2010-11 academic year

Mathematics (20639)

Degree/study: Degree in Business Sciences
Year: 1st
Term:1st and 2nd
Number of ECTS credits: 10 credits
Hours of studi dedication: 250 hours
Teaching language or languages: catalan
Teaching Staff: Joan Miralles and Ramon Villanova

1. Presentation of the subject

Mathematics is designed as an introductory module for the student and is therefore included in both terms of the first year.

The subject is divided into two self-contained and consecutive terms. The student will begin working on the acquisition of competences related to working methods used in situations requiring a formal approach.

The course will focus on the use of mathematical language and the acquisition of working methods that are especially suitable and useful for formalizing economic situations. This subject specifically develops the fundamental aspects of mathematical calculus of one or more variables (with optimization) and of linear algebra which are more widely used in economics; in this sense it is a subject which is instrumental in providing mathematical tools that are used in mainly economic contexts.

2. Competences to be attained

General competences

Specific competences

Instrumental

1. Capacity for analysis and sythesis
2. Capacity for organization and planning
3. General basic knowledge
4. Problem solving
5. Written and oral communication in student's own language

Interpersonal

6. Critical thinking

Systemic

7. Investigative skills
8. Capacity to learn
9. Ability to work autonomously
10. Capacity to generate new ideas (creativity)

Others

11. Oral and written communication using specialized language

1. Formalization of models and situations through the use of mathematical language
2. Solving of mathematical models
3. Knowledge and application of basic tools for mathematical analysis and linear algebra

3. Contents

First Term:

Module 1. Real functions of a real variable
Module 2. Derivation
Module 3. Optimization
Module 4. Integration
Module 5. Systems of equations and matrices

Second term:

Module 1. Real functions of two or more real variables
Module 2. Partial derivation, differentiability, applications
Module 3. Concavity, convexity, polynomial approximations
Module 4. Local optimization
Module 5. Restricted optimization
Module 6. Global optimization

4. Assessment

Assessment of the subject at the end of each term is based on three points:

-Evaluations carried out during the "solving of mathematical problems sessions" (SRP). During the course there will be three evaluations, each one of 30 minutes duration. Each one will be comprised of two or three problems similar to those covered during the solving of mathematical problems sessions. Each evaluation makes up 8% of the final mark.

-Problem solving session assessment. The participation of the student during the sessions and the quality of the individual exercise lists submitted during the class will be evaluated. This evaluation makes up 16% of the final mark, distributed as follows:

-Attendance and submission of the individual exercise list: 8%.
-Participation: 8%.

-Final Examination . The final examination covers all the contents of the course and lasts two hours. It accounts for 60% of the final mark. In order to pass the subject, a minimum mark of 4 must be attained in the final exam. In the case someone is not taking a final exam of some term, he will obtain a "not taken" of the term and the academic year.

The final grade for the subject is calculated using an average of the marks awarded during the two terms, providing the student has achieved a mark of at least four in each one. In the event that either term mark is below four, a fail grade will be awarded.

During the extraordinary examination sitting, the final exam of the term(s) failed can be repeated. In this case, the final mark is recalculated based on 80% of the extraordinary examination and 20% of the "solving of mathematical problems sessions" (SRP) during the year. The rules of the ordinary exam sitting are applied to determine the final mark.

5. Bibliography and teaching resources

5.1. Basic bibliography

SYDSAETER, K.; HAMMOND, P. J. Mathematics for Economic Analysis. Madrid: Prentice Hall, 1996.

5.2. Complementary bibliography

TAN, S. T. Matemáticas para Administración y Economía. (Applied mathematics for the managerial life and social sciences) International Thomson, 1998.
LARSON, R. E.; HOSTETLER, R. P.; EDWARDS, B. H. Calculus with Analytic Geometry. Vol. 1. Madrid: McGraw-Hill, 1999. 6th. ed.

5.3. Teaching resources

Theory summaries, lists of solved problems, self-learning presentations (SIREMA) and Moodle questionnaires are available in the Virtual Classroom.

6. Metodology

The student is expected to complete the following tasks each week:

- Before theory classes: Read the theory summaries (individual work)

- Attend theory classes (classroom).

- Carry out individual study, study solved problems, revise notes, and read the textbook (individual work).

- Before the "solving of mathematical problems sessions" (SRP): Completion of Moodle questionnaires via internet (individual work).

- Before the SRP: Completion of the exercise list (individual work).

- Participation in the SRP (classroom).

7. Planning of activities

Except for the first two weeks in which there will be no "solving of mathematical problems sessions" (SRP), the schedule will be the following:

Week

Classroom activity

Activity outside the classroom Group / type of activity

Week x

Session 1 Theory (whole group)

Session 2 Theory (whole group)

Session 3 Solving of mathematical problems (SRP) (subgroups)

- Reading theory summaries (individual work)

- Individual study, study solved problems, revise notes, read the textbook (individual work).

-Completion of Moodle questionnaires via internet (individual work).

- Completion of the exercise list (individual work).

The student can find a detailed description of the contents to be covered in each theory session and in each "solving of mathematical problems" session in the virtual classroom.