This entry is from Summer semester 2021 and might be obsolete. You can find a current equivalent here.

# CS 280 — Basic Real Analysis (dt. Grundlagen der Analysis)

 Level, degree of commitment Basic module, required module Forms of teaching and learning,workload Lecture (4 SWS), recitation class (2 SWS), 270 hours (90 h attendance, 180 h private study) Credit points,formal requirements 9 CP Course requirement(s): Successful completion of at least 50 percent of the points from the weekly exercises. Examination type: Written examination Language,Grading German,The grading is done with 0 to 15 points according to the examination regulations for the degree program B.Sc. Computer Science. Duration,frequency One semester, each summer semester Person in charge of the module's outline Prof. Dr. Hajo Holzmann, Dr. Dorothea Strauer

## Contents

Basics of the mathematical language

• Basics of logic and sets
• Proof methods, mathematical induction
• Real numbers, functions, inequations
• Countability
• Factorials, binomial coefficients, binomial theorem

Sequences and series

• Properties of sequences and series, limits
• Convergence criteria
• Landau symbols

Functions of one variable

• Exponential function and trigonometric functions
• Limit values, continuity, monotony
• Intermediate value theorem, theorem of minimum and maximum
• Power series

Differentiability

• Affine-linear approximation
• Derivation rules
• Mean value theorem of differential calculus
• Local extrema
• Taylor expansion

Integrability

• Main theorem of differential and integral calculus,
• Integration rules
• Improper integrals

## Qualification Goals

The students shall

• acquire basic knowledge and skills in analysis, in particular an understanding of the concept of limit values for sequences, series, functions and power series,
• Recognize connections to their own discipline,
• practice mathematical and in particular analytical ways of thinking and working on concrete questions, also on technically motivated problems,
• develop mathematical intuition and learn how to translate it into precise terms and formal justifications,
• to train their abstraction skills,
• improve their oral communication skills in the exercises by practicing free speech in front of an audience and during discussion

## Prerequisites

None. The competences taught in the following module are recommended: Basic Linear Algebra.

## Applicability

Module imported from B.Sc. Computer Science.

It can be attended at FB12 in study program(s)

• B.Sc. Data Science
• B.Sc. Computer Science
• LAaG Computer Science

When studying B.Sc. Business Informatics, this module must be completed in the study area Mathematical Modules.

• Dörfler, W.; Peschek, W. : Einführung in die Mathematik für Informatiker, Hanser
• Wolff, M.; Gloor, O.; Richard, Chr. : Analysis Alive, Birkhäuser
• Forster, O. : Analysis 1, Vieweg
• Hachenberger, D.: Mathematik für Informatiker, Pearson
• Oberguggenberger, M.; Ostermann, A.: Analysis for Computer Scientists, Springer
• Teschl, G.; Teschl, S.: Mathematik für Informatiker, Band 2: Analysis und Statistik, Springer