## Module Handbook

• Dynamischer Default-Fachbereich geändert auf MAT

# Module MAT-14-12-M-3

## Module Identification

Module Number Module Name CP (Effort)
MAT-14-12-M-3 Introduction to Symbolic Computing 9.0 CP (270 h)

## Basedata

CP, Effort 9.0 CP = 270 h 1 Sem. in SuSe [3] Bachelor (Core) [DE] German Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Fieker, Claus, Prof. Dr. (PROF | DEPT: MAT) Malle, Gunter, Prof. Dr. (PROF | DEPT: MAT) Schulze, Mathias, Prof. Dr. (PROF | DEPT: MAT) Thiel, Ulrich, Prof. Dr. (PROF | DEPT: MAT) Böhm, Janko, Dr. (WMA | DEPT: MAT) [MAT-MaNF] Special Offers for Mathematics as a Minor [INF-88.79-SG] M.Sc. Computer Science [NORM] Active

## Courses

Type/SWS Course Number Title Choice in
Module-Part
Presence-Time /
Self-Study
SL SL is
required for exa.
PL CP Sem.
4V+2U MAT-14-12-K-3
Introduction to Symbolic Computing
P 84 h 186 h
U-Schein
- PL1 9.0 SuSe
• About [MAT-14-12-K-3]: Title: "Introduction to Symbolic Computing"; Presence-Time: 84 h; Self-Study: 186 h
• About [MAT-14-12-K-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

## Contents

• 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

Building on solid knowledge of linear algebra and analysis, as taught in a proof- and structure-oriented approach, the students have acquired basic theoretical and practical knowledge in an area of practical/applied mathematics.

They know and understand modern methods of symbolic computing and their complexity. In particular, they have developed a feeling for the design of algebraic algorithms as well as their practical implementation, and they are able to critically assess the possibilities and limits of the use of the algorithms. They can reproduce the proofs and independently prove or disprove statements.

In the exercise classes the students have acquired a confident, precise and independent handling of the terms, propositions and methods from the lecture.

## Literature

• 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.

## Registration

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

## Requirements for attendance of the module (informal)

Profound knowledge of linear algebra and analysis, e.g. from the module [MAT-10-1-M-2] or from the modules [MAT-02-13-M-1] and [MAT-02-11-M-1].

None