Simulation and Scientific Computing

Code:

M4058

Acronym:

M4058

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2015/2016 - 2S

Active?	Yes
Web Page:	https://moodle.up.pt/course/view.php?id=2172
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Master in Mathematical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M:AST	0	Plano de Estudos oficial desde_2013/14	1	-	6	56	162
			2
M:ENM	18	Official Study Plan since 2013-2014	1	-	6	56	162

Teaching language

Suitable for English-speaking students

Objectives

It is intended that the students learn the paradigm of computational simulation (and modeling) based on Monte Carlo methods, namely MCMC, as well as the principles of stochastic calculus, in a framework of critical application to the data analysis of complex systems in various areas such as biology and medicine, economics and finance, physical phenomena and the environment.

Learning outcomes and competences

The student should be able to:

- Identify problems, build models and develop computer simulation projects based on stochastic techniques and Monte Carlo methods.

- Know and apply the principles of generation of random variables and integration of Monte Carlo, with results analysis and control of the variance. Understand and apply Monte Carlo methods via Markov Chain (MCMC).

- Understand the principles of stochastic calculus. Study problems modeled by stochastic differential equations, in particular, involving diffusion and Langevin equations.

- Apply critically the methods studied in the data analysis of complex systems in various areas such as biology and medicine, economics and finance, physical phenomena and the environment.

Working method

Presencial

Program

Introduction to statistical simulation and computation. Comprehensive hands-on excursion of Monte Carlo methods: from random number generation algorithms and Monte Carlo integration, to Markov Chain Monte Carlo. Metropolis-Hastings and Gibbs algorithms, including convergence monitoring.

 

Computational introduction to stochastic problems: selected case studies and applications from Brownian motion, the Wiener process, the Langevin equation, the diffusion equation, Fick’s equation.

Participate in the "III Iberian Modeling Week", DM-FCUP, 11 -  15 April  2016: http://www.fc.up.pt/mat/3imw/

Mandatory literature

Kroese Dirk P.; Handbook of monte carlo methods. ISBN: 978-0-470-17793-8
Robert Christian P.; Introducing monte carlo methods with R. ISBN: 978-14419-1575-7
Papoulis Athanasios; Probability, random variables, and stochastic processes. ISBN: 0-07-112256-7
Evans Lawrence C. 1949-; An introduction to stochastic differential equations. ISBN: 9781470410544

Comments from the literature

Other Bibliography under Springer Link available at FCUP

Teaching methods and learning activities

Lectures TP organized in accordance with the syllabus and the intended outcomes to present and illustrate the topics. Problems / Projects with strong laboratorial computation component using (Matlab, R). The curricular unit has a strong practical component and classes with computers are essential. The computational projects allow the consolidation and critical application of the syllabus topics.

Software

Matlab
R

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Applied mathematics

Evaluation Type

Distributed evaluation without final exam

Assessment Components

designation	Weight (%)
Prova oral	20,00
Teste	20,00
Trabalho escrito	40,00
Trabalho laboratorial	20,00
Total:	100,00

Eligibility for exams

45% in the computational work/project (oral presentation/discussion + report)

Calculation formula of final grade

Final classification: 0.2 T + 0.2 O + 0.4 R + 0.2 MW,

T – test

O – oral presentation + discussion

R- Report (including computacional part)

MW- "III Iberian Modeling Week", DM-FCUP, 11 -  15 April  2016: http://www.fc.up.pt/mat/3imw/


Remark: Students who missed the Modeling Week are evaluated according the formula announced in the semester beginning: 0.2 T + 0.25 O + 0.45 R + 0.1 MW

Examinations or Special Assignments

n.a.

Special assessment (TE, DA, ...)

n.a.

Classification improvement

Only component T can be improved (ER).