Universitat Internacional de Catalunya

Mathematics 1

Mathematics 1
6
7794
1
First semester
FB
Mètodes Quantitatius per a empresaris
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.
If the student is enrolled for the English track then classes for that subject will be taught in the same language.

Teaching staff


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

Introduction

In the event that the health authorities announce a new period of confinement due to the evolution of the health crisis caused by COVID-19, the teaching staff will promptly communicate how this may effect the teaching methodologies and activities as well as the assessment.


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.

 

Competencies

 

  • 17 - To be familiar with the mathematical models used to describe financial phenomena.
  • 18 - To provide mathematical models for financial phenomena.
  • 19 - To analyse quantitative financial variables and take them into account when making decisions.
  • 20 - To make decisions on resource optimisation using mathematical tools.
  • 31 - To develop the ability to identify and interpret numerical data.
  • 32 - To acquire problem solving skills based on quantitative and qualitative information.
  • 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.
  • 43 - To acquire skills for using statistical software.
  • 44 - To be able to select appropriate econometric methods.
  • 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.
  • 64 - To be able to plan and organise one's work.
  • 65 - To acquire the ability to put knowledge into practice.
  • 66 - To be able to retrieve and manage information.

Learning outcomes

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



 

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 the one that favours the student the most

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.

Teaching and learning material