Module Handbook

  • Dynamischer Default-Fachbereich geändert auf MAT

Course MAT-14-12-K-3

Introduction to Symbolic Computing (4V+2U, 9.0 LP)

Course Type

SWS Type Course Form CP (Effort) Presence-Time / Self-Study
- K Lecture with exercise classes (V/U) 9.0 CP 186 h
4 V Lecture 56 h
2 U Exercise class (in small groups) 28 h
(4V+2U) 9.0 CP 84 h 186 h


CP, Effort 9.0 CP = 270 h
Position of the semester 1 Sem. in SuSe
Level [3] Bachelor (Core)
Language [DE] German
Area of study [MAT-GRU] Mathematics (B.Sc. year 1 and 2)
Livecycle-State [NORM] Active


The course is accompanied by a programming lab course: [MAT-14-12P-K-3].

Possible Study achievement

  • Verification of study performance: proof of successful participation in the exercise classes (ungraded)
  • Examination number (Study achievement): 83240 ("Exercise Class Introduction to Symbolic Computing")
  • Details of the examination (type, duration, criteria) will be announced at the beginning of the course.


  • primality testing and factorisation of integers,
  • polynomial arithmetic (fast polynomial multiplication, modular gcd computation, factorisation),
  • modules over principal ideal domains (structural theorem, Hermite and Smith normal form),
  • Gröbner bases for ideals and modules,
  • lattices (rational reconstruction, LLL algorithm, application to polynomial factorization).

Competencies / intended learning achievements

The students are familiar with modern methods of symbolic computing and their complexity. In particular, they have developed a feeling for the design of algebraic algorithms and their practical implementation. The latter is deepened in the optional programming lab course.


  • H. Cohen: A Course in Computational Algebraic Number Theory,
  • D. A. Cox, J. Little, D. O'Shea: Ideals, Varieties, and Algorithms,
  • W. Decker, G. Pfister: A First Course in Computational Algebraic Geometry,
  • J. von zur Gathen, J. Gerhard: Modern Computer Algebra,
  • D. Knuth: The Art of Computer Programming. Volumes 1,2,3,
  • R. Lidl, H. Niederreiter: Introduction to Finite Fields and Their Applications,
  • G.-M. Greuel, G. Pfister: A SINGULAR Introduction to Commutative Algebra.


Further literature will be announced in the lecture(s); exercise material is provided.


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

Requirements for attendance (informal)



Requirements for attendance (formal)


References to Course [MAT-14-12-K-3]

Module Name Context
[MAT-14-10L-M-3] Topic Module B: Mathematics as an Interdisciplinary Cross-Sectional Science WP: Obligation to choose 4V+2U, 9.0 LP
[MAT-14-12-M-3] Introduction to Symbolic Computing P: Obligatory 4V+2U, 9.0 LP
Course-Pool Name
[MAT-14-KPOOL-3] Practical Mathematics (B.Sc. Mathematics)