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Mathematics

Module name (EN):
Name of module in study programme. It should be precise and clear.
Mathematics
Degree programme:
Study Programme with validity of corresponding study regulations containing this module.
International Tourism-Management, Bachelor, ASPO 01.10.2015
Module code: BITM-140
SAP-Submodule-No.:
The exam administration creates a SAP-Submodule-No for every exam type in every module. The SAP-Submodule-No is equal for the same module in different study programs.
P420-0206
Hours per semester week / Teaching method:
The count of hours per week is a combination of lecture (V for German Vorlesung), exercise (U for Übung), practice (P) oder project (PA). For example a course of the form 2V+2U has 2 hours of lecture and 2 hours of exercise per week.
4V (4 hours per week)
ECTS credits:
European Credit Transfer System. Points for successful completion of a course. Each ECTS point represents a workload of 30 hours.
5
Semester: 1
Mandatory course: yes
Language of instruction:
English/German
Assessment:
Written exam (90 minutes / can be repeated semesterly)

[updated 17.09.2018]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

BITM-140 (P420-0206) International Tourism-Management, Bachelor, ASPO 01.10.2013 , semester 1, mandatory course
BITM-140 (P420-0206) International Tourism-Management, Bachelor, ASPO 01.10.2015 , semester 1, mandatory course
BITM-140 (P420-0206) International Tourism-Management, Bachelor, ASPO 01.10.2017 , semester 1, mandatory course
Workload:
Workload of student for successfully completing the course. Each ECTS credit represents 30 working hours. These are the combined effort of face-to-face time, post-processing the subject of the lecture, exercises and preparation for the exam.

The total workload is distributed on the semester (01.04.-30.09. during the summer term, 01.10.-31.03. during the winter term).
60 class hours (= 45 clock hours) over a 15-week period.
The total student study time is 150 hours (equivalent to 5 ECTS credits).
There are therefore 105 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
None.
Recommended as prerequisite for:
Module coordinator:
Prof. Dr. Teresa Melo
Lecturer: Prof. Dr. Teresa Melo

[updated 02.09.2011]
Learning outcomes:
After successfully completing this module students will:
 
- be able to model economic problems in the language of mathematics,
- be able to explain the basic formalities of differential and integral calculus, as well as matrix calculus,
- be able to test fundamental mathematical methods of analysis and linear algebra using examples,
 
- have mastered basic concepts and calculation methods of financial mathematics with regard to interest, annuity and sinking fund calculations,
 
- be able to model and solve economic linear optimization problems,
 
- be able to demonstrate the properties and possible applications of mathematical methods and assess their limits,
- be able to economically interpret and implement the results obtained by means of mathematical methods,
 
- have developed analytical skills by independently solving tasks in the subject area.
 
Differential calculus:
 


[updated 17.09.2018]
Module content:
 
-Functions of a variable, differentiation rules
-Application of differential calculus to basic business functions
-Functions with several variables, partial derivatives, extreme values with and without consideration of constraints
Integral calculus
  
 
-Root functions, elementary integration rules
-Special integration techniques: integration by parts, substitution
-Specific integral and economic applications of integral calculus
  
Elements of financial mathematics:
-Interest-rate models
-Annuity calculation
-Sinking fund calculation
  
Basics of linear algebra:
-Description of business processes using matrices (e. g. production processes)
-Elementary calculations with matrices, matrix multiplication
 
-Creation of linear systems of equations and solution methods (e. g. Gauss algoritm)
Linear programming:
 
 
-Creating models for business problems (e. g. production,
 logistics, marketing, investment)
-Graphical solution method for solving linear programming models
-Simplex method and economic interpretation of optimal solutions


[updated 17.09.2018]
Teaching methods/Media:
Lecture and discussion in a large group using transparencies (projectors) and the blackboard (theory and example calculations).
The lecture will be supplemented by exercises and tutorials. A large number of exercise sheets covering the wide range topics in this module will be provided for work at home. Afterwards, the solutions will be discussed with the students.
Both the lecture notes and the exercise sheets will be available to students in electronic form.


[updated 17.09.2018]
Recommended or required reading:
Gohout, Operations Research: Einige ausgewählte Gebiete der linearen und nichtlinearen Optimierung_, 4. erw. Auflage, Oldenbourg Verlag, München, 2009
Karmann, Mathematik für Wirtschaftswissenschaftler: Problemorientierte Einführung, 6. Auflage, Oldenbourg Verlag, München/Wien, 2008
Luderer/Würker, Einstieg in die Wirtschaftsmathematik, 9. aktual. Auflage, Springer Gabler, Wiesbaden, 2015
Sydsaeter/Hammond, Mathematik für Wirtschaftswissenschaftler: Basiswissen mit Praxisbezug, 4. aktual. und erw. Auflage, Pearson Studium, München, 2014
Tietze, Einführung in die angewandte Wirtschaftsmathematik, 17., erw. Auflage, Springer Spektrum, 2013
Tietze, Einführung in die Finanzmathematik - Klassische Verfahren und neuere Entwicklungen: Effektivzins- und Renditeberechnung, Investitionsrechnung, Derivative Finanzinstrumente, 12. erw. Auflage, Springer Spektrum, 2015
Werners, Grundlagen des Operations Research mit Aufgaben und Lösungen, 3. Auflage, Springer Gabler, Berlin/Heidelberg, 2013
Zimmermann: Operations Research: Methoden und Modelle für Wirtschaftsingenieure, Betriebswirte, Informatiker, 2. Auflage, Vieweg, Wiesbaden, 2008
English literature:
Hillier/Lieberman: Introduction to Operations Research, 10th edition, McGraw-Hill Education, 2014
Sydsæter/Hammond/Storm: Essential Mathematics for Economic Analysis, 4th edition, Prentice Hall, 2012
Sydsæter, Hammond, Seierstad, Strøm: Further Mathematics for Economic Analysis, 2nd edition, Prentice Hall, 2008
Winston: Operations Research: Applications and Algorithms, 4th edition, Duxbury Press 2004


[updated 17.09.2018]
 
[Tue Apr 23 12:12:50 CEST 2024, CKEY=iml, BKEY=itm3, CID=BITM-140, LANGUAGE=en, DATE=23.04.2024]