Faculty of Business Economics

UPCT

Course unit description:

Mathematics for Business II

Degree/s: Degree in Business Administration and Management

Course: 2014-15

1. Subject data

Name Mathematics for Business II (Group A)

Subject area Mathematics

Module Quantitative Methods for Business

Code 510102010

Degree programme Degree in Business Administration and Management

Curriculum 2009

Centre Faculty of Business Sciences

Type Mandatory

Length of subject One semester Semester 1st Course 2nd

Language Spanish-English

ECTS 4.5 Hours / ECTS 25 Total workload (hours) 112.5

2. Lecturer data

Lecturer in charge Roberto J. Cañavate Bernal

Department Quantitative and Computer Methods

Knowledge area Quantitative Methods for Business and Economics

Office location Faculty of Business Sciences - 3rd floor

Telephone +34 968325783 Fax +34 968325745

email r.canavate@upct.es

URL / WEB http://metodos.upct.es

Office hours To be announced

Location Office number 325

Teaching and research

profile

Teaching experience

Research lines

Work experience

Other

3. Subject description

3.1. General description

The subject Mathematics for Business II provides the student with mathematical support that they will need throughout their education during the Degree, at a higher level than in the courses of the first Degree year. This course leads students to simple simulated decision making situations, similar to real situations related to resources optimization. It is a course with educational nature that goes deep into the use of logical-deductive reasoning which will allow a better approach to the problems, and rigor and order when solving problems and proposing decisions based on them.

3.2. How the subject contributes to a professional career

It allows the students to use Mathematics techniques to address some economic and business optimization problems either by hand or by using specific software

3.3. Relationship with other subjects in the programme

The course Mathematics for Business II is part of the block Mathematics, which is moreover formed by the courses Mathematics for Business I (1st year, 6 ECTS, 1st Semester, mandatory) and Operations Research (3rd year, 4.5 ECTS, 2nd Semester, elective). Some previous knowledge in Basic Algebra and Calculus with more than one variable is needed.

3.4. Incompatibilities defined in the programme

None

3.5. Recommendations to do the subject

It’s recommended that students had passed Mathematics for Business I before taking this subject.

3.6. Special provisions

Any student who has particular circumstances and may require special resources should let the professor know at the beginning of the semester.

4. Competences and learning outcomes

4.1. Basic curricular competences related to the subject

Que los estudiantes hayan desarrollado aquellas habilidades de aprendizaje necesarias para emprender estudios posteriores con un alto grado de autonomía.

4.2. General curricular competences related to the subject

Aplicar los métodos matemático-estadísticos y las tecnologías de la información y la comunicación para el tratamiento, valoración, y previsión de la información económico-empresarial.

4.3. Specific curricular competences related to the subject

Capacidad de razonamiento lógico y abstracto Habilidad de elección del tratamiento cuantitativo adecuado Capacidad para aplicar métodos cuantitativos informáticos en la empresa

4.4. Transversal curricular competences related to the subject

Aprender de forma autónoma (nivel 2)

4.5. Subject learning outcomes

- Making use of mathematical reasoning in economic and business situations. - Modeling easy economic and business situations related to decision-making and resource optimization - Interpreting quantitative results and managing economical decision making based on them - Understanding and expressing by English spoken and written language concepts related to the course - Using specific software for Mathematics and Linear Programming

5. Contents

5.1. Curricular contents related to the subject

Strengthen knowledge of mathematical concepts and techniques related to Optimization and Decision Making, focusing on the needs for other courses in the Degree (as Operation Research) as well as on the general education and training as a future Business professional. The aim of this course is to foster the abilities for reasoning, analysis, deduction, modeling, interpreting results and decision making, both in Spanish and English.

5.2. Theory syllabus (teaching modules and units)

Módulo I: Optimización Unit 1. Optimización local 1.1 Optimización sin restricciones 1.2 Optimización con restricciones de igualdad 1.2.1 Método de sustitución

1.2.2 Método de los multiplicadores de Lagrange

Unit 2. Convexidad y concavidad 2.1 Conjuntos convexos 2.2 Funciones convexas y cóncavas 2.3 Aplicaciones a la Optimización 2.4 Aplicaciones a la Programación Lineal Módulo II: Introducción a la Programación Lineal Unit 3. Programación Lineal. El método del símplex 3.1 Características de la Programación Lineal 3.2 Formulación de problemas 3.3 Resolución gráfica. Clasificación de los problemas lineales 3.4 El método del símplex

5.3. Practice syllabus (name and description of every practical)

Exercises for modeling and solving simulated situations related to the concepts studied during the course. These practical activities will take place on and off-campus once per week, individually and/or by groups. Some of them will be carried out in the computers classroom to use generic mathematical software and specific software for Operations Research as a tool for the computations.

5.4. Theory syllabus in english (teaching modules and units)

Module I: Optimization Unit 1. Local optima 1.1 Optimization without constraints 1.2 Optimization with equality constraints 1.2.1 Substitution method

1.2.2 Lagrange multipliers method

Unit 2. Convexity and concavity 2.1 Convex sets 2.2 Convex and concave functions 2.3 Applications to Optimization 2.4 Applications to Linear Programming Module II: Introduction to Linear Programming Unit 3. Linear Programming. The Simplex method 3.1 Situations of Linear Programming 3.2 Problem modeling 3.3 Graphic method. Classification of linear problems 3.4 The Simplex method

5.5. Detailed description of learning goals for every teaching module

Module I. Knowing and using mathematical techniques for solving optimization problems of functions of several variables either by hand or with the help of specific mathematical software. Module II. Performing Mathematical models of easy economic and business situations, especially those that may be formulated by linear models. Recognize problems that are studied by Linear Programming. Being able to solve linear problems using specific software. Interpreting the results obtained in the resolution and making decisions about the original situation.

