Academic Integration between Brazil and the United States
Science, Engineering, and Technology
Focus: Practice and Research
Control and Dynamical Systems Alliance: USA-Brazil partnership - 2001 and beyond
corresponding author: Jair Koiller
Fundação Getulio Vargas/RJ and Brazilian Mathematics Millenium Institute AGIMB
Alberto Saa (Unicamp) , Clarence Rowley (Princeton); Jerrold Marsden (Caltech) ; João Hespanha
(UCSB); Marco Antonio Teixeira (Unicamp); Richard Murray (Caltech)1.
Abstract. The Control and Dynamical Systems Alliance (CDSA) has its hub at Caltech’s Control and
Dynamical Systems Department (www.cds.caltech.edu). Our main goal is to develop a shared control and
dynamical systems curriculum at leading research and educational institutions in the USA, Latin America
and Europe. Main partners outside USA are Unicamp/Brazil (www.ime.unicamp.br) in Latin America and
Lund University/Sweden (http://www.control.lth.se) in Europe. Other partners in USA are Princeton’s
Mechanical and Aerospace Engineering (www.mae.princeton.edu) and UCSB’s Dept. of Electrical and
Computer Engineering (www.ece.ucsb.edu) and Mechanical and Environmental Engineering
(www.me.ucsb.edu). Other partners in Brazil are UFRJ’s Engineering School, (www.coppe.ufrj.br),
Fundação Getulio Vargas (www.fgv.br/gradrj) and Instituto de Matemática Pura e Aplicada (www.impa.br).
Following the motto “we teach because we do research” by the late Brazilian scientist Carlos Chagas Filho, in
this report we focus both on practice and research. We describe some of the work done by the students in our
FIPSE-CAPES exchange program2 during the last three years. Caltech, Princeton and UCSB have received so
far nineteen Brazilian students. Two students from Caltech and one form UCSB visited Unicamp, UFRJ,
IMPA and FGV. Unicamp has a very special position in Brazil, since it receives undergraduate students
from all over the country. Graduate programs of Unicamp, UFRJ, IMPA and FGV attract students from all
over Latin America.
Some comments on our work related to curriculum development are also presented here. We assert that the
combination of the two mathematical disciplines, Control and Dynamical Systems, will have in the 21th
century a pivotal role in shaping a common scientific language across a variety of areas, from mechanical,
aerospace and environmental engineering, to bioengineering, applied physics, communications, and
economics. This wide range of applications makes these disciplines ideally suited for cross-disciplinary
fertilization and fosters applications attractive to a wide scientific public. One of the activity's key foci is
developing new approaches to education and outreach for the dissemination of basic ideas to nontraditional
audiences.
What we have achieved? Our project started in 2003, centered on student exchanges and work missions.
Here are the participants, and in a nutshell, the main results:
Brazilian Students (undergraduates)
2003:
Alex Lúcio Ribeiro Castro (IMECC/Unicamp to Caltech)
1
Send email to: jair@impa.br or jkoiller@fgv.br and correspondence to: Fundação Getulio Vargas,
Praia de Botafogo 190 3º andar, 22250-040 Rio de Janeiro RJ, Brazil.
Caltech: Control and Dynamical Systems 107-8, 1200 E. California Blvd, Pasadena, CA 91125, USA
UCSB: Dept. of Electrical & Computer Eng. University of California, Santa Barbara, CA 93106-9560, USA
Princeton: Mechanical and Aerospace Engineering, Engineering Quad, Princeton, NJ, 08544, USA
Unicamp: Instituto de Matemática, Estatística e Computação Científica, Cidade Universitária, Caixa Postal
6065, 13083-859 Campinas, SP, Brasil.
2
http://www.fipse.aed.org/grantshow.cfm?grantNumber=P116M020017
André Ricardo Fioravanti (FEEC/Unicamp to Caltech)
Pedro Walmsley Frejlich (IMECC/Unicamp to UCSB)
Ricardo Augusto Emmanuel Mendes (IMECC/Unicamp to Caltech)
Thyago Consort (Electrical/UFRJ to Caltech)
Guilherme França (Mechanical/UFRJ to UCSB)
2004
Daniel Cariello (IMECC/Unicamp to Caltech)
Mauricio Richartz (IFGW/Unicamp to Caltech)
Nataly Horner Hoe de Castro (IFGW/Unicamp to Caltech)
Thiago Barros Rodrigues Costa (IC/Unicamp to Caltech)
Guilherme Aires (Electrical UFRJ to UCSB)
Bruno Givisiez (Mechanical/UFRJ to Princeton)
Eduardo Lobão (Mechanical/UFRJ to Princeton)
2005
Raphael Santarelli (IFGW/Unicamp to Caltech)
Guilherme Côco Beltramini (IFGW/Unicamp to Caltech)
Lonardo Rabelo (IMECC/Unicamp to Caltech)
Angelo Luiz Rocha Polydoro (FGV/RJ to Caltech)
Neimar Machado da Silva (Electrical/UFRJ to UCSB)
Summary: 2003: Ricardo and Alex were supervised by Jerrold Marsden and Eva Kanso, André and Thyago
by Richard Murray. Guilherme Foerster and Pedro by Profs. Frank Doyle and Igor Mezic. Pedro spent half of
his stay at Caltech, with Marsden. There was also a work mission of the LNCC Ph.D. student Gerusa Araujo
to Princeton, where she participated in a Biomathematics School (coorganized by Naomi Leonard) at the
Program for Women in Mathematics, Institute for Advanced Study. 2004: students visiting Caltech were
supervised by Richard Murray and Hideo Mabuchi, and at Princeton, by Clancy Rowley. At UCSB,
Guilherme Aires was supervised by João Hespanha, who has an ongoing collaboration with COPPE/UFRJ’s
Control Lab. In 2005, Angelo traveled earlier to the USA, to participate in the SURF (summer undergraduate
research program) and is being supervised by Prof. Jacob Goeree. At the moment this report is being written
four other Brazilian students just traveled to the USA.
USA Students (all beginning graduate students)
2004
Timothy Hahndeut Chung (Caltech)
Michael Epstein (Caltech)
2005
Dale Lukas Peterson (UCSB)
Tim and Michael spend the (USA) summer at Rio and Campinas. They visited all partners Institutions, taught
a mini-course on Control to the FGV scientific initiation students and wrote teaching materials on applications
of control to Economics. A work mission of Prof. Ronaldo Dias to Caltech is resulting in a collaboration for
one problem in Tim’s Ph.D. thesis. Luke is collaborating in a research project and did supervised study in
mathematical tools for Engineering. At the moment this report was finished he just returned to the USA.
