Module Handbook

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Module MAT-12-10L-M-2

Fundamentals of Mathematics C: Geometry, Elementary Algebra and Number Theory (M, 10.0 LP)

Module Identification

Module Number Module Name CP (Effort)
MAT-12-10L-M-2 Fundamentals of Mathematics C: Geometry, Elementary Algebra and Number Theory 10.0 CP (300 h)

Basedata

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
Lecturers of the department Mathematics
Area of study [MAT-EDU] Mathematics (B.Ed./M.Ed.)
Reference course of study [MAT-31.105-SG] B.Ed. LaGR Mathematics
Livecycle-State [NORM] Active

Notice

The courses [MAT-12-11-K-2] Algebraic Structures und [MAT-12-22-K-3] Introduction to Algebra are also offered as distance learning course as part of the early entrance programme FiMS, see https://fims.mathematik.uni-kl.de

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

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
2V+2U MAT-12-11-K-2
Algebraic Structures
P 56 h 109 h
qU-Schein
- 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.

Module Part #B "Geometry" (Obligatory, 4.5 LP)

Type/SWS Course Number Title Choice in
Module-Part
Choice in
Course-Pool
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
KPOOL MAT-18-KPOOL-3
Geometry (B.Ed. Mathematics)
P WP-1
U-Schein
- PL1 [4.5] *
  • About [MAT-18-KPOOL-3]: Title: "Geometry (B.Ed. Mathematics)";
  • About [MAT-18-KPOOL-3]: A course from the course pool must be selected.
  • About [MAT-18-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: 82401 ("Combined examination")
    If the proseminar [MAT-18-04-K-3] is chosen as the course in the part "Geometry", the module examination consists of two separate examinations: an individual oral examination covering the course [MAT-12-11-K-2] and a written and/or oral examination for the proseminar (usually a combination of an oral presentation and a written paper). In this case, the type and duration of the examination will be announced by the lecturer (at the latest) at the beginning of the proseminar.

Evaluation of grades

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


Contents

  • Basic geometric terms;
  • At least one further area from geometry (e.g. Euclidean geometry, projective geometry, constructions with compasses and ruler, differential geometry of curves and surfaces in ℝ² and ℝ³);
  • Basic structures of elementary algebra: groups, rings, fields (in particular: symmetric group), substructures and factor structures (normal divisors and isomorphism theorems);
  • Fundamentals of number theory: congruence calculation, residues, Chinese remainder theorem with applications, principal ideal domains (Z and K[t], in particular: Euclidean algorithm).

Competencies / intended learning achievements

The students
  • are proficient in basic geometric concepts and the fundamentals of elementary algebra and elementary number theory and they comprehend their interrelationship; in particular, they can grasp the difference and recognise the cross-fertilisation of intuitive perception and rigorous proofs;
  • are familiar with the typical ways of thinking and working in mathematics (crystallizing essential structures): recognizing common structures in different contexts, applying general knowledge in different situations;
  • can judge how classical results of abstract mathematics can find practical applications;
  • are able to prepare and present mathematical statements in a suitable form.

Literature

  • G. Fischer: Lineare Algebra,
  • H.-J. Reiffen, G. Scheja, U. Vetter: Algebra,
  • H.-D. Ebbinghaus, et al.: Zahlen,
  • S. Lang: Algebraische Strukturen,
  • Bosch: Einführung in die Algebra.

Literature for the part "Geometry" can be found in the respective course descriptions in [MAT-18-KPOOL-3].

Materials

Further literature will be announced in the lectures; Exercise material is provided.

Registration

Registration for the exercise classes via the online administration system URM (https://urm.mathematik.uni-kl.de).

Requirements for attendance (informal)

None

Requirements for attendance (formal)

None

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

Course of Study Section Choice/Obligation
[MAT-31.105-SG] B.Ed. LaGR Mathematics Compulsory Modules [P] Compulsory
[MAT-66.105-SG] M.Ed. LaBBS Mathematics Compulsory Modules [P] Compulsory
[MAT-B4.105-SG] ZEP LaG Mathematics Compulsory Modules [P] Compulsory
[MAT-B2.105-SG] ZEP LaRSP Mathematics Compulsory Modules [P] Compulsory
[MAT-B5.105-SG] ZEP LaBBS Mathematics Compulsory Modules [P] Compulsory