6. Teaching method

6.1. Teaching method

Teaching activity Teaching techniques Student workload Hours

Theory lesson Presentation lesson taught using the lecture method. Answering questions raised by the students.

In-class: Taking notes, asking questions Self-study: Study of the subject

50

Solving problems

Problems are raised and solved. Participation by the students is strengthened through group and cooperative learning. Occasionally, problems will be solved by using computers.

In-class: Active participation, problem solving, asking questions. Self-study: Study of the subject, solving of problems raised by the professor

25

Practical sessions. Computer room sessions

Solving practical problems with specific software for Operations Research as a tool for the computations.

In-class: Solving problems with specific software for Operations Research, asking questions. Self-study: Training with the computer software, solving of problems raised by the professor

12

Assignments and partial written tests

Some assignments and written tests will be proposed to analyze the progression of the students. Some of them will be able to be done by groups and/or by using computers.

In-class: Preparing assignments and tests Self-study: Presenting results and doing tests

12

Tutorships

Proposing and answering questions about contents, solving problems and assignments (in the classroom, lecture’s office and on-line through the web page).

In-class: Asking of questions during the tutorship hours. Self-study: Asking questions by e-mail and forum participation.

2

Exams Written evaluation with computer (official exam), and grading of the contents.

In-class: Doing the exams Self-study: Preparing the exams

11.5

112.5

6.2. Learning outcomes (4.5) / teaching activities (6.1) (optional) Learning outcomes (4.5)

7.

Teaching activities (6.1) 1 2 3 4 5 6 7 8 9 10

7. Assessment method

7.1 Assessment method

Assesment activity

Type

Assessment methods and criteria

Percentage (%) Assessed learning

outcomes (4.5)

Sum

mat

ive

Form

ativ

e

Assignments X X

The student will be asked to do assignments proposed by the lecturer, individually and/or by groups. These activities could be proposed on-campus.

General attitude, regular attendance and participation during the course will be able to be considered as well in this section’s mark.

Up to 10% (only for February

session)

- Making use of mathematical reasoning in economic and

business situations.

- Modeling easy economic and business situations

related to decision-making and resource optimization

- Interpreting quantitative results and managing

decision making based on them.

- Understanding and expressing by English spoken

and written language concepts related to the

course

- Using specific software for Mathematicas an Linear

Programming

Partial written tests

X

Theoretical and/or practical written tests (in English) about some units in the general programme. Some of the questions could be asked to do in groups and by using mathematical software.

Up to 20% (only for February

session)

- Making use of mathematical reasoning in economic and

business situations.

- Modeling easy economic and business situations

related to decision-making and resource optimization

- Interpreting quantitative results and managing

decision making based on them.

- Understanding and expressing by English spoken

and written language concepts related to the

course

- Using specific software for Mathematicas an Linear

Programming

Global exam X Individual final exam (in English) about the

February session: - Making use of mathematical

contents of the course and their applications to economic and business situations.

At least 70%(*)

June and September sessions:

100% in any case

(*) According to UPCT policy,

students who meet certain

requirements can ask for a special, global exam in

June that is worth 100% of the gradeJune

session: Up to 50%(*)

September and February

sessions: 100%

(*) According to UPCT policy

students who meet certain

requirements can ask for a special, global exam in

June that is worth 100% of the

grade

reasoning in economic and business situations.

- Modeling easy economic and business situations

related to decision-making and resource optimization

- Interpreting quantitative results and managing

decision making based on them.

- Understanding and expressing by English spoken

and written language concepts related to the

course

- Using specific software for Mathematicas an Linear

Programming

7.2. Control and monitoring methods (optional)

Class attendance, attitude and participation: Classroom attendance and participation during the course is not compulsory but it is highly advisable. The student's participation in the theoretical and practical lessons will be evaluated. The student’s participation in the forum of the course’s web will be taken into account for the final grade. Assignments will be assessed during the course. Partial and final exams: two partial tests and one final exam will be done on the contents covered during the course, which will include theoretical and practical questions and problems to be solved. The characteristics of the exams, as well as the date, time and location will be indicated on the announcement, which is given at least 15 days before the scheduled exams period.

All the assessed activities will be asked to be done in English. These tests (exams, classroom participation, solving practical cases, etc) enable detecting possible gaps and make it possible to consolidate the most important concepts of the course.

8. Bibliography and resources

8.1. Basic bibliography

Hoy, M., J. Livernois, et al. Mathematics for Economics. Third Edition. The MIT Press, 2011 Hillier, F.S. and Lieberman, G.J. Introduction to Operations Research. McGraw-Hill, 2001 Sydsaeter, K. and P. Hammond. Essential Mathematics for Economic Analysis. Third Edition. Prentice Hall, 2008

8.2. Supplementary bibliography

Chang, Y., Desai, K. WinQSB version 2.0: decision support software for MS-OM. John Wiley & Sons Llorens Fuster, J.L. Introducción al uso de DERIVE. Aplicaciones al Álgebra y el Cálculo. Universidad Politécnica de Valencia, 1995 Taha, H.A. Operations Research: An introduction. Pearson Education, 2010

8.3. On-line resources and others

Cañavate, R. YouTube channel. http://www.youtube.com/user/robertocanavate Cobacho, B. Mathematics for Business I in OCW UPCT. http://ocw.bib.upct.es/course/view.php?id=121 Quesada Ibarguen, V.M., Vergara Schmalbach, J.C. Análisis Cuantitativo con WINQSB. http://www.eumed.net/libros/2006c/216/index.htm Pronunciation in English: Amazon. Ivona Text to Speech. http://www.ivona.com/en/ Pronunciation of mathematical expressions. http://sigloxxi.fcie.uam.es/informatica/media/math-pronunciation.pdf