Work Missions and coordinator’s meetings participants:
Richard Murray (Caltech)
Clarence Rowley (Princeton)
Marco Teixeira (IMECC)
Jair Koiller (FGV)
Alberto Saa (IMECC)
Ronaldo Dias (IMECC)
Maria Cristina Terra (FGV)
Schools, Workshops and Virtual Institutes. One important associated event was the Latin American
School on Control3, held at Unicamp in July 2003, sponsored by the International Centre for Pure and Applied
Mathematics. A section on Control4 was also held subsequently at the 24th Colloquim (Brazilian
Mathematics meeting) at IMPA. Some students that participated in the exchange program presented their
work at the Scientific Initiation workshop 5 at IMPA, 2004. Pending on funding, at the end of the project, we
would like to organize in Brazil, in July during the USA summer vacations, and Brazil’s winter break, a
“Student/teacher workshop in Control & Dynamical Systems” followed by a joint camping trip in some of
the wonderful ecological niches of Brazil .
Brazil’s partentships: Control and Dynamical Systems Lab at Unicamp 6 and the Brazilian
Mathematics Millenium initiative7. The Millennium Institute - Global and Integrated Advancement of
Mathematics in Brazil and Contribution to the Region - IM-AGIMB - started January, 2002. Its activities
have a comprehensive character aiming at the global advancement of Mathematics and Applications in Brazil.
It should also contribute to the enhancement of Mathematics in Latin America. The Mathematics Millenium
initiative in Brazil has a chapter in Control and a chapter in Dynamical Systems. One of the upshots of our
FIPSE/CAPES project was the creation of the Laboratório de Controle e Sistemas Dinâmicos (CSD) at
Unicamp. This is an inter-departmental initiative by IMECC to foster research and outreach activities in
Control and Dynamical systems, in its mathematical as well as applied aspects. We expect that this Lab will
have a similar impact in Brazil as CDS/Caltech did in the USA.
USA partnerships. Caltech has a strong history of collaboration with both Princeton and UC Santa Barbara.
Caltech and Princeton have collaborated on many projects in the area of dynamics and control of mechanical
systems, in particular problems in underwater locomotion and flow control. Over the past years, Caltech
students have spent 2-4 months working at Princeton, primarily in collaboration with Naomi Leonard and Phil
Holmes. One of those students, Clancy Rowley, is now an Assistant Professor at Princeton. In addition,
Princeton faculty and students are frequent visitors to Caltech. A similar level of interaction is present
between Caltech and UC Santa Barbara. Because of its close proximity (about 90 minutes drive), there are
frequent interactions and exchanges. Linda Petzold has been a co-investigator on several grants at Caltech
and both she, Igor Mezic and João Hespanha are frequent particants in activities sponsored by CDS and
CIMMS (the Center for Integrative Multiscale Modeling and Simulation). In addition, Richard Murray and
Andy Teel co-organize a semi-annual nonlinear control workshop that is open to all universities in the
southern California area. At the last workshop, a dozen Caltech students travelled to Santa Barbara for two
days of presentations and discussions.
Going beyond. Nineteen Brazilian students (including those traveling this year) already participated, a
number in accordance with our expectations. We would like to increase the number of USA students, which
according to our original planning should be first or second year graduate students in Engineering. We are
hopeful to extend the exchange with the undergraduate program from the Economics Department at
Princeton. This can happen on a one-to-one basis, as Prof. Cristina Terra from FGV discussed with
Princeton’s Study Abroad Program during her work mission. There is great enthusiasm of FGV students, of
course. We hope to stir up interest of some Princeton students to choose their junior or senior projects in
Latin American Economies, with emphasis in the application of quantitative tools.
Our project is soon entering its last year, and frankly speaking, what we are most concerned about is funding.
Private sources in Brazil are very difficult to find. We hope that the success stories we report here will
sensibilize both Governments to continue their support. There is no need to mention here the similarities in
cultures and way of life, and the complementary of the two countries economies. As we hope to demonstrate
as clearly as the other FIPSE-CAPES projects, these exchanges are life-changing experiences for the students.
3
See www.cimpa-icpam.org//Anglais/AnciensProg-a/2003/Brazil03.html .
www.impa.br/pesquisa/pesquisa_coloquio_brasileiro_de_matematica/CBM24/Sessoes/Controle/index.html
5
See http://webold.impa.br/Conferencias/Jornadas_IC/index.html .
6
See http://vigo.ime.unicamp.br/csd.html .
7
See http://milenio.impa.br/novo/english/index.htm .
4
Some student’s comments. The main objective of this report is to describe some of the students’ projects.
To begin, it is perhaps worth quoting (with their permission) just a sample of the many emails we got from
them (we make a free translation from Portuguese to English).
Bruno Givisiez (18 de julho de 2005, a few months after returning ): “ I have been quite busy with my senior
thesis and with the lab… Atila [UFRJ’s Turbulence lab director] brought some kids from UFPA and I am sort
of “watching over” the experiments so that nothing weird happens…
[Towards my senior thesis] I am not working in the same subject that I did in Princeton, but what I learned
has helped me to solve some problems in the lab that before seemed impossible. Since I always had an
Academic inclination, the USA experience gave me a new push, in a certain way expanding my interest to a
more mathematical approach, that I was not accustomed. It is worth saying that a program like this is not
only excellent from the professional perspective, it is also an unique personal experience, contributing a lot
to one´s maturity” .
[Por aqui eu ando meio ocupado com o meu projeto de fim de curso e com o laboratório... o Atila trouxe uns
meninos da UFPA pra trabalhar aqui e eu tô meio que "tomando conta" dos experimentos que eles tão
fazendo pra não acontecerem imprevistos... Por isso eu só tô respondendo ao seu e-mail hj. ... Um breve
comentário sobre a minha experiência no estágio.
Depois que voltei dos EUA, votei a estagiar no laboratório onde já estagiava por três anos antes do
intercâmbio. Atualmente não estou trabalhando com o mesmo assunto que trabalhei em Princeton, mas o que
aprendi tem me ajudado a resolver antigos problemas no laboratório que antes pareciam insolúveis.
Como eu sempre tive uma certa inclinação acadêmica, o estágio nos EUA acabou me impelindo ainda mais
para essa área, mas de certa forma expandindo o meu interesse para abordagens mais matemáticas do que as
que eu estava habituado a trabalhar. Vale apena destacar que, além de um programa como esses ser excelente
no âmbito profissional, também é uma experiência pessoal única, e contribui grandemente para o
amadurecimento do indivíduo.]
May 3 2005 : “ Hi Jair, do you remember our Princeton [robotic] “fish” ? Well, you know, I sent an email to
Clancy and he told me another student is going to continue the project, and that perhaps they will use
glycerol instead of water in order to increase the drag force. This was your suggestion, actually. It seems that
our work there was good. Clancy said that it will be most useful for the next student to continue.”
[Lembra do nosso peixe de Princeton? Pois é, eu mandei um e-mail pro Clancy e ele me disse que um outro
aluno vai retomar o projeto, e que talvez eles usem glicerina no lugar da água, pra aumentar a força de arrasto.
