Lecturers: Laurenz Wiskott.

Enrollment: Students from RUB simply enroll in the Moodle course and participate. Students from other study programs should contact Laurenz Wiskott at <laurenz.wiskott@rub.de>. You might also have to enroll for this course in your examination office, but this is something you'll have to figure out yourself.

Credits: 5 CP

Workload: 150 h

Semester: any

Cycle (Turnus): each SS

Duration (Dauer): 1 semester

Contact time (Kontaktzeit): 4 SWS (60 h)

Self studies (Selbststudium): 90 h

Group size (Gruppengröße): ca 30

Language: English

Requirements: Basic knowledge of calculus and linear algebra

Learning outcomes (Lernziele): After the successful completion of this course the students

Content (Inhalt): This course covers some mathematical methods that are relevant for modeling and data analysis. Particular emphasis is put on an intuitive understanding as is required for a creative command of mathematics. The following topics are covered:

• Functions and how to visualize them
• Vector spaces
• Matrices as transformations
• Systems of linear differential equations
• Qualitative analysis of nonlinear differential equations
• Bayesian theory
• Markov chains

Teaching format (Lehrformen):

This course is given with the flipped/inverted classroom concept. First, the students work through online material by themselves. In the lecture time slot we then discuss the material, find connections to other topics, ask questions and try to answer them. In the tutorial time slot the newly acquired knowledge is applied to analytical exercises and thereby deepened. I encourage all students to work in teams during self-study time as well as in the tutorial. In particular I expect that students have worked through the material of the first unit when they come to the first session.

Exam (Prüfungsformen):

The course is concluded with a digital written exam for 90 minutes within a 100 minutes time slot. We offer two dates in the semester of the course and none in the next semester. You are free to pick either of the two dates, but if you pick the second and you fail, the next opportunity to retry the exam is only about one year later.

The exam will be in presence, and it will be a closed book exam, thus you are not allowed to use any tools except for a one sided DIN A4 handwritten page of formulary that you create yourself.

Registration for the exam with us happens at the end of the course. In addition to being registered for the regular Moodle course you also have to register for the Exam Moodle, and then you simply take the exam. You might also have to register for this exam in your examination office, but this is something you'll have to figure out yourself. Registering with us and with the examination office are independent of each other. If possible we will report your grade to the examination office in any case, whether you have registered there or not. There are no prerequisits for the exam, like 50% points in tutorials or the like.

A mock exam will be available towards the end of the course. It will be shorter than the final exam. The main purpose is to give you a good impression of the style of the exam and therefore facilitate exam preparation.

Condition for granting the credit points (Voraussetzungen für die Vergabe von Kreditpunkten):

To pass this course and receive credit, you need a score of at least 50 out of 100 on the final exam. The score S differs from the points P that you achieved on the final exam. The default mapping is: S=100*(P-C)/(M-C), where C is the expected number of points one would get by pure guessing and M the maximum possible number of points. For example, with pure guessing, i.e. P=C, you would get a score of 0 on average and with perfect answers, i.e. P=M, you get a score of 100. The percentage grades will then be translated into the grading schemes required for your study program, e.g. grades from 0.7 or 1.0 to 5.0.