Main content

This entry is from Winter semester 2016/17 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): Written examination
Examination type: Successful completion of at least 50 percent of the points from the weekly exercises.
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

  • Real numbers: Axioms and properties, completeness axiom and interval nesting, representation in computer,
  • Sequences and series: properties, limits and inheritance rules, convergence criteria, Landau symbols,
  • Functions: Limit values and continuity, intermediate value theorem, theorem of minimum and maximum, differentiability incl. affin-linear approximation, derivation rules, numerical differentiation, local extremes, integrability, integration rules, numerical integration, non-actual integrals, mean value theorems, main theorem of differential and integral calculus,
  • Function sequences and series: point by point and uniform convergence, power series, Taylor development

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

Translation is missing. Here is the German original:

Keine. Empfohlen werden die Kompetenzen, die im Modul Grundlagen der Linearen Algebra vermittelt werden.


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

When studying B.Sc. Data Science, this module must be completed in the study area Basic 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 2016/17. 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.