Foi sua essa sugestão, lembra? Parece que o nosso trabalho lá foi bom. O Clancy disse que vai ser muito útil
para o próximo aluno a trabalhar no peixe se basear. Por enquanto é isso então Jair. Abração. Bruno.]
Thyago Consort 8 “Caltech was important to make me more open minded; there I had the chance to know
people from all over the world that I still keep as friends. The first two weeks of the Caltech graduation
program was composed only by informative and recreative activities. Through these two weeks I was able to
understand a bit more of the American culture and way of life, what to expect, how to treat people. There
were also some funny activities that helped me to make friends and to know good things to do on weekends.”
Angelo Polydoro: [July 12 2005] “After just a month I already did a lot of stuff…I explained to a student here
at Caltech to program in Ztree; Roy and me did 4 experimens in Economics; we run 2 of these experiments in
UCLA’s social sciences lab; I did an online class in experiments at UCLA; I programmed some calculations
for a paper a woman professor from Caltech is writing. I am also starting to go out. Last weekend I went to
Hollywood with some friends I made here. Sunday we went to the beach in Santa Barbara …
(August 15 2005) “How are things? I will make a presentation at EPNES (Electric Power Networks
Efficiency and Security) joint CDS/HSS group. I will send you the material when it is ready!
8
Take a few minutes to look at the pictures in http://www.cds.caltech.edu/~Thyago/ , specially the one with
the following caption: “Here we are! Knowing a little bit about night life in LA. At Caltech's parties
everything is free, in other places like pubs I paid 5 bucks for a beer. Too much just for a Bud .”
(August 21 2005): Good news! Jacob send the article I was participating with to a meeting in the USA, and it
was accepted! He invited us (me and my Caltech colleague) to come together. Joisa [Campanher Dutra, from
FGV´s Center of Experimental Economics] will be there. This meeting is gonn’a be in the end of September.
[(12/7/2005) Depois de um mês já fiz um monte de coisas... Ensinei um aluno aqui do Caltech que esta
trabalhando comigo a programar em Ztree; Eu e esse aluno fizemos 4 experimentos em economia; Rodamos 2
desses experimentos no laboratorio de ciencias sociais na UCLA; Fiz um cursinho on line em experimentos
em humanos na UCLA; Programei umas contas para uma professora aqui do Caltech em um paper que ela
esta escrevendo. Fora isso estou começando a passear. No final de semana passado eu fui a Hollywood com
uns amigos que eu fiz aqui. No domingo fomos a praia de Santa Barbara...Um abraco, Ângelo.]
[Como estao as coisas ai? Eu vou apresentar o artigo no EPNES (Grupo de trabalho do CDS em conjunto
com o HSS na area de eletricidade). Assim que tiver uma versao do artigo vou envia-lo!]
(31 de agosto de 2005) boas noticias: Jacob enviou o artigo que estou participando para um congresso aqui
nos EUA e ele foi aceito! Ele me convidou para irmos (eu e o garoto do caltech) ao meeting e a Joisa vai estar
la! Esse seminario sera no final de setembro....]
Guilherme França. 9 (February 2 2004). “I want to tell you the last news here from Santa Barbara …
Yesterday and today I went to Caltech to see the Campus and a bit of Pasadena. It was great to see the gang
again. The infrastructure there surprised me. Thyago showed me the car form the project he is involved with,
and we talked a lot about life… Here everything’s fine. I am doing Dynamics II and Multiphase Flow, and I
am doing a project with Prof. Doyle. I am enjoying a lot Igor’s classes…”
[ Jair, gostaria de te contar as ultimas novidades aqui de Santa Barbara...Estive hoje e ontem com a turma do
Caltech, e aproveitei pra conhecer o campus e um pouco de Pasadena. Foi muito bom e gostei bastante de
rever o pessoal! A infra-estrutura de lá me surpreendeu. O Thyago me mostrou o carro do projeto do qual ele
esta participando, e colocamos a conversa em dia...
Por aqui esta tudo correndo bem. Estou fazendo Dinamica II e Multiphase Flow e ainda estou no projeto do
Prof. Doyle. Estou gostando muito da aula do Igor. Grande abraco, Guilherme ...
(November 16 2004, message to Igor Mezic) “Hi Prof. Mezic, how are you and things over there ? Did you
enjoy hearing Pixinguinha? Well, if you are interested, I can give you many other hints about nice Brazilian
composers10. Here everything is going pretty well. I've started in September a Masters in Mechanical
Engineering at the COPPE/UFRJ (my former university in Brazil). Now I'm learning about Time Series and
also about Probability and Statistics. There are nice applications in state space reconstruction which I'm
learning, and I'm really thinking of going into depth in this topic. I'm also taking a Real Analysis course at
IMPA and improving my math background.
… I used my circadian work with Frank Doyle for my undergraduate project and now I'm going to give a
presentation of it at IMPA. I'm really glad to have all the work recognized at last. And I also feel that I've got
a strong basis with the Advanced Dynamics courses you taught, and I'm using it for my masters studies now !
So for right now I don't have plans to apply for UCSB, but maybe for a PhD later. Anyway, I'll let you know
(of course if you want to) beforehand of any plans of trying to go to UCSB. Best regards, Guilherme. ]
Eduardo Lobão: [Fom his CAPES final report]: “Princeton is probably the World’s best Institution to
technological research, not to mention its housing infrastructure, location, and leisure opportunities. The
Brazilians are much liked both at the University and at the city”.
Nataly Horner [From her CAPES final report]: “The scientific dialogue with the Professors at Caltech is
privilegied, thus making science as a whole is much easier and accessible. In Academic terms, there was a
great interdisciplinarity between the different departments - without losing theit admirable organization thus allowing an intense dialogue between different areas of knowledge, which is immensely beneficial and
productive... I had some difficulty to adapt to the work systems there, since I was not so accustumed to give
emphasis in practical learning (exercises) in contrast with theoretical learning (reading and reflecting).”
9
See his personal web site http://paginas.terra.com.br/lazer/gui07/ .
Guilherme studies classical guitar seriously.
10
[Em termos acadêmicos, havia uma interdisciplinaridade muito grande entre os diferentes departamentos da
instituição – e mesmo assim, sem perder a organização admirável - permitindo assim um diálogo intenso entre
as diferentes área de conhecimento, o que é imensamente benéfico e produtivo numa produção científica de
qualidade...
Como facilidade, destaco o acesso ao conhecimento e a tecnologia, que era amplo e extremamente facilitado.
