Subject

Mathematics 1

  • code 07794
  • course 1
  • term Semester 1
  • type FB
  • credits 6

Module: Mètodes Quantitatius per a empresaris

Matter: Mathematics

Main language of instruction: Spanish

Other languages of instruction: Catalan, English

If the student is enrolled for the English track then classes for that subject will be taught in the same language and also in Spanish.

Teaching staff

Head instructor

Dra. Maria Dolors GIL - mdgil@uic.es

Office hours

By appointment. In order to make an appointment, please request one by writing to: mdgil@uic.es

Introduction

During the 18th and 19th centuries the study of economics took a spectacular turn, as economic reasoning began to be formalised and developed, incorporating increasingly complex theories with multiple variables involved.

Agustin Cournot was the first to use the language of mathematics to study demand curves and resolve optimisation problems. By using the language of mathematics has models on the behaviour of economic variables have been created.

Students of economics require a solid base in mathematics in order to have the linguistic means required to understand these theories.

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Pre-course requirements

In order to enrol in this module, it is recommended that students be able to solve equation systems, calculate derivatives and solve second- and third-degree equations.

Objectives

The objective of this course is to master infinitesimal calculus with functions of one variable, since these concepts are used as a basic tool in the mathematical description of economic phenomena.

The main problem in economics lies in optimising the always limited resources; therefore special attention should be paid to optimisation problems that can be formulated using functions of one variable, showing that a greater understanding of mathematical analysis can lead to a natural solution for such problems.

 

Competences / Learning outcomes of the degree programme

 

  • 19 - To analyse quantitative financial variables and take them into account when making decisions.
  • 31 - To develop the ability to identify and interpret numerical data.
  • 36 - To interpret quantitative and qualitative data and apply mathematical and statistical tools to business processes.
  • 40 - To be able to choose statistical methods appropriate to the object of analysis.
  • 41 - To be able to descriptively summarise information.
  • 42 - To be able to empirically analyse financial phenomena.
  • 45 - To be able to work with academic papers.
  • 50 - To acquire the ability to relate concepts, analyse and synthesise.
  • 51 - To develop decision making skills.
  • 52 - To develop interpersonal skills and the ability to work as part of a team.
  • 53 - To acquire the skills necessary to learn autonomously.
  • 54 - To be able to express one’s ideas and formulate arguments in a logical and coherent way, both verbally and in writing.
  • 56 - To be able to create arguments which are conducive to critical and self-critical thinking.
  • 65 - To acquire the ability to put knowledge into practice.
  • 66 - To be able to retrieve and manage information.
  • 18 - To provide mathematical models for financial phenomena.
  • 64 - To be able to plan and organise one's work.
  • 17 - To be familiar with the mathematical models used to describe financial phenomena.
  • 20 - To make decisions on resource optimisation using mathematical tools.
  • 32 - To acquire problem solving skills based on quantitative and qualitative information.
  • 44 - To be able to select appropriate econometric methods.
  • 43 - To acquire skills for using statistical software.

Learning outcomes of the subject

By the end of the course, students will have acquired the following learning outcomes:

  • To identify and understand the fundamental concepts of Mathematics 1.
  • To be familiar with the terminology, notation and methods of Mathematics 1.
  • To analyse and summarise the information obtained from lectures and the supplementary material provided by the lecturer.
  • To understand, use and analyse the information obtained from various sources.
  • To solve problems similar to those completed in class.
  • To apply theoretical knowledge to practical situations.
  • To select the appropriate mathematical method for solving a financial problem.
  • To solve case studies in predictable contexts, interpret the results obtained and draw conclusions.

 

Syllabus

Chapter 1: Real Function of One Variable

1.1. Definition of Real Function of One Variable. Domain

1.2. Functional Limits

1.3. Continuity. Types of Discontinuities

1.4. Definition of a Derivative. Tangent Line. Calculation of Derivatives

1.5. Elasticity of a Function

1.6. Applications of Derivatives: Increasing and Decreasing Functions, Extreme Values, Curvature and L'Hôpital's Rule

1.7. Economic Applications

 

Chapter 2: Integration

2.1. Calculation of Primitives. The Indefinite Integral

2.2. The definite integral. Barrow’s Rule

2.3. Applying the Definite integral to the Calculation of Areas

2.4. Improper Integral

2.5. First Order Differential Equations

2.6. Economic Applications

 

Chapter 3: Linear Algebra

3.1. Systems of Linear Equations

3.2. Definition of a Vector Space

3.3. Linear Combination

3.4. Linear Independence

3.5. Spanning Set

3.6. Basis of a Vector Space

3.7. Definition of a Vector Subspace

3.8. Scalar Product, Norm, Angle and Distance

3.9. Quadratic Forms

3.10. Economic Applications

 

