Mathematics III (20835)

Degree/study: degree in Business Management and Administration / degree in Economics 
Year: 1st
Term: 3rd
Number of ECTS credits: 5 credits
Hours of studi dedication: 125 hours
Teaching language or languages: catalan
Teaching Staff: Elisa Alòs, Adam Mahdi, Iván Torrecilla

1. Presentation of the subject

Mathematics III is a basic training subject for the student and focuses on those mathematical techniques that are  most needed in economic analysis.

It is the last of a sequence of three subjects in the junior year. After getting familiar with the mathematical language, the student begins using it to tackle real problems of a greater degree of complexity.

During the course, the optimization concepts that have already been introduced in "Mathematics II" in the case of 2 variables are now revised and applied to problems which are closer to real economics where the number of variables is usually high. On the other hand, difference equations and differential equations are introduced anew and used to model mathematically economic reality.

2. Competences to be attained

General competences	Specific competences
Instrumental 1. Analysis and synthesis. 2. Organization and planning 3. Basic general knowledge 4. Problem solving 5. Oral and written skills. Interpersonal 6. Analysis capacity. Systemic 7. Research skills 8. Learning capacity 9. Autonomous work 10. Creativity Other 11. Oral and written skills in a specialized language	1. Modeling through mathematical language 2. Solving mathematical problems 3.Acquiring and applying optimization techniques in n variables and the use of difference equations and differential equations:

3. Contents

Block 1. Revision of two-variable optimization 

Block 2. Matrix diagonalizing 

Block 3. Multivariate optimization 

Block 4. Prerequisites for the study of difference equations and differential equations: trigonometric functions and integration by parts. 

Block 5. Difference equations of order 1. 

Block 6. Difference equations of order 2.

Block 7. Differential equations of order 1. 

Block 8. Differential equations of order 2.

4. Assessment

The grades for the course will be obtained as follows:

Course work:

Homework + attendance to the SRP                                                       10%

Three tests  (3´10%)                                                                          30%

Participation in class and SRP                                                                10%

 

Exam:

Final exam                                                                                           50%

Total                                                                                                  100%

 

Pass the course
In order to pass the course, the minimum grade is a total of 5 out of 10 (i.e. 50%) with the additional condition of getting at least a grade 4 out of 10 in the final exam (i.e.  20 out of the 50% of the exam weight). For instance, a grade of 3.4 out of 10 in the final exam (i.e. 17 out of the 50%) will not be a pass even though the total grade exceeds 5/10. With a grade of 4/10 in the final exam, at least  a 6/10 in the SRP/homework/tests will be needed to pass: 0.5 ´ (4/10) + 0.5 ´ (6/10) = 5.

  

September retake

In September

In September, the grades will be obtained assigning a 70% weight to the September exam and a 30% to the SRP/homework/tests of the course. Again, a minimum total grade of 5 out of 10 is needed to pass with the additional condition of getting at least a grade 4 out of 10 in the September  exam (i.e.  28 out of the 70% of the exam weight). Notice the difference in the exam weight. Thus, a 4/10 in the September exam needs at least a 7.4/10 in the SRP/homework/tests part in order to pass: 0.7 ´ (4/10) + 0.3 ´ (7.4/10) = 5.

5. Bibliography and teaching resources

5.1. Basic bibliography

SYDSAETER, K.; HAMMOND, P. J. Mathematics for Economic Analysis: Prentice Hall, 1995

Spanish translation:

SYDSAETER, K.; HAMMOND, P. J. Matemáticas para el análisis económico. Madrid: Prentice Hall, 1996

5.2. Complementary bibliography

BORRELL, J. Métodos matemáticos para la economía. Programación matemática.  Madrid:Pirámide,1992.
HERAS, A. and altri. Programación matemática y modelos económicos: un enfoque teórico-práctico. Madrid: AC, 1990.

5.3. Teaching resources

Class notes and problem list in Aula Global.

6. Metodology

A student ought to carry out the following weekly work plan:

BEFORE the plenary session: reading of the class notes (personal work).

Attendance to the plenary sessions.

Personal study of solved problems, notes revising, textbook reading

BEFORE the SRP. Working out the problem list (personal work).

Attendance to the SRP.

Review and check the personal work on the problem list against the published solutions (personal work).

7. Planning of activities

There are no SRP during the first two weeks of the term. For the rest of the term the schedule will be: 

Week	Classroom activity	Homework  Group work / activity
Week x	Session  1 Plenary lesson (whole group)     Session 2 T Plenary lesson (whole group)                   Session 3 Problem seminar (SRP) (subgroups)	- Reading of the class notes (personal work)   - Reading of the class notes (personal work)   - Personal study. Review of solved problems, notes revision, textbook reading (personal work). - Working out the problem list (personal work).       - Checking of the personal work on the problem list against the published solutions (personal work).

In Aula Global there will  be found a complete description of the contents of each plenary session and each SRP.