Computer Algebra

What it is about

You learn fundamental algebraic structures and their representation on the computer (e.g., integers, rational numbers, field extensions, finite fields, polynomials, rational functions). You also cover fundamental algorithms such as primality tests, prime factorization, gcd computation and polynomial factorization; optionally formal summation/integration as well as basics on varieties, ideals and Gröbner bases are offered. In the end you will understand concepts and methods of computer algebra and design, analyze, implement and apply algebraic algorithms.

What you will be able to do

• Understand fundamental algebraic data representations
• Apply primality tests and factorization procedures
• Compute gcd and factor polynomials
• Design, analyze and implement algebraic algorithms
• Basic knowledge on formal summation/integration (optional)
• Fundamentals on varieties, ideals and Gröbner bases (optional)

What the module consists of

• VorlesungConveying the contents through lectures with demonstrative examples and discussion
• Übung/Practice-SessionDeepening through worksheets, solutions and independent work

Teaching method

• VorlesungPresentation of the content, motivation and stimulation for independent analysis and literature work
• Übungsstunden mit Aufgaben und HausaufgabenPractical deepening and self-assessment of learning progress