O diálogo cientifico era também privilegiado, de forma que o fazer ciência como um todo apresentou-se
muito mais fácil e acessível na instituição em questão. Como dificuldade, destaco o choque cultural, devido
ao caráter mais afetuoso e espontâneo da cultura brasileira, em contraste com as diferentes culturas que tive
contato ali. Houve também uma certa dificuldade em se adaptar ao sistema de trabalho ali, uma vez que não
estava tão acostumada a dar uma ênfase tão grande no aprendizado prático (exercícios) em relação ao
aprendizado teórico (leitura, reflexões)]
Maurício Richartz. “The time I stayed studying at Caltech was very productive, not only for my academic
but also for my personal life. I met people from all over the World and I made many friends. I learned about
the culture from several countries (and of course of the North American culture, which is quite different from
ours) and that was very interesting. Moreover, Caltech´s structure is phenomenal – the Sports center is
wonderful, the libraries are complete… The reception to new foreign students is very organized and helps the
new student to adapt to the North American culture. I was very well received at CDS and during the six
months that I studied there I was very well treated. I learned many new things. Besides studying Control and
Dynamical Systems for the first time in my life, I was able to deepen my Physics background. I did
introductory and intemediate classes in Control and Dynamical Systems, and intermediary Quantum
Mechanics course and one at Graduate level in General Relativity”.
[O tempo que eu passei estudando na Caltech foi muito proveitoso, tanto para minha vida academica quanto
para minha vida pessoal. Conheci pessoas de todas as partes do mundo e fiz algumas amizades. Aprendi um
pouco da cultura de varios paises (além, é claro, da norte-americana, que é bastante diferente da nossa) e isso
foi muito interessante. Além disso, a estrutura da Caltech é fenomenal - o complexo esportivo é magnifico, as
bibliotecas são completas, ... A recepcao de novos alunos estrangeiros é muito organizada e ajuda o calouro a
conviver com a cultura norte-americana. Fui recepcionado pelo Departamento de Controle e Sistemas
Dinamicos e, durante os seis meses que passei lá, fui bem tratado. Aprendi muitas coisas novas lá. Além de
estudar Controle e Sistemas Dinâmicos pela primeira vez na vida, pude aprofundar meus conhecimentos em
Física. Fiz cursos introdutórios e intermediários em Controle e Sistemas Dinamicos, um curso intermediário
de Mecânica Quântica e um de nivel de pós- graduacão de Relatividade Geral.]
Dale L. (Luke) Peterson: (9/11/2005) “Jair, I made it safely back to the US. Thanks again for everything -- I
really ppreciate all of your time and effort. The lunch card was also great!! I need to convince my advisor to
pay for my lunches! …”
(January 2005, when planning the stay: “Lukas is my middle name and Luke is what I have people call me,
but for official stuff it needs to say Dale. I wanted to give you a bit of background on me, so at the end of this
email I have excerpts from my resume. My primary interests are in Dynamics and Control. I would like to
use the summer to strengthen my real analysis skills, as I feel this is a requisite for a deeper understanding of
control system theory. Nearly all of my graduate coursework has been in the area of control, and I would like
to also improve my knowledge and understanding of nonlinear dynamics. Additionally, since I will be in
Brazil, I would love to learn more about the Portuguese language and Brazilian culture.”
Timothy H. Chung and Michael Epstein (End of Summer 2004): “We have done some good work. We have
written notes detailing how we applied feedback controls to the neo-classical model from Chapter 1 of the
book by Barro and Sala Martin. I've attached the preliminary version for you to have a look at, but note that
we are still finalizing it.”
(From Tim, 13 Jul 2004): We met with Bruno at UFRJ this morning, who showed us his lab in detail. ...
We will be meeting with Fernando [Lizarralde] this afternoon, and I will meet one of his students to discuss
his research problem on autonomous motion-planning. Other than that, things are going well. My [Tim's]
girlfriend will be arriving tomorrow, so I will be going to pick her up from the airport. Also, Mike and I have
begun to take a look at some interesting areas with respect to the economic models and control theory tools.
Perhaps if you have a chance, we can discuss briefly some ideas we have been working on, and maybe you
can guide us towards some additional interesting problems to work on. In addition, maybe it would be good
for us to meet with Samuel [Pessoa, FGV's expert in Economic Growth] to discuss some of the economics
concepts. Blue skies,Tim”.
Some Projects. In a report such as this one, we should try to minimize the technical details. Nonetheless, we
feel that is important for a general audience to give an idea of the work that is being developed.
Thyago Consort11. “I mainly worked on a project to design a completely autonomous ground vehicle to
compete on the 2004 DARPA Grand Challenge. On this project I worked under the advisory of Richard
Murray but there were others professors evolved, specialy the ones related to JPL. The big goal of this
reserarch is detecting obstacles and using this information in a robust way in order to manage avoiding them
and following the desired track. This would be useful for rescuing and military applications.
I took four courses recommended by Richard Murray. For three of them: CDS110 - Introduction to Control
Theory, CDS140 - Introduction to Dynamics and CDS125 – Spacecraft Systems Engineering; it was
necessary to reserve 3 hours for classes and 6 hours for homework and general studing per week. Most of my
time I dedicated to the fourth and most important of them, CDS300 - Research at the DARPA
Grandchallenge project. The spare time I used to improve my English, taking English as Second Language
classes.
Deep basis of Control Theory were aquired through CDS110, I developed considerably my math through the
CDS140 and through AE125 I had a change to work in groups and participate a little bit of the manager level
project of a space mission. The research was the real challenge because I don't often have chances to work
with experimental project at my university besides, of course, being really big one. I used my share of this
project to present as my final thesis [in Brazil]. I also had to make presentations, specially at AE125 and
CDS300.”
Guilherme Foerster do Monte França12. Guilherme’s senior thesis resulted in two presentations in
meetings in Brazil: "Phase Control of Limit Cycle Oscillators - an Application to the Control of the
Drosophila Melanogaster's Rhythm", in the “Workshop on Mathematical Methods and Modeling of
Biophysical Phenomena”, Angra dos Reis, RJ. February 14-26 2005 and "Controle de Fase de Osciladores
com Ciclo Limite", at the “ Jornada de Iniciação Científica do IMPA”, 2004.
This is a free translation of the senior thesis synopsis: “This work presents a method to control the phase of an
oscillator with stable limit cycle, via a curve of phase response. The control is exerted by agents that perturb
the parameters of the oscillator, provoking a deviation from its trajectory during the perturbation. After that,
it returns to the limit cycle with a new phase. I tested Matlab codes in a ten state model for Drosophila
Melanogaster proposed by J. C. Leloup et al. in 1998. The results show that our method could be a viable
alternative to other control techniques in use, because of its robustness and simplicity.
These results were obtained in a study that I started in September 2003, when I participated in a student
exchange in Control and Dynamical Systems at UCSB with a CAPES fellowship. With the supervision of
Frank Doyle and his group, I joined his research line on circadian rythms. I started from scratch, learning the
basic concepts of Dynamical Systems, such as phase space, limit cycles, and Poincaré maps, but having a
problem in mind helped maturing the ideas much faster. I think my main contribution was to implement in
real time a measurement of the phase difference between the output signal and a reference signal. This
allowed us to close the control network.”
11
Thyago finished his undergraduate studies in 2004, and is now in Nice, France, working with the joint
Brazil-France Consortium of communications satellites.
