Introduction to Symbolic Computing (4V+2U, 9.0 LP)
|SWS||Type||Course Form||CP (Effort)||Presence-Time / Self-Study|
|-||K||Lecture with exercise classes (V/U)||9.0 CP||186 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|| Bachelor (Core)|
+ further Lecturers of the department Mathematics
|Area of study||[MAT-GRU] Mathematics (B.Sc. year 1 and 2)|
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 (https://urm.mathematik.uni-kl.de).
Requirements for attendance (informal)
Requirements for attendance (formal)None
References to Course [MAT-14-12-K-3]
|[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|
|[MAT-14-KPOOL-3]||Practical Mathematics (B.Sc. Mathematics)|