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Mathematics and Numerical Methods for Economics and Finance I
(1
º Sem
2019/2020)
Code:
03091
Acronym:
03091
Level:
3rd Cycle
Basic:
No
Teaching Language(s):
English
Friendly languages:
Be English-friendly or any other language-friendly means that UC is taught in a language but can either of the
following conditions:
1. There are support materials in English / other language;
2. There are exercises, tests and exams in English / other language;
3. There is a possibility to present written or oral work in English / other language.
1
9.0
0.0 h/sem
24.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
0.0 h/sem
1.0 h/sem
25.0 h/sem
200.0 h/sem
0.0 h/sem
225.0 h/sem
Since year
2019/2020
Pre-requisites
Basic knowledge of calculus, linear algebra, probability and programming are welcome.
Objectives
In this course we will review some fundamental concepts and techniques of differential and integral calculus and of linear algebra, we will introduce basic notions of programming in MATLAB and we will implement and analyze numerical methods for the resolution of equations and linear and non-linear systems of equations. We will also introduce the basics of measure theory and integration, with special emphasis given to its connection to probability theory, and introduce algorithms of stochastic simulation.
Program
I. Introduction to MATLAB. II. Sequences and metric spaces. a) Facts about the real numbers b) Sequences of real numbers. c) Metric spaces. III. Equations in one variable. (a) Review of single variable calculus (b) Numerical solutions of equations in one variable: IV. Systems of linear and non-linear equations (a) Some basic notions of linear algebra (b) Direct and iterative methods for solving linear systems. (c) Review of vector calculus. (d) Newton's method for systems of (non-linear) equations. V. Measure, Probability and Integration (a) Riemann's integral. (b) Introduction to Measure Theory and the Lebesgue integral. (c) Probability theory: (d) Generation of random variables. (e) Monte Carlo Methods.
Evaluation Method
The final grade will be based on homework assignments, done in groups of 4 students, (50%) and a final (individual) exam (50%). The evaluation of the homework assignments is subjected to oral discussions. Under appropriately justified circumstances the number of elements in the home work groups may be different from 4. The final exam has a minimum grade of 7.5 out of 20. Due the nature of the evaluation in this course, there is no 2nd chance exam.
Teaching Method
The classes are run as theoretical-practical lectures. The theoretical exposition is followed by computer lab sessions, using MATLAB.
Observations
-
Basic Bibliographic
1) Richard Burden, J. Douglas Faires, Annette Burden (2015). Numerical Analysis, Cengage Learning. 2) J. E. Marsden and A. Tromba, Vector Calculus, 5a ed., W. H. Freeman and Company (2003). 3) M. Adams and V. Guillemin (1996).Measure Theory and Probability, Wadsworth & Brooks, 4) Ross, S. M (1997). Simulation. San Diego: Academic Press.
Complementar Bibliographic
5) Paolo Brandimarte (2006). Numerical Methods in Finance and Economics: A MATLAB-Based Introduction, John Wiley & Sons. 6) Kolmogorov, A. N. (1970). Introductory real analysis. Englewood Cliffs, N.J. :Prentice-Hall. 7) Mario J. Miranda and Paul L. Fackler (2002). Applied Computational Economics and Finance, MIT Press.