12
Guilherme is now enrolled in the M.Sc. program at Mechanical Engineering at COPPE/UFRJ. His areas of
interest are inverse problems/identification and continuum mechanics.
Nataly Horner. “At first, I was particularly excited with the wide range of scientific research possibilities
that Caltech made available for us, undergraduate students. Within the most diverse fields of studies, I was
very amazed with the research done in Prof. Christof Koch's neuroscience lab, which studies consciousness.
During the winter term, I started to do some data work on fear conditioning at his lab, under the guidance of
one of his grad students, McKell Carter. This experience has opened a completely new and challenging
horizon in my career: I intend to finish my Physics degree this year and pursue my graduate studies in
Neuroscience, a very promising area whose development in Brazil is unfortunately still very timid.
It was deeply touching to see how diverse areas of knowledge harmonize and converge into a single point,
which is make pioneer science - something that was only possible in such a scientific oriented and unique
place, which is Caltech.”
Eduardo Lobão (also for Bruno Givisiez). This is an excerpt from his CAPES final report. “My
supervisor, both in terms of classes and lab work was Prof. Clarence Rowley, from MAE. He also
complemented my CAPES fellowship from his start up grant. [Although I was a senior undergraduate], I had
the status of visiting graduate student, so I had all my homeworks and exams graded. I took two classes
during the whole fall-winter semester (September to January with two one week breaks), which is considered
the default for a student also involved in lab work.
I had the freedom to choose my classes, after discussing with Clancy and my coordinators in Brazil. The idea
was to complement my theoretical formation with mathematical techniques not covered in the UFRJ
undergraduate syllabus. I took Advanced Dynamics, a more sophisticated approach than the traditional
Particle and Rigid Body Mechanics given at any Mechanical Engineering School. In particular, special
attention was given to the foundations of Lagrangian and Hamiltonian Mechanics. This class was given by
Prof. Jeremy Kasdin. The other discipline was Applied Dynamical Systems, that Prof. Rowley taught
together with Prof. Phil Holmes. This is an Applied Mathematics course in the area of Nonlinear Dynamics,
up to an introduction to chaotic systems.
Re to the lab work, my project consisted to operate an experimental apparatus to simulate the motion of a
swimming fish. The idea was to measure the hydrodynamical forces acting on the structure during different
motion regimes. The instrument was calibrated comparing static measurements with the available technical
literature. In the end of the fellowship, a report was given to Prof. Rowley about the work. This included a
diagnosis of the initial state of the equipment and the technical problems we faced, our proposed solutions and
experiments performed, future suggestions. Some theoretical analysis were also given.
[O professor assistente Clarence Rowley do departamento de Engenharia Mecânica e Aeroespacial (MAE) foi
o responsável pela orientação em meus estudos e trabalhos realizados, assim como pelo complemento a bolsa
mensal do Capes. Logo tanto as aulas por mim assistidas quanto o laboratório em que trabalhava eram no
MAE. O que esta de perfeita coerência com a minha formação acadêmica em Engenharia Mecânica na
Universidade Federal do Rio de Janeiro (UFRJ). Os cursos que decidi acompanhar foram uma opção minha
em consenso com o professor Jair Koiller aqui do Brasil juntamente com o professor Rowley, já mencionado.
Sua escolha fora feita com base na idéia de complementar minha formação teórica com o aprendizado de
ferramentas matemáticas não cobertas pelo curso de graduação da UFRJ, mas totalmente pertinentes a
pesquisa na área de sistemas dinâmicos. A primeira disciplina chamava-se Advanced Dynamics (Dinâmica
Avançada) que consistia numa abordagem mais matemática do curso tradicional de Dinâmica da partícula e
corpos rígidos presente no programa de qualquer faculdade de Engenharia Mecânica, além de uma atenção
especial a Mecânica Lagragiana/Hamiltoniana e suas consequências. Este era um curso ministrado pelo
professor Jeremy Kasdin tambem do MAE.
A outra matéria por mim cursada chamava-se Applied Dynamical Systems (Sistemas Dinâmicos Aplicados) a
qual o próprio professor Rowley lecionava juntamente com o professor Phil Holmes. Esta tratava-se de um
curso de matemática aplicada na área de dinâmica não linear chegando a cobrir uma introduão a teoria de
sistemas caóticos. Assuntos tais que não deixam de ser uma continuação do curso do professor Kasdin.
Quanto aos trabalhos de laboratório, meu projeto consistia em operar um aparato experimental que simulava
os movimentos de um peixe nadando. A idéia era medir os esforços hidrodinâmicos atuantes na estrutura
durante diferentes regimes de funcionamento e validar os resultados através da comparação de medições
estáticas com a literatura técnica disponível. Ao final de minha estadia foi entregue ao professor Rowley um
relatório sobre os trabalhos realizados. Este incluia um diagnóstico do estado inicial do equipamento e seus
problemas técnicos, com análises teóricas, soluções promovidas, sugestões futuras e resultados dos
experimentos realizados.]
Alex Castro13. “During my stay at Caltech I focused on studying Geometric Mechanics, under Profs.
Jerrold Marsden and Eva Kanso. I used the material for my senior thesis and also for the scientific initiation
meeting at IMPA in 2004. My senior thesis in Brazil was directed by Prof. Patricio Letelier. It is a
dissertation on the mathematical foundations of classical gauge theory. I wanted to know what astronauts,
gymnasts, cats and divers, bacteria and elementary particles have in common...
In gauge theory, the configuration variables have some internal symmetries, and these symmetries form a
group action. Modulo the group, the reduced (base space) is called the “shape space”. For instance, the
unlocated configuration of a falling cat or of a smimming protozoa. By performing a cyclic change of shape,
the cat can reorient herself, the microorganism can translate. I discuss also the problem of finding optimal
motions under the constraint of no external forces.
With Eva Kanso at Caltech and Patricio Letelier in Brazil I studied variational integrators, from January to
April 2004, as a presentation to the course Topics in Control and Dynamical Systems at Caltech. The purpose
of this class is to introduce the students interested in Dynamical Systems to topics that are not present in the
traditional curriculum and that could eventually furnish problems for future research. I chose this topic due to
the current interest on these numerical methods for solving problems of classical mechanics, Physics,
Engineering and also Economic growth.”
