Description

The Summer Program is a traditional event that occurs every year since 1987, during the months of January and February. It congregates both senior undergraduates, graduates, and researchers in Mathematics with activities involving research and teaching. The Summer Program is also part of the selection process to the DM-UFSCar's Graduate Program in Mathematics - (PPGM), booth Master and Ph.D.

The Summer Program aims are:

• Select students to the Graduate program, Master and Ph.D., offered by the PPGM.
• Offer graduate courses to students and professors interested to join the DM-UFSCar's Graduate Program.
• Promote interactions between researchers in Mathematics of different universities.
• Stimulate research activities.

** The PPGM encourages all students who are senior undergraduates or have just finished both undergraduate course or Master degree to participate.**

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Program 2010

From January 04th to February 26th

Courses:

Real Analysis - (Undergraduate course)

Linear Algebra - (Graduate/Advanced undergraduate course)

PDE - (Graduate course)

Workshops:

III PDE Symposia, February, 10th to 14th

III Mathematics & Physics symposia, February, 22th to 24th

Mini-courses:

Introducción a la Teoría de Sistemas Dinámicos, February, 10th to 12th

Introducción Matemática a la Relatividad General, February, 22th to 24th

Visiting researches in the following areas:

Algebra

PDE

Mathematics Physics

Differential Geometry

Singularities

Algebraic Topology

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Courses (all taught in Portuguese)

Real Analysis (Undergraduate course)

Professor: Rodrigo da Silva Rodrigues, DM - UFSCar

Goals: Formal treatment to the concepts introduced in the Differential and Integral Calculus of real functions of one real variable, such as: Construction axiomatic of the real numbers system; Real line Topology. Stimulate: the logic through deductions of the results and the formal writing.

Topics: Real numbers: Properties and completeness. Real line Topology. Continuous functions: open set and sequential limit characterization. Differentiable functions in the real line. Main results, such as the medium value theorem. Riemann integral and the fundamental theorem of calculus. Sequence and series of functions: simple and uniform convergence. Arzelá-Ascoli and Weierstrass Theorems and aplications.

From: January 04th to February 26th

Time: de Tuesday to Friday from 2PM to 4PM

Local: Room 20 at Mathematics Department - DM

Bibliography:

1. Figueiredo, D. G., Análise I
2. Lima, E. L., Análise Real, Volume 1
3. Lima, E. L., Curso de Análise

Linear Algebra (Graduate/Advanced Undergraduate course)

Professor: Waldeck Schutzer, DM - UFSCar

Goals: Select students to the DM-UFSCar's Master program. Depending on the grade obtained it can be used to waive the student to the written comprehensive qualifying exam. (veja mapa do mestrado).

Topics: Vector Spaces; Linear Transformations; Determinants; Canonical forms: rational and Jordan; Inner product spaces; Symmetric, orthogonal, hermitian and normal transformations; Bilinear and Quadratic forms; Applications.

From: January 04th to February 26th

Time: de Tuesday to Friday from 8AM to 10AM

Local: Room 20 at DM

Bibliography:

1. Herstein, I, Tópicos em Álgebra
2. Hoffmann, K & Kunze, R, Álgebra Linear
3. Greub, W, Linear Álgebra

PDE (Graduate course)

Professor: Rafael Augusto dos Santos Kapp, DM - UFSCar

Goals: Select students to the DM-UFSCar's Ph.D. program. Depending on the grade obtained it can be used to waive the student to the written comprehensive qualifying exam.

Topics: Introdution to distribution theory; First order equations: characteristic curves; Transport equation; Laplace equation: fundamental solution, mean value formula, harmonic functions, energy methods. Heat equation: fundamental solution, maximum principle, uniqueness of Cauchy problem, energy methods. Wave equation: solutions, energy methods.

From: January 04th to February 26th

Time: Mondays, Tuesdays, Thursdays and Fridays from 10AM to 12PM

Local: Room 20 at DM

Bibliography:

1. Evans, L. C. - Partial Differential Equations
2. Strauss, W. - Partial Differential Equations: An introdution
3. Garabedian, P. R. - Partial Differential Equations
4. Folland, G. - Introduction to Partial Differential Equations
5. Treves, F. - Basic Linear Partial Differential Equations
6. Hounie, J. - Teoria Elementar das Distribuições
7. Hormander, L. - The Analysis of Linear Partial Differential Equations
8. John, F. - Partial Differential Equations

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Mini-courses

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Visiting Professors

Algebra

PDE

Ziad Adwan (University of Texas)

Adalberto Panobianco Bergamasco (ICMC/USP)

Jurandir Ceccon (UFPR)

Paulo Cordaro (IME/USP) - to confirm

Paulo Leandro Dattori (FFCLRP/USP)

Marcelo Ebert (FFCLRP/USP)

Alexandre Kirilov (UFPR)

Olímpio Hiroshi Miyagaki (UFV)

Renato José de Moura (UFMG)

Marcos Montenegro (UFMG)

Franciso Odair de Paiva (UNICAMP)

Ezequiel Rodrigues (UFMG)

Paulo Santiago (UFPE)

Uberlândio Batista Severo (UFPB)

Evandro Raimundo da Silva (ICMC/USP) - to confirm

Joaquim Tavares (UFPE)

Sérgio Luiz Zani (ICMC/USP) - to confirm

Mathematics Physics

Differential Geometry

Algebraic Topologia

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Financial Aid

The PPGM has financial aid to a limited number of students attending the Summer Program.

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Registration

Deadline: Novembro 20th, 2009

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Previous Summer Programs