Spezialisierung Mathematics for Data Science

The main goal of this course is to introduce topics in Discrete Mathematics relevant to Data Analysis. We will start with a brief introduction to combinatorics, the branch of mathematics that studies how to count. Basics of this topic are critical for anyone working in Data Analysis or Computer Science. We will illustrate new knowledge, for example, by counting the number of features in data or by estimating the time required for a Python program to run. Next, we will apply our knowledge in combinatorics to study basic Probability Theory. Probability is everywhere in Data Analysis and we will study it in much more details later. Our goals for probability section in this course will be to give initial flavor of this field. Finally, we will study the combinatorial structure that is the most relevant for Data Analysis, namely graphs. Graphs can be found everywhere around us and we will provide you with numerous examples. We will mainly concentrate in this course on the graphs of social networks. We will provide you with relevant notions from the graph theory, illustrate them on the graphs of social networks and will study their basic properties. In the end of the course we will have a project related to social network graphs. As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in Python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in Data Analysis, starting from motivated high school students.

Hi! Our course aims to provide necessary background in Calculus sufficient for up-following Data Science courses. Course starts with basic introduction to concepts concerning functional mappings. Later students are assumed to study limits (in case of sequences, single- and multivariate functions), differentiability (once again starting from single variable up to multiple cases), integration, thus sequentially building up a base for the basic optimisation. To provide an understanding of the practical skills set being taught, the course introduces the final programming project considering the usage of optimisation routine in machine learning. Additional materials provided during the course include interactive plots in GeoGebra environment used during lectures, bonus reading materials with more general methods and more complicated basis for discussed themes.

The main goal of the course is to explain the main concepts of linear algebra that are used in data analysis and machine learning. Another goal is to improve the student’s practical skills of using linear algebra methods in machine learning and data analysis. You will learn the fundamentals of working with data in vector and matrix form, acquire skills for solving systems of linear algebraic equations and finding the basic matrix decompositions and general understanding of their applicability. This course is suitable for you if you are not an absolute beginner in Matrix Analysis or Linear Algebra (for example, have studied it a long time ago, but now want to take the first steps in the direction of those aspects of Linear Algebra that are used in Machine Learning). Certainly, if you are highly motivated in study of Linear Algebra for Data Sciences this course could be suitable for you as well.