Thiago Barros. “The experience I had at Caltech contributed to my development in many ways. The first is
related to the interdisciplinary nature of the program. The university offers excellent opportunities for the
student to increase his/her knowledge in a given discipline but at the same time to place them in context with
other sciences. The courses cursos CDS110 (Introduction do Control of Physical Systems) and CDS140
(Introduction to Applied Dynamics) are good examples. My interest in the advanced math exposed in
CDS140 increased in the measure that I perceived, in CDS110, the applications of dynamical systems in so
many areas. I liked the subject so much that I am now considering very strongly the possibility to do a Ph.D.
in the theme. Another subject of interdisciplinary nature that I did was foi CS191 (Biomolecular
Computation), that involved concepts of computing, chemistry, biology and mathematics (including
dynamical systems). Besides taking classes, I also worked in the “Darpa Grand Challenge”, the project to
construct a self guided vehicle. I found extraordinary the creative atmosphere of the project. The other thing
that impressed me at the University was the high level of the classes, the homework assignements, and of my
colleagues. This was particularly clear in the two classes I took in the Mathematics Department: : MA120
(Abstract Algebra) and MA121(Combinatorial Analysis). To me this was a great stimulus to study more
Mathematics, and in fact my mathematical base improved a lot. After I returned from the exchange program
I participated in the International Mathematics Competition for University Students (IMC), and I obtained a
“First Prize” level, a better result than I was getting previously.”
[A experiência que tive no Caltech contribuiu para minha formação em muitas maneiras. A primeira delas
está relacionada com a caracteristica interdisciplinar do programa. A universidade oferece excelentes
oportunidades para o aluno desenvolver seus conhecimentos e ao mesmo tempo inseri-lo num contexto com
outras disciplinas. Os cursos CDS110 (Introduction do Control of Physical Systems) e CDS140 (Introduction
to Applied Dynamics) são um bom exemplo disso. O meu interesse pela matemática avançada desenvolvida
em CDS140 aumentou medida que percebi, com CDS110, as aplicações de sistemas dinâmicos em tantas
diferentes áreas. Gostei tanto do assunto que passei a considerar fortemente a possibilidade de fazer uma pósgraduao na área. Outra matéria interessante que eu fiz, de caráter interdisciplinar, foi CS191 (Biomolecular
Computation), que envolveu conceitos de computação, química, biologia e matemática (incluindo sistemas
dinâmicos). Além de assistir aulas, ainda trabalhei no Darpa Grand Challenge, o projeto de construção do
carro automático. Achei o ambiente criativo do projeto extraordinário. Outra coisa que me deixou
13
Alex participated actively in the 2004 and 2005 Biomathematics schools at IMPA, sponsored by the
Millenium Institute AGIMB, and together with his colleagues, organized a yahoo discussion group. He
obtained a fellowhip to work for his Ph.D. under Prof. Richard Montgomery at UCSC, starting Fall 2005.
impressionado com a Universidade foi o alto nível das aulas, listas de exercícios e dos próprios alunos. Isso
ficou claro pra mim nas duas matérias que fiz no Instituto de Matemática: MA120(Abstract Algebra) e
MA121(Combinatorial Analysis). Para mim foi um timo estímulo para estudar matemática, e de fato acabei
melhorando bastante minha base matemática geral. Quando cheguei do intercâmbio participei da International
Mathematics Competition for University Students (IMC) e acabei ganhando um "First Prize", resultado bem
superior ao que eu vinha recebendo nos ultimos anos.]
Angelo Polydoro. Angelo, from the 2005-2006 group, traveled to Caltech earlier, to be able to participate
in the Summer Undergraduate Reasearch program (SURF). Among other activities, he helped to perform and
analyse some experiments in auctions by Prof. Jacob Goeree. The results will be reported soon in the 2005
North American meeting of the Economic Science Association 14 . This is the abstract of the paper: “An
Experimental Test of Qualifying Auctions (Roy Chen, Angelo Polydoro, Jan Boone, and Jacob K. Goeree).
This paper explores the use of auctions for privatizing public assets. In our model, a single "insider" bidder
(e.g. incumbent management of a government-owned firm) possesses information about the asset's risky
value. In addition, bidders are privately informed about their costs of exploiting the asset. Due to the insider's
presence, uninformed bidders face a strong winner's curse in standard auctions with devastating consequences
for revenues. One format that is frequently used in this context is a two-stage qualifying auction: in the first
stage, non-binding bids for an item are placed by interested parties; in the second stage, all but the lowest first
stage bidder compete in a standard second-price auction. This paper reports the results of a series of
experiments that compare the performance of the qualifying auction to that of the English and second-price
auction.”
Tim Chung. One of the problems that Tim is facing in his thesis is how to use stochastic methods to help
optimizing the trajectory of an autonomous vehicle. Ongoing collaboration with Ronaldo Dias started during
his visit to Caltech in 2005.
“Let us suppose that an autonomous vehicle has to move from point A (say the origin) to point B (say (B,0)).
Obstacles can appear in the range of its sensors in a random manner (not necessarily a Poisson random
process). The objective is to find the best (in some sense) trajectory from point A to point B avoiding the
obstacles. It is clear that a straight line is the best trajectory if no obstacle occurs.
First we consider that the vehicle cannot stay very close to the obstacle, that is, there exists a radius r, such
that the vehicle have to be at least distance r from the obstacle. Moreover, we assume that the vehicle cannot
have rough trajectories, that is it cannot change directions abruptly.
The goal is to find a trajectory from (0, 0) to (B, 0) that has the shortest length and at the same time avoids
obstacles by staying off them in their neighborhood. This can be posed as a penalized optimization problem.
However, the penalization should be discontinuous due to the constraints, and there is no smooth solution for
this kind of penalization problem. The problem is therefore not only very relevant from the Control
Engineering perspective, but also mathematically very challenging.”
Curriculum development and teaching materials. We present here just few comments, referring the
interested reader to some of our already published material. For instance, this is an excerpt from the report
Appealing to a Non-traditional Audience: A New Approach to Teaching Feedback, by Richard M. Murray and
collaborators, S. Waydo, L. B. Cremean and H. Mabuchi (IEEE Control Systems Magazine, 2004)15:
“To address the growing need for a broader approach to teaching control, the Control and Dynamical Systems
(CDS) Department at Caltech has revised its entry-level curriculum in dynamics, feedback, and control, with
the goals of updating the subject matter to include modern tools and making control tools accessible to a nontraditional audience. Consequently, we have expanded the diversity of our control curriculum by providing
examples from a broad set of application domains and catering to a wide array of mathematical backgrounds.
To pursue these goals, we are developing several new approaches to control education, two of which are
14
15
See http://www.cirano.qc.ca/experimentaleconomics/ESA2005_Tucson/
See http://www.cds.caltech.edu/~murray/papers/2004y_mwcm04-csm.html .
described here. The first approach is to divide the introductory control theory class into two tracks, with a
conceptual track geared toward students who need only a conceptual overview of control tools, and an
analytical track providing a more detailed mathematical treatment of feedback. In this article we primarily
discuss the conceptual track. The second approach is the development of a new undergraduate minor in
Control and Dynamical Systems.”
The results of a panel on future directions for Control and Dynamical Systems 16 was recently published by
SIAM: “Control in an Information Rich World: Report of the Panel on Future Directions in Control,
Dynamics, and Systems”, edited by R. Murray, SIAM, 2003.
