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The website http://symbolicalgebra.etf.rs  is dedicated to the topics of Symbolic algebra that are taught on some courses of the Department of Applied Mathematics at the Faculty of Electrical Engineering , University of Belgrade.

The basic elements of Symbolic algebra are discussed in the course Practicum in computer tools in Mathematics - http://raum.etf.rs/ that is held in the fifth semester of the Computer Science and Informatics bachelor program and in the third semester of the other bachelor programs.

For the master students we will organize the course Symbolic algebra and for the phd students we will organize the course Selected Chapters from Symbolic algebra. The two previous courses are held in the spring semester

You can get information on the courses from the teachers Branko Malesevic and Ivana Jovovic.




Teachers




dr Branko Malesevic, associate professor, 
room 98, e-mail: malesevic@etf.rs

dr Ivana Jovovic, assistant professor,
room 25, e-mail: ivana@etf.rs












Master studies



The course Symbolic algebra is held in the spring semester of the master studies.
 
This courses requests that the students have passed and understood the courses Mathematics 1, Mathematics 2 and Discrete Mathematics that are held on the bachelor studies. Knowledge of computer tools that are explained at the course Practicum in computer tools in Mathematics (http://raum.etf.rs/) is also recommended. In this course students will be taught the basic algorithms that are used in Symbolic algebra. The aim of this course to get students to master the Groebner bases technique and its applications in various fields in Mathematics, artificial intelligence, computer graphics and various fields of technology.

Exam regulations. The final course grade will be computed by weighting the exams and project roughly as follows: midterm exam or homework, 30%; final exam, 70%. Final exam is taken at the end of the term, based on the software project and taking the written test, unrespectable of the software project. The presentation of the software project involves testing of theory which had been applied on the software project.
 
The course is based on some parts of the following books: 
 
1. J. L. Cohen: Computer Algebra and Symbolic Computation – Mathematical Methods, A.K. Peters, Ltd., 2003. (book "Computer Algebra and Symbolic Computation" available at http://books.google.com).
 
2. K. Geddes, S. Czapor, G. Labahn: Algorithms for Computer Algebra, Kluwer, Boston, MA, 1992. (book "Algorithms for Computer Algebra" је доступна прекo http://books.google.com). 
 
we recommend the following articles:
 
1. A. Heck: Bird's-eye view of Gröbner Bases, Nuclear Inst. and Methods in Physics Research A 389 (1997), 16-21, (extended version).
 
2. K. Forsman: Hitchhiker guide to Gröbner bases, Research Institute for Symbolic Computation, Linz, Tehnical Report 0374  (1992).
 
3. A. Dolzmann, T. Sturm, V. Weispfenning : A New Approach for Automatic Theorem Proving in Real Geometry, Journal of Automated Reasoning Volume 24 , Pages 357-380, Issue 3 (December 1998), pdf.
 
4. Marc R. C. van Dongen: Using Gröbner Basis Theory to Compute Constraint Networks in Globally Solved Form, In Proc. AICS'1999, pages 15-21, Cork, Ireland, pdf.
 
5. P. Grayson: Robotic Motion Planning, MIT Undergraduate Journal of Mathematics, Number 1, June 1999, PAGES 57-68, pdf. 








Phd studies



The course Selected chapters from Symbolic algebra is held in the spring semester of the phd studies (xls).
 

Basic course information

Course title

Selected chapters from Symbolic algebra
Type

Elective
Year and semester

First year of the bachelor program, spring semester
ESPB Credit

9

Professor

др Branko Malesevic
Aim of the course

The course has the aim to enable phd students for researching the field of Symbolic algebra with applications in the theory or algebraic differential equations using the Groebner bases technique. We observe a system of algebraic and algebraic-differential equations with applications in Computer graphics, theory of electrical circuits and other various fields of technology. A phd thesis on this topic, as a final goal, would be a result of the newest research in Computer applications of Symbolic algebra.  
Prerequisites

Mathematics 1, Mathematics 2 and Discrete Mathematics. We also recommend computer tools in Mathematics.
Course contents

Algebraic structures, rings and fields. Ring of a polynomial of one and more variables. Introduction to the theory of polynomial ideals. Monomial ideals. The definition of Groebner bases and a sytem of polynomial equations. Buchbergers algorithm and its improvements. The software realization of the Groebner bases in modern CAS packets. Theory of differential fields and differential Groebner bases. System of algebraic differential equations. Computer applications in various fields of technology.
Recommended literature

We recommend parts of the following references:
 
[1.] R. Karp: Great Algorithms, CS Cousre 294-5, spring 2006, Berkeley. 
(http://www.cs.berkeley.edu/~karp/greatalgo/)
 
[2.] J. Grabmeier, E. Kaltofen, V. Weispfenning (Eds.): Computer Algebra Handbook - Foundations, Applications, Systems, Springer 2003.
 
[3.] D.A. Cox, J.B. Little, D. O'Shea: Ideals, Varieties, and Algorithms - An Introduction to Computational Algebraic Geometry and Commutative Algebra, Springer 3rd ed. 2007.
 
[4.] R. Fröberg: An Introduction To Gröbner Bases, John Wiley & Sons Ltd 1998. 
 
[5.] J.F. Ritt: Differential algebra, Amer. Math. Soc. Publication 1950.
 
[6.] Ј.С. Cohen: Computer algebra and symbolic computation,  AK Peters, Ltd 1st edition, 2003.
 
[7.] K. Geddes, S. Czapor, G. Labahn: Algorithms for Computer Algebra, Kluwer, Boston, MA, 1992.
 
* parts of the books are available at http://books.google.com 
 
[8.] A. Heck: Bird's-eye view of Gröbner Bases, Nuclear Inst. and Methods in Physics Research A 389 (1997) 16 - 21.
 
[9.] A. Dolzmann, T. Sturm, V. Weispfenning: A New Approach for Automatic Theorem Proving in Real Geometry, Journal of Automated Reasoning Volume 24 , Pages 357-380, Issue 3 (1998).
 
[10.] B. Malesevic, M. Obradovic: An Application Of Groebner Bases To Planarity Of Intersection Of Surfaces, Filomat 23:2 (2009), pp. 43-55. (Thompson SCI Expanded list 2009.)
Methods of teaching

Lectures, with the help of the recent math software packets. Also, every student has a mentor, and consultations with the professors.
Testing and evaulation of knowledge

Grade from 5-10, that is obtained by grading students homework and tests that have a theoretical and practical part. 








Presentations




We mention a few presentations that are related to Symbolic algebra.
  • B. Maleševic, I. Jovović, B. Banjac:Visualization in teaching and learning mathematics in elementary, secondary and higher education,  pdf, Proceedings of International Conference on Engineering Graphics and Design, Timişoara, Romania ( 13 - 15 june 2013), pp. 37-40.


  • Branko Malesevic: A way to improve the use Computer Algebra Systems for integration, structured abstract - pdf, 6-th CAME (Computer Algebra in Mathematics Education) symposium; Improving tools, tasks and teaching in Computer Algebra Systems - based mathematics education, Belgrade 2009.


  • Branko Malesevic, Sinisa Jesic, Natasa Babacev, Ivana Jovovic:

    Some aspects of symbolic calculation in mathematics pdf
    200 years anniversary of the University of Belgrade, Matemathics today conference, Center Sava, 13.-14. October. 2008., Belgrade.


  • Milorad Pop-Tosic, Igor Skender: Maple, C and Assembly Language - Performance Comparison, pdf, Maple applications published on http://www.maplesoft.com/ 2008.


  • Branko Malesevic, Ivana Jovovic: A procedure for finding the k-th power of a matrix, pdf, Maple applications published on http://www.maplesoft.com/ 2007.




    • Graduate thesis




    Here are a few graduate thesis that are related to Symbolic algebra.
  • Александар Грујић Ђајић:  Numerical-symbolic integration with GeoGebra software (Applets).
     
  • Milan Campara: JAVA applet for calculating the Groebner bases of an ideal (Applet).
    The JAVA applet from Milan Campara graduate thesis was applied in the paper:  

    B. Malesevic. I. Jovovic, M. Campara: Groebner bases in JAVA with applications in computer graphics, pdf, Proceedings of the second International Conference for Geometry and Engineering Graphics “moNGeometrija2010”, Paper No. 29, pp. 1-10, Belgrade 24th - 27th of June 2010.










    • Master thesis




    Here are a few master thesis that are related to Symbolic algebra.
  • Vesna Danilovic: Java applet for use of Groebners basis on basic problems in theory of polynomial ideals (Applets). 

  • Banjac Bojan: Java applets for visualisation in theory of Groebners basis (Applets). 

    •



    Participation on conferences "Mathematic and application" Mathematical faculty in Belgrade