Math for Computer Scientists 2 (MA2)
2. Semester
5 ECTS | 4 SWS
Written Exam 90 Minutes (K90)
Deepen your mathematical foundations: You will learn about number theory, linear algebra, and the fundamentals of cryptography. Using mathematical proof techniques, you will analyze and solve problems in computer science.
Contents
- Number Theory (Prime Numbers, Prime Factorization, Euler`s Totient Function, Positional Number Systems, Number Systems with Arbitrary Bases, Binary Representation, Computer Number Representation)
- Mathematical Foundations of Cryptography (Extended Euclidean Algorithm, Modular Arithmetic, Residue Class Rings, Multiplicative Inverses in Residue Class Rings, Fermat–Euler Theorem)
- Fundamentals of Linear Algebra and Applications in Computer Science (Systems of Linear Equations, Gaussian Elimination, the Vector Space Rⁿ, Vector Operations, Dot Product, Cross Product, Lines, Planes, Matrices, Rotation Matrices, Reflections, Symmetric Matrices, Inverse Matrices, Determinants, Eigenvalues)
Competencies
Students are able to
- understand mathematical reasoning and proof techniques.
- apply mathematical problem-solving strategies to computer science problems.
- understand and analyze fundamental cryptographic problems.
- classify and analyze data-related problems.
- apply methods of linear algebra.
Literature
- Howard Anton: Lineare Algebra (Einführung, Grundkurs, Übungen)
- Matthias Plaue , Mike Scherfner: Mathematik für das Bachelorstudium I
- Gilbert Strang: Lineare Algebra
- Günter Gramlich: Lineare Algebra
- Günter Gramlich: Anwendungen der Linearen Algebra
- Fetzer, Fränkel: Mathematik, Band 1
- Peter Stingl: Mathematik für Fachhochschulen, Technik und Informatik
- Lothar Papula: Mathematik für Ingenieure und Naturwissenschaftler, Band 2
- Albrecht Beutelspacher: Lineare Algebra
Lecturer
- Prof. Dr. Elena Fimmel
- Prof. Dr. Miriam Föller-Nord
- Prof. Dr. Lutz Strüngmann
- Dr. Yordan Todorov
- Prof. Dr. Ivo Wolf
Recommended Previous Knowledge
Module Details
| Semester |
2 |
| Lecture Language |
German |
|
Frequency
|
Every Term
|
| Credit Points (ECTS)
|
5 |
| Course Coordinator |
Prof. Dr. Lutz Strüngmann |
| Duration |
1 Semester |
|
Course Achievement
|
None |
|
Prerequisite for exam
|
Compulsory Assignment (PU) |
|
Exam
|
Written Exam 90 Minutes (K90) |
Weekly Hours (SWS)
| Lecture |
2 SWS |
| Exercises |
2 SWS |
| Sum |
4 SWS |
Work Load
| Lecture |
45 h |
| Self Study |
60 h |
| Assignments |
15 h |
| Exam Preparation |
30 h |
| Sum |
150 h |
