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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 01.10.2020
Module code: BITM-141
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+2U (6 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:
German
Assessment:
Written exam (90 minutes / Can be repeated semesterly)

[updated 14.11.2022]
Applicability / Curricular relevance:
All study programs (with year of the version of study regulations) containing the course.

BITM-141 (P420-0206) International Tourism-Management, Bachelor, ASPO 01.10.2020 , 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).
90 class hours (= 67.5 clock hours) over a 15-week period.
The total student study time is 150 hours (equivalent to 5 ECTS credits).
There are therefore 82.5 hours available for class preparation and follow-up work and exam preparation.
Recommended prerequisites (modules):
None.
Recommended as prerequisite for:
BITM-231 Statistics
BITM-410 Investment and Financing


[updated 06.03.2020]
Module coordinator:
Prof. Dr. Teresa Melo
Lecturer: Prof. Dr. Teresa Melo

[updated 25.11.2019]
Learning outcomes:
After successfully completing this module, students will be able to:
 
- understand the basics of differential and linear algebra and be able to apply them to smaller examples
- explain, differentiate and apply basic concepts and calculation methods of financial mathematics with regard to interest, annuity and sinking fund calculations
- develop linear optimization models from informally described practical planning problems
- use Excel Solver for modeling and solving economic optimization problems and interpret their results
- assess which of the mathematical methods learned are appropriate for specific economic problems
- illustrate economic problems using mathematical relations or models from analysis/algebra
- interpret the results obtained by means of mathematical methods
- In addition, students will be have developed analytical skills and the ability to abstract by solving tasks independently.


[updated 14.11.2022]
Module content:
Differential calculus:
- Functions of a single variable and differentiation rules
- Functions of several variables
- Differential calculus for functions of several variables
- Optimization with and without constraints for functions of several variables
- Economic applications for functions involving one and more variables
 
Basics of linear algebra:
- Calculations with matrices
- Creating linear systems of equations
- Solving systems of linear equations (e.g. Gauss algorithm), systematization of solution behavior
- Economic applications of matrix calculus (e.g. production processes).
 
Elements of financial mathematics:
- Interest-rate models
 - Annuity calculation
 - Sinking fund calculation
 
Linear programming:
- Modeling economic planning problems as linear optimization problems
- Solving linear optimization problems graphically
- Properties of linear optimization problems
- Solving a linear optimization problem using Excel Solver
- Conducting a sensitivity analysis


[updated 14.11.2022]
Teaching methods/Media:
Lecture and discussion using transparencies (projector) 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. 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 14.11.2022]
Recommended or required reading:
- Arrenberg: Wirtschaftsmathematik für Bachelor. Mit Aufgaben und Lösungen, 5. überarbeitete Auflage, UVK-Verlag, München, 2019
- Arrenberg: Finanzmathematik. Lehrbuch mit Übungen, 3. aktualisierte Auflage, de Gruyter Oldenbourg, Berlin, 2015
- Domschke, Drexl: Einführung in Operations Research, 9. über. und verb. Auflage, Springer Gabler, Berlin, Heidelberg, 2015
- Domschke, Drexl, Klein, Scholl, Voß: Übungen und Fallbeispiele zum Operations Research, 8. aktualisierte u. verb. Auflage, Springer Gabler, Berlin, Heidelberg, 2015
- Luderer: Einstieg in die Wirtschaftsmathematik, 9. aktualisierte Auflage, Springer Gabler, Wiesbaden, 2015
- Luderer: Klassische Finanzmathematik: Grundideen, zentrale Formeln und Begriffe im Überblick, 1. Auflage, Springer Spektrum, Wiesbaden, 2019
- Sydsaeter, Hammond, Strom, Carvajal: Mathematik für Wirtschaftswissenschaftler: Basiswissen mit Praxisbezug, 5. aktualisierte Auflage, Pearson Studium, München, 2018
- Tietze: Einführung in die angewandte Wirtschaftsmathematik: Das praxisnahe Lehrbuch - inklusive Brückenkurs für Einsteiger, 18. Auflage, Springer Spektrum, Berlin, Heidelberg, 2019
- Tietze: Einführung in die Finanzmathematik: Klassische Verfahren und neuere Entwicklungen: Effektivzins- und Renditeberechnung, Investitionsrechnung, Derivative Finanzinstrumente, 12. erw. Auflage, Springer Spektrum, Wiesbaden, 2015
- Tietze: Übungsbuch zur angewandten Wirtschaftsmathematik: Aufgaben, Testklausuren und ausführliche Lösungen, 9. überarb. u. erw. Auflage, Springer Spektrum, Wiesbaden, 2014
- Tietze, Übungsbuch zur Finanzmathematik: Aufgaben, Testklausuren und ausführliche Lösungen, 8. verbesserte Auflage, Springer Spektrum, Wiesbaden, 2015
 


[updated 14.11.2022]
 
[Fri Dec 27 18:44:03 CET 2024, CKEY=imy, BKEY=itm5, CID=BITM-141, LANGUAGE=en, DATE=27.12.2024]