Some online teaching materials for Dynamical Systems were developed during a visit by Jair Koiller to
Caltech in the Fall and Winter 2001-2002, prior to the beginning of this project. A second visit is planned for
the Winter quarter 2005-2006, with a Fullbright fellowship. The first experience is described in an invited
review for the AMS Bulletin17. Here´s an edited excerpt:
“This is a teaching experience I was involved with at Caltech in the Control and Dynamical Systems
Department during the 2001- 2002 academic year. This ongoing experiment is evolving as a partnership
between the USA and Brazil. The course is a combined 2 - 3 quarters sequence in Dynamics and Control for
beginning graduate students and senior undergraduates (Physics, Mathematics, Engineering, Chemistry and
Biology majors interested in mathematical modeling). The two quarter sequence "Introduction to Modern
Dynamics" is Caltech's CDS140ab (www.cds.caltech.edu), which attracted many students in the 2002-2003
academic year (see also the 2001-2002 class web page, for which I was the instructor). Students can also
enroll at the same time in Caltech's 101ab, "Principles of Feedback and Control", which also attracted a wide
audience (ranging from Aeronautics to Zoology). Students interested in obtaining a more thorough intrinsic
background can also enroll in CDS 202, "Geometry of Nonlinear Systems", which includes manifolds and
mappings, transversality, vectorfields and flows, distributions and Frobenius' theorem, matrix Lie groups and
Lie algebras, exterior differential forms and Stokes' theorem.
The fall quarter has a 50% - 50% mix of basic Particle Mechanics and Dynamical Systems. For the latter, I
recommend sources such as Strogatz, Smale/Hirsch, Verhulst, Perko, Guckenheimer/Holmes, covering the
basic tools and concepts of ODEs (both qualitative and quantitative, including computer simulations) up to,
say, Lyapunov stability theory. Strogatz can be covered entirely in a quarter by a diligent student (it is
wonderful when some real lab demonstrations proposed there are performed). For basic Particle Mechanics,
there is still good old Sommerfeld: terse, intelligent exercises, interesting for all publics – a masterpiece
(written after about 50 years of teaching in Munich).
In the winter quarter, again a 50% - 50% mix. One would cover more groundwork material of Dynamical
Systems (starting, say, with Floquet theory and including an introduction to homoclinic phenomena and other
chaos concepts and diagnostics); regarding Mechanics, we propose following a little more mathematically
sophisticated avenue, using Arnold or Marsden/Ratiu. Basic concepts and notations about manifolds and Lie
groups, and some invariant language can be introduced without difficulty, taking the rigid body as a concrete
realization.
The spring quarter could have a more open agenda, according to the instructor's preferences, focusing on
his/her personal research interests; mine have been divided between Geometric Mechanics applications such
as geometric phases, nonholonomic and subriemannian systems, and biological motion.”
…..
16
17
See http://www.cds.caltech.edu/~murray/cdspanel/
See http://www.ams.org/bull/2003-40-03/S0273-0979-03-00984-4/home.html
Appendices
A. Independent evaluation: This is an excerpt from the report:
“All exchange students cited discernable growth in their academic development. The Americans tended more
to benefit in complementary disciplines, rather than their own field of study, and agreed that they felt more
well rounded when they returned home. The Brazilians, on the other hand, reveled in the opportunity to visit
some of the highest esteemed institution in the world and learn under world class faculty. One Brazilian
student remarked about how thrilling it was to meet face to face with people whose books he had been
studying for years. Many of the Brazilians were able to complete their senior undergraduate thesis based on
the work they did in the US institutions.
Many Brazilian exchange students followed an independent course of study at their host university, but some
joined existing research projects. Some of these include:
 RoboFlag: a version of capture the flag featuring cooperative control of multi-robot teams in
dynamic, uncertain, adversarial environments.
 Team Cal Tech: an entry in the DARPA Grand Challenge, an autonomous vehicle road race.
 CIMMS: Center for Integrative Multiscale Modeling and Simulation.
 RUNES: Reconfigurable Ubiquitous Networked Embedded Systems, exploring the possibility of
allowing sensors embedded in appliances like cell phones, refrigerators, etc. to communicate with
each other.
 Fish Experiment: measuring hydrodynamic forces exerted on a swimming fish.
All three American participants, all of whom were graduate students, agreed that rather than being structured
and regimented, there was more of an independent-study feel to their visit. Instead of enrolling in classes, they
tended to work one-on-one and spend time meeting Brazilian professors and lecturing undergraduate-level
classes. The Brazilians, on the other hand, all enrolled in classes at their host university and cited the quality
of the research facilities and the resources to which they had access during their stay. Cal Tech, in particular,
drew rave reviews for its ability to cater to and support foreign students.
B. About the partner Institutions
Caltech, University of California and Princeton are known everywhere, so we just give some pointers to the
departments involved in our exchange program:
Caltech: www.cds.caltech.edu
UCSB: www.ece.ucsb.edu and http://www.me.ucsb.edu/
Princeton: www.mae.princeton.edu
Further informations about IMPA, UNICAMP, LNCC and FGV can be found from their web sites:
www.impa.br
www.ime.unicamp.br
www.coppe.ufrj.br
www.lncc.br
www.fgv.br
Reference Institution for Pure Math research in Brazil
Reference Institution for Undergraduate and Graduate teaching in Brazil
Reference Institution for Post-Graduate work on Engineering
Reference Institution for Scientific Computation
Referencie Institution for Economics and Social Sciences in particular
It is perhaps worth to present some information about the Brazilian Partner Universities.
UNICAMP (Campinas University)
From the web site18: “The University campus is named after its founding father, Zeferino Vaz, one of Brazil's
most renowned educators, who dreamed of UNICAMP and saw its birth in 1966. The sloping verdant
meadows where it is located were the home for coffee and sugar cane plantations, and they now house a twomillion square-meter university campus, luxuriant with parks and flowering trees.
The University has approximately 9,900 undergraduate students and 9,000 graduate students. The majority of
the undergraduate students come from São Paulo state, while the graduate students come from literally all
over the nation. The academic staff includes nearly 2,000 professors. Our institution is an autarchy,
autonomous in matters of educational policy but dependent on the state government for funds. Thus, the
financial resources are obtained mainly from São Paulo State Government and secondarily from national and
international financial agencies. Students do not pay tuition, because the University is supported by the state
government.
A city originally named for its meadows, Campinas was founded in 1774 and lies 16 kilometers south of the
University. With a population of nearly one million people, Campinas is today an important and growing
educational, industrial and financial center. The city has its own Symphony Orchestra - considered one of
Brazil's best - cinemas, theatres, museums, parks, and fine shopping centers. Restaurants serve a variety of
regional and international dishes while pubs or "barzinhos" are popular meeting places for stimulating
conversations and great music. Campinas is also the home of two popular soccer teams: Guarani and Ponte
Preta.
Recreation in the vicinity of Campinas is also rich and varied. São Paulo, one of the world's largest cities and
an important cultural center, is located 100 kilometers southeast of Campinas - a one-hour ride by car or bus.
In addition, many country resorts and parks are accessible, offering a taste of life in the "interior". Finally, the
famous beaches of the coast are only a two-hour drive away.
COPPE/UFRJ: School in Engineering of the Federal University in Rio de Janeiro 19
(we thank our colleague Atila P. Silva Freire for the following text)
Brazil is a country with a considerable presence in the international scenario. In addition to its large territorial
extent, 8,511,956 square kilometers, and population, 179,000,000 million people, the present degree of
economical and technological developments are comparable to some of the more advanced countries. Despite
all that, post-graduation in engineering in Brazil is in its infancy. From a historical point of view, three
institutions greatly contributed to the development of technology in Brazil: the Technology Center of the Air
Force, the Institute for Technology Research in Sao Paulo and the Post-Graduate School in Engineering
(COPPE/UFRJ) of the Federal University in Rio de Janeiro.
We believe that COPPE is the ideal institution in Brazil for the establishment of collaborative academic and
scientific programs in Engineering. Our rich scientific atmosphere is a sure guarantee that initiatives of this
type will be crowned with the expected success. We are much interested to exchange experiences also in
undergraduate programs. Although our faculty has been involved fro many yeares both in graduate and
undergraduate teaching, only recently we obtained full responsability for the undergraduate activities.
Modernizing our undergraduate Engineering Programs is one of our main tasks.
COPPE's defining characteristic is the overriding priority assigned to teaching and basic engineering research,
graduating highly qualified engineers, as well as to the generation of advanced state-of-the-art concepts in the
service of social, technical, and economic development of Brazil.
18
International Cooperation: http://www.cori.unicamp.br/index-engilsh.htm
http://www.coppe.ufrj.br/english/ . For Turbulence lab: http://www.pem.ufrj.br/labs/mecturbu/
For Robotics lab:
http://www.coep.ufrj.br/gscar/apresei.htm
19
COPPE's contribution to undergraduate teaching has been growing each year since almost all its faculty are
involved in teaching duties in one of the undergraduate schools. Moreover four new engineering courses are
being offered at UFRJ in 2004. These new degrees are an output of the partnership among COPPE, and the
Chemistry and Engineering Schools. The new courses are: Automation and Control Engineering, Petroleum
Engineering, Environment Engineering, and Computer and Information Engineering.
In the industry sector, in average, COPPE executes over a 1.000 R&D projects a year, for more than 500
different companies.
COPPE has a faculty of about 300 lecturers distributed in twelve departmental areas, nominally: Biomedical,
Chemical, Civil, Electrical, Energy Planning, Mechanical, Metallurgical and Materials, Nuclear, Ocean,
Production, Systems & Computing, and Transport. All department of COPPE hold Ph.D. programs, totaling
about 3.000 students.
In short: Since its foundation in 1963, COPPE has constructed a solid reputation based on its defense of the
development on a national capability in engineering sciences, being unique in Brazil in combining both basic
science and engineering. There is no doubt that COPPE has had a history of complete success, setting
research trends that are well disseminated in the whole of the continent. COPPE is reputably the best and the
biggest engineering school in Latin America.
Fundação Getulio Vargas/RJ
FGV, founded in 1944, had as its initial objective preparing qualified personnel for Public Administration
and Business. Foreseeing the new times to come, the Foundation expanded its activities to Social Sciences,
advancing to Research and Information. FGV pioneered in Brazil the Graduate Schools in Economics,
Public Administration, Business, Accounting, Psychology and Education. The work done at FGV to quantify
the Economic foundations is still a reference for those trying to understand better the performance of the
Brazilian Economy.
FGV exerts a leadership role in Academic research in areas such as macro and micro-economics, finance, law,
health, social security, povership and unemployment, pollution and sustainable development, as well as
history, social sciences, education, citizenship and politics.
The mission statement addressed by FGV´s president Dr. Simonsen Leal ends by saying that “it should be
sressed here the importance for FGV of maintaining the independence and plurality of viewpoints, which are
by the way, one of FGV’s landmarks”.
FGV´s Undergraduate Course in Economics in Rio de Janeiro20. Here´s an excerpt from the brochure:
[Our course] is noted for the range of majors offering Finance, Economic Policy and Markets and Contracts ,
its strong complementary foundations in the areas of the exact sciences and humanities, and for its highly
qualified Faculty. With an emphasis on developing analytical capabilities, it endeavors to train professionals
who can ally rigorous technical knowledge to the versatility required by the modern world, while sensitive to
the political and social problems of the nation.
Course Structure – The program of the Undergraduate Course in Economics is composed of two main blocks
of courses: The Basic Cycle and the Professional Cycle. Taking up the first four semesters, the Basic Cycle
aims at offering students the fundamental concepts in the education of both Economists and Managers. Basic
training includes the following areas of knowledge: Economics, Computer Science, Management, Social
Sciences and Mathematics. The Professional Cycle comprises the last four semesters of the program, and is
composed of courses given to all students as further development of the fundamental concepts offered in the
Basic Cycle, as well as courses geared specifically to each of the three majors.
20
Course List.
http://www2.fgv.br/gradrj/cursos/idx_economia.html
Overview. Offering Majors in three well-established fields of professional economics, the course covers
traditional areas of research: Finance, Macroeconomics and Microeconomics.
Major in Finance – Provides an ample overview on the workings of the financial markets, their institutional
organization and role as an instrument for allocating wealth and risk efficiently in the economy. The main
topics include the economic goals of firms, identifying and evaluating opportunities for economic enterprises,
and the optimal use of assets and financial tools to reach those goals. With this major, students will be
qualified to work as financial analysts, managers, or investors. They will acquire a consistent and unified
theoretical view of market behavior, being exposed to the most up-to-date professional techniques and
practices.
Major in Economic Policy – Aims to develop knowledge primarily of the field of macroeconomics, seeking
an understanding of the phenomena and of the political and economical decision-making that determines the
aggregated state of the economy. This major explores, both theoretically and through empirical evidence, the
intricate relationship that conditions the macroeconomic variables and policy decisions, both of fundamental
interest in the management of private and public initiatives. Students taking this major will become skilled
economic analysts, being able to predict and quantify macroeconomic scenarios, to determine and evaluate
alternatives in carrying out policies, while judging its impact on economic activity, as well as on the growth
and well-being of the economy.
Major in Markets and Contracts – Studies the mediation of the individual behavior of economical agents,
consumers, businesses and government at depth, through the economic institutions that allow for performing
transactions: markets and contracts. The issues highlighted seek to develop an understanding of strategic and
non-strategic processes of market price formation and of the system of incentives underlying contractual
terms, as well as its impact on the public and private decision making processes. This major allows students to
analyze market behavior and competitiveness, so as to propose market strategies for businesses or
governments, according the economic aims of maximizing private value and social well being.