• Singular Integral Operators - 1994/1996
   
• Linear Operators - 1996/1997
   
• Algebras of Singular Integral Operators - 1995/1996, 1997/1998, 2003/2004
  
  Program:
  
  Fredholm operators and the Calkin algebra
  Characterization of Fredhom operators. Perturbation of Fredholm operators and index properties. Semi-Fredholm operators and their generalized inverse.
  
  The Cauchy singular integral operator
  Classical perspective and the Cauchy singular integral operator in Lebesgue spaces. Generalizations to weighted Lebesgue spaces and to systems of curves. The transpose of the Cauchy singular integral operator.
  
  Singular intgeral operators and the factorization theory
  The concept of factorization of functions. The singular integral operator with rational coefficients. The singular integral operator with continuous coefficients. Factorization in decomposing Banach algebras. Generalized factorization of functions. Some results concerning the factorization of functions with a finite number of discontinuities. Generalization to the matrix case of the results about factorization of functions. Application to boundary valued problems from diffraction theory.
  
  The Gelfand theory and generalizations to non-commutative algebras
  The Gelfand transformation and some of its applications. Ideals and invertibility. Localization principles. PI-algebras. Introduction to the local trajectory method.
  
  Invertibility in algebras of singular integral operators and in Toeplitz algebras
  Application of the two-idempotent theorem to the algebra generated by the Cauchy singular integral operator and by multiplication operators by piecewise continuous functions on the unit circle. The algebra generated by Toeplitz plus Hankel operators. Localization over orbits and the invertibility in C*-algebras with shift operators.
  
   
  Program:
  
  
• Operator Algebras - 2000/2001, 2001/2002, 2002/2003, 2004/2005
  
  General results for Banach algebras:
  Spectrum and spectral radius. The Gelfand representation theory for commutative Banach algebras. Functional calculus. Spectral theorem.
  
  C* Algebras:
  The Gelfand Naimark theorem for commutative algebras. The functional calculus for normal operators. Positive elements. Positive linear functionals. States and pure states. The Gelfand-Naimark-Segal construction. The Gelfand-Naimark theorem. Liminal and postliminal C* algebras. Von Neumann algebras. Double commutant theorem. Kaplansky density theorem. Crossed products. The isomorphism theorem for commutative groups and algebras. Local-trajectory method.
  
  Representations of Banach algebras:
  Primitive ideals. Primitive algebras. Irreducible representations. The Jacobson radical. The Jacobson topology. Representations of algebras that satisfy a polynomial identity. Algebras generated by two idempotents. The Allan-Douglas localization principle and the representation theory.
  

•   Applied Mathematics for Electrical Engineers I, 1978-1983.      

•   Applied Mathematics for Electrical Engineers II, 1978-1983.

•   Linear Algebra, 1998-1991.

•   Mathematical Analysis I

     for students of:

-    Civil Engineering; Territorial Engineering, 1992-93 .

-  Mechanical Engineering; Mining and Geological Engineering; Naval Architecture and Marine Engineering, 1993-94.

-    Information Systems and Computer Engineering, 1994-95.

-  Chemical Engineering; Mining and Geological Engineering, Naval Architecture and Marine Engineering, Materials Engineering, 1995-96.

-    Information Systems and Computer Engineering, 1997-98.

-  Mechanical Engineering, Mining and Geological Engineering, Naval Architecture and Marine Engineering, Materials Engineering, 1999-2000.

-  Mechanical Engineering, Mining and Geological Engineering, Naval Architecture and Marine Engineering, Materials Engineering, 2000-2001.

-    Mechanical Engineering, 2001-2002.

-   Civil Engineering, Territorial Engineering,  Naval Architecture and Marine Engineering, 2004-2005.

•   Mathematical Analysis II

     for students of:

-    Civil Engineering; Territorial Engineering, 1992-93.

-   Mechanical Engineering; Mining and Geological Engineering; Naval Architecture and Marine Engineering, 1993-94.

-    Information Systems and Computer Engineering, 1994-95.

-    Chemical Engineering;  Mining and Geological Engineering,  Naval Architecture and Marine Engineering, 1995-96.

-    Civil Engineering, Territorial Engineering, 1999-2000.

•    Differential and Integral Calculus I

-    for students of Information Systems and Computer Engineering,  2006-2007.

Lectures Notes

•  Bastos, M. A., Santos, P.A, “Introduction to Operator Algebras” Textbook in progress.

•  Bastos, M. A., Lebre, A. B.: "Apontamentos de Álgebras de Operadores Integrais Singulares",  280pp, 1998.

•  Bastos, M. A.: "Noções de Álgebra, Trigonometria e Análise Matemática "Curso Internacional de Hidrologia Operativa, Manual, Vol. I, 1-37, 1984.