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

Level, degree of commitment Basic module, compulsory elective 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

Students

  • Know basic calculus,
  • understand the concept of limits in sequences, series, functions and power series,
  • can recognize cross connections to their own discipline,
  • can apply mathematical and, in particular, analytical ways of thinking and working to concrete problems, including technically motivated problems,
  • have a mathematical intuition that can be translated into precise concepts and formal reasoning,
  • have a trained ability to abstract,
  • can discuss content from calculus in a structured manner in a group.

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
  • B.Sc. Business Informatics
  • LAaG Computer Science
  • BA Minor Mathematics
  • BA Minor Computer Science

When studying B.Sc. Data Science, this module can be attended in the study area Basic and Continuing Modules in Mathematics.


Recommended Reading

  • 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



Please note:

This page describes a module according to the latest valid module guide in Winter semester 2023/24. Most rules valid for a module are not covered by the examination regulations and can therefore be updated on a semesterly basis. The following versions are available in the online module guide:

The module guide contains all modules, independent of the current event offer. Please compare the current course catalogue in Marvin.

The information in this online module guide was created automatically. Legally binding is only the information in the examination regulations (Prüfungsordnung). If you notice any discrepancies or errors, we would be grateful for any advice.