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    Course description

    • REQUIREMENTS AND PRIOR KNOWLEDGE

      To follow this course properly, a basic knowledge of linear algebra and calculus is needed (first year university course of linear algebra and calculus in an engineering degree in Spain, or equivalent in other countries). 

       

      GENERAL DESCRIPTION OF THE SUBJECT

      Symbolic computation provides algorithmic tools and methods that, in one hand are useful to support the learning and understanding of Mathematics and, on the other, contribute to the resolution of computational aspects arising in engineering.

      Although an important part is theoretical, the character of the course will be highly practical. This philosophy will be carried out by means of computer lab classes where the teaching of the symbolic concepts will be combined with the use of the symbolic software in an interactive mode.

       
      OBJECTIVES: KNOWLEDGE AND SKILLS

      The main goal of this course is to present efficient symbolic algorithms, fast in most cases or in the most relevant ones, to solve mathematic problems and their applications. This will allow the student to use these methods in some real life applications. For this purpose the student will become familiar with the existing symbolic computation software.

       

      TEACHING MATERIAL

      Class notes.

      Computer lab assignments.

       

      EVALUATION ACTIVITIES OR PRACTICAL TASKS

      Computer lab assignments and final report.

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    Syllabus

    • Chapter 1: SYMBOLIC COMPUTATION: INTRODUCTION AND MOTIVATION.

      Chapter 2: PROGRAMMING SYSTEMS IN COMPUTATIONAL MATHEMATICS.

      Chapter 3: INTRODUCTION TO THE COMPLEXITY OF ALGORITHMS.

      Chapter 4: SYMBOLIC ALGORITHMS IN LINEAR ALGEBRA: BAREISS METHOD.

      Chapter 5: SYMBOLIC RESOLUTION OF SYSTEM OF ALGEBRAIC EQUATIONS:

                   5.1 RESULTANTS.

                   5.2 GRÖBNER BASES.

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    Bibliography

    • Básic
      • B-B-001. Rincón F., García A, Martínez M.A. Cálculo Científico con Maple. Rama (1995).
      • B-B-002. Soto M.J., Vicente J.L. Algebra Lineal con Matlab y Maple. Prentice Hall (1995).
      • B-B-003.  Sendra J.R., Pérez Díaz S., Sendra J., Villarino C. (2009). Introducción a la computación simbólica y facilidades Maple. Addlink Media (2009). ISBN: 987-84-612-9191-5. http://www.addlink.es/go/IalCSyFM.htm

       

      Advanced
      • B-B-004. Davenport J.H., Siret Y., Tournier E., (1988): Computer Algebra: Systems and Algorithms for Algebraic Computation. Academic Press. London.
      • B-B-005. Von zur Gathen J., Gerhard J., (1999): Modern Computer Algebra. Cambridge University Press, New York.
      • B-B-005. Geddes K. O., Czapor S.R, Labahn G., (1992): Algorithms for Computer Algebra. Kluwer Academic Publishers.
      • B-B-005. Mishra B., (1993): Algorithmic Algebra. Springer Verlag.
      • B-B-005. Sendra J.R.,Winkler F., P´erez-Diaz S., (2007).Rational Algebraic Curves: A Computer Algebra Approach. Series: Algorithms and Computation in Mathematics, Vol. 22. Springer Verlag.
      • B-B-005. Winkler F. Polynomial Algorithms in Computer Algebra. Springer Verlag (1996).

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    Course material

    • Chapter 1: SYMBOLIC COMPUTATION: INTRODUCTION AND MOTIVATION.

      • CM-F-001. Introducción (PDF).

      Chapter 2: PROGRAMMING SYSTEMS IN COMPUTATIONAL MATHEMATICS.

      • CM-F-002. Programming systems (PDF)

      Chapter 3: INTRODUCTION TO THE COMPLEXITY OF ALGORITHMS.

      • CM-F-003. Complexity (PDF)

      Chapter 4: SYMBOLIC ALGORITHMS IN LINEAR ALGEBRA: BAREISS METHOD.

      • CM-F-004. Bareiss (PDF)

      Chapter 5: SYMBOLIC RESOLUTION OF SYSTEM OF ALGEBRAIC EQUATIONS:

      • 5.1 CM-F-005. Resultants (PDF)
      • 5.2 CM-F-006. Gröbner (PDF)

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    Labs

      • L-F-001. LAB # 1: OVERVIEW OF THE COMPUTATIONAL SYSTEM MAPLE (PDF). 
      • L-F-002. LAB # 2: PROGRAMMING SYSTEMS IN COMPUTATIONAL MATHEMATICS: MAPLE (PDF). 
      • L-F-003. LAB # 3: SYMBOLIC ALGORITHMS IN LINEAR ALGEBRA (PDF). 
      • L-F-004. LAB # 4: SYMBOLIC ALGORITHMS IN LINEAR ALGEBRA (PDF). 
      • L-F-005. LAB # 5: SOLVING SYSTEMS OF ALGEBRAIC EQUATIONS:RESULTANTS AND GRÖBNER BASIS (PDF). 

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    Authors of material