Chapter 4: Numerical Sequences and Series

4.1. Sequences of Real Numbers

4.2. Properties of Sequences

4.3. Finite and Infinite Series

4.4. Convergence Criteria

4.5. Economic Applications



 


Chapter 0 Presentation of the subject
      Material
            Ch.0 ppt presentation - English mathi-presentation.pdf 
            Ch.0 ppt presentation - Catalan matesi-presentacio.pdf 

Chapter 1 Real function of one variable
      Material
            Ch.1 Glossary - English glossarychapter1-mathi.pdf 
            Ch.1 Glossary - Catalan glossaritema1-matesi.pdf 
            Ch.1 ppt presentation - English mathi-chapter1.pdf 
            Ch.1 ppt presentation - Catalan matesi-tema1.pdf 

Chapter 2 Integration
      Material
            Ch.2 Glossary - English glossarychapter2-mathi.pdf 
            Ch.2 Glossary - Catalan glossaritema2-matesi.pdf 
            Ch.2 ppt presentation - English mathi-chapter2.pdf 
            Ch.2 ppt presentation - Catalan matesi-tema2.pdf 

Chapter 3 Linear algebra
      Material
            Ch.3 Glossary - English glossarychapter3-mathi.pdf 
            Ch.3 Glossary - Catalan glossaritema3-matesi.pdf 
            Ch.3 ppt presentation - English mathi-chapter3.pdf 
            Ch.3 ppt presentation - Catalan matesi-tema3.pdf 

Chapter 4 Numerical sequences and series
      Material
            Ch.4 Glossary - English glossarychapter4-mathi.pdf 
            Ch.4 Glossary - Catalan glossaritema4-matesi.pdf 
            Ch.4 ppt presentation - English mathi-chapter4.pdf 
            Ch.4 ppt presentation - Catalan matesi-tema4.pdf 

Teaching and learning activities

In person

Theoretical aim:

The theory of the module is presented in detail, yet avoiding excessive formalisation that could override the true purpose of the course: to apply mathematical language to economics. For this reason, abstract mathematical concepts are illustrated using applications and practical exercises in connection with economics.

Practical aim:

The concepts should be consolidated by solving the problems given to the students throughout each chapter. These problems will be solved and discussed in class. It would also be useful for students to solve other problems from the recommended books in the bibliography.

TRAINING ACTIVITY

COMPETENCES

lecture
in-class practical work (solving problems/videos/text comments/essays)
individual study
report presentations & discussions
solving problems in classroom
report presentations

17

lecture
in-class practical work (solving problems/videos/text comments/essays)
report presentations & discussions
solving problems in classroom
report presentations

18

lecture
in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
report presentations

19

in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
report presentations

20

in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
report presentations

32

lecture
in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
report presentations

50

in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
report presentations

51

report presentations & discussions
solving problems in classroom
report presentations

56

individual study
report presentations

64

in-class practical work (solving problems/videos/text comments/essays)
individual study
solving problems in classroom
report presentations

65

in-class practical work (solving problems/videos/text comments/essays)
report presentations & discussions
report presentations

54

 

Evaluation systems and criteria

In person

The module will be evaluated on the basis of three elements: continuous evaluation, mid-course examination and final examination, as follows:

Continuous evaluation

15%

15%

Mid-course examination

15%*

30%*

Final examination

70%*

55%*

* This percentage will be determined by the mark obtained in the mid-course examination.

Second sitting

For students taking the second-sitting examination, evaluation will take place as follows:

Continuous evaluation

15%*

Final examination

85%

* The continuous evaluation mark for the module will be the same as for the first sitting.

 

Bibliography and resources

  • Sydsaeter, K.; Hadmmond, P.J.: Mathematics for Economic Analysis. Prentice Hall.
  • Adillon, R.; Álvarez, M.; Gil, D.; Jorba, L.: Mathematics for Economics and Business. Publicacions i Edicions de la UB. Economy UB.
  • Vegas Pérez, A.; López, M.: Elementos de matemáticas para economistas 1 & 2. Pirámide.
  • Alegre, P.; et al.: Ejercicios resueltos de matemáticas empresariales 1 & 2. A.C.
  • López, M.; Vegas, A.: Curso básico de matemáticas para la economía y dirección de empresas, vol. I & II. Pirámide.

Evaluation period

E: exam date | R: revision date | 1: first session | 2: second session:

  • E2 20/06/2019 12:00h b502
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