Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Module MAT-12-10A-M-2

Pure Mathematics A (M, 10.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-12-10A-M-2 Pure Mathematics A 10.0 CP (300 h)


CP, Effort 10.0 CP = 300 h
Position of the semester 2 Sem. from WiSe/SuSe
Level [2] Bachelor (Fundamentals)
Language [DE] German
Module Manager
Lecturers of the department Mathematics
Area of study [MAT-GRU] Mathematics (B.Sc. year 1 and 2)
Reference course of study [MAT-82.105-SG] B.Sc. Mathematics
Livecycle-State [NORM] Active


The courses are (partly) also offered as distance learning course as part of the early entrance programme FiMS, see

Module Part #A "Algebraic Structures" (Obligatory, 5.5 LP)

Type/SWS Course Number Title Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-12-11-K-2
Algebraic Structures
P 56 h 109 h
ja PL1 5.5 WiSe/SuSe
  • About [MAT-12-11-K-2]: Title: "Algebraic Structures"; Presence-Time: 56 h; Self-Study: 109 h
  • About [MAT-12-11-K-2]: The study achievement [qU-Schein] proof of successful participation in the exercise classes (incl. written examination) must be obtained. It is a prerequisite for the examination for PL1.

Module Part #B "Pure Mathematics A1" (Obligatory, 4.5 LP)

Type/SWS Course Number Title Choice in
Choice in
Presence-Time /
SL SL is
required for exa.
PL CP Sem.
Pure Mathematics (B.Sc. Mathematics)
P WP-1
- PL1 [4.5] *
  • About [MAT-10-KPOOL-3]: Title: "Pure Mathematics (B.Sc. Mathematics)";
  • About [MAT-10-KPOOL-3]: A course from the course pool must be selected.
  • About [MAT-10-KPOOL-3]: The study achievement [U-Schein] proof of successful participation in the exercise classes (ungraded) must be obtained.

Examination achievement PL1

  • Form of examination: oral examination (20-30 Min.)
  • Examination Frequency: each semester
  • Examination number: 82027 ("Module Exam Pure Mathematics A")
    As far as the module part #B is concerned, it is generally possible to give the module examination PL1 to another courses than the required study achievement (proof of successful participation in the exercise classes). This requires that none of the courses involved has already been included in another module.

Evaluation of grades

The grade of the module examination is also the module grade.


A. Algebraic structures:
  • Basic algebraic structures: groups, rings, fields (in particular: symmetric group);
  • Substructures and factor structures (in particular: normal subgroups, isomorphism theorems);
  • principal ideal domains: ℤ, polynomial ring K[t] (in particular: Euclidean algorithm).

B. Pure Mathematics A1:

Introduction to an area of pure mathematics of choice from: Algebra, Differential Equations, Elementary Number Theory, Functional Analysis, Complex Analysis, Measure and Integration Theory, Topology, Vector Analysis or any other area of pure mathematics.

Competencies / intended learning achievements

Upon successful completion of this module, the students know and understand the axiomatic methodology of mathematics and the basic structures and methods of algebra. In addition, they have acquired basic knowledge in an area of pure mathematics, building on the knowledge they acquired in the first semester. They have learned to recognise general mathematical structures and to formulate statements about them precisely. Their creativity in dealing with abstract structures was promoted. They have learned to understand mathematical proofs and to independently prove or disprove mathematical statements in simple examples.

In the exercise classes they have acquired a confident, precise and independent handling of the terms, propositions and methods from the lectures. Special attention has been paid to learning a logically correct, complete argumentation.


see course descriptions


Registration for the exercise classes via the online administration system URM (

Requirements for attendance (informal)

see course descriptions

Requirements for attendance (formal)


References to Module / Module Number [MAT-12-10A-M-2]

Course of Study Section Choice/Obligation
[MAT-82.105-SG] B.Sc. Mathematics Pure Mathematics [P] Compulsory
[MAT-82.276-SG] B.Sc. Business Mathematics General Mathematics [WP] Compulsory Elective