Detailed information 
Original study plan 
Bachelor's programme Technical Mathematics 2022W 
Objectives 
In the last decades big parts of mathematics has been algorithmized and many mathematical problems (or problems coming from natural and technical sciences that can be modeled in mathematics) can be solved with the computer. A major contribution for this algorithmic revolution is the computer algebra. This lecture aims at introducing the most crucial algorithms in this field and illustrating how they can be used for nontrivial applications.

Subject 
We discuss constructive symbolic methods for simplification of expressions and solving algebraic (i.e., polynomial) systems of equations.
Among others, the following algorithms are explored:
 basic structures and algorithms
 the extended Euclidean algorithm, polynomial remainder sequences and applications
 modular methods based on Hensel lifting and the Chinese Reemainder Theorem (resultants, gcd, factorization)
 a gentle introduction to Gröbner bases
 symbolic summation and integration

Criteria for evaluation 
Depending on the needs of the participants there will be a written or oral exam.

Methods 
The different algorithms will be presented on the blackboard. Concrete examples will be carried out with the computer.

Language 
English 
Study material 
Joachim von zur Gathen and Jürgen Gerhard, "Modern Computer Algebra", Cambridge University Press, 2013 (or earlier versions).

Changing subject? 
No 
Further information 
Until term 2018S known as: 201ALGECALV12 VL Computer Algebra

Corresponding lecture 
^{(*)}ist gemeinsam mit 201ALGECALU12: UE Computer Algebra (1,5 ECTS) äquivalent zu TM1WHKVCASY: KV Computeralgebra (4,5 ECTS)
