Information on individual educational components (ECTS-Course descriptions) per semester

Discrete Mathematics

The part "Linear Algebra" comprises the following chapters:

• linear spaces
• linear independence
• bases
• dimensions
• linear maps
• matrices
• determinants,
• linear equation systems
• Euclidean vector spaces
• orthogonal maps
• eigenvalues and eigenvectors
• major axis transformation.

The "Analysis" part comprises the following chapters:

• sequences and series
• convergence
• continuity
• elementary functions
• differential quotient
• local extremes
• mean theorem
• limit values of functions
• definite integral
• indefinite integral
• main law of integral calculus
• improper integrals
• power series
• Taylor series.

Technical and methodological competence (F / M)

In the first part of the course, students develop an understanding of the structure of a linear space and linear images. Students know and understand various applications of linear maps, e.g. Google algorithm (page rank), solution of systems of equations, jpeg compression, linear codes.

In the second part, the students develop an understanding of the topological structures of standardized spaces, they can analyze and know nonlinear maps and understand their applications: solving nonlinear equations, optimization, qualitative and quantitative behavior of system dynamics.

Through specifically selected forms of learning and teaching, this course also contributes to the training of the following general skills:

Social and communicative competence (S / K)

• Reliability: Comply with rules and agreements and do your own work in the promised quality

Self-competence (S)

• Learning competence and motivation: Ability and willingness to acquire new knowledge independently and to learn from successes and failures
• Adaptability: Engaging in changing conditions and being able to deal with changing situations
• Expressiveness: Ability to use a clear and understandable form of expression and written language as well as a situation-appropriate choice of words

Transfer Competence (T)

• Ability to analyze and present / communicate: Capture and organize assets, extensive and complex relationships in a short time, filter out the essentials and present them in a generally understandable way
• Assessment and problem-solving ability: assessing facts and being able to use them to derive consequences and approaches
• Organizational skills: Be able to implement goals in work tasks and make optimal use of the available resources

Lecture in front of the whole group, exercises in three groups on paper and on the computer. Individual feedback on homework.

Two written exams, assessment of cooperation in the seminar and homework.

For a positive grade, overall across all parts of the examination a minimum of 50% of the possible points must be achieved AND in the following parts of the examination a minimum of 50% of the points must be achieved:

Two witten exams

Non applicable

Classroom teaching