous to decide on a direction early on and to secure a commitment to supervision in the desired area.

Fifth Semester (29 ECTS)

  • from the module DGL: VO+UE "Partielle Differentialgleichungen" 7 ECTS
  • from the module ALG: VO+UE "Algebra 2" 7 ECTS
  • module MIK: (Lehrveranstaltung aus der Auswahlliste) 3 ECTS
  • from the module TFA: VO+UE "Grundbegriffe der Topologie" 5 ECTS
  • one module from the elective module group "Mathematisches Wahlfach" 7 ECTS

Sixth Semester (31 ECTS)

  • from the module TFA: VO+UE "Funktionalanalysis" 7 ECTS
  • module BAS (SE "Bachelorseminar") 10 ECTS
  • two modules from the elective module group "Mathematisches Wahlfach" 14 ECTS

Wahlmodule

In the 5th and 6th semesters, 3 elective modules each with 7 ECTS, totaling 21 ECTS, are expected.

Elective module offering

The currently-offered elective modules can be found in the course catalog. In general, the following elective modules are offered regularly: Modellierung every summer semester; Finanzmathematik every winter semester; Biomathematik, Optimierung once a year; Logik every three semesters; Bild- und Signalverarbeitung every second year. The elective modules offered in each case are indicated by the courses listed under the module code in the course catalog. If no lecture or exercise class is listed under the module title, the corresponding module is not offered that semester.