Symbolic computation and dynamic geometry *

There are no prerequisites.

Symbolic computation as a tool for solving problems, verifying results, exploring special cases, forming hypotheses, and checking identities. Capabilities and limitations of symbolic computation systems. Representation and simplification of mathematical objects. Algebraic algorithms and their didactic value. Basic programming constructs. Generation of mathematical problems, including the possibility of individualizing them for specific students. Representation of knowledge in symbolic and graphical form, use of sound. Notebooks and preparation of instructional materials. Computer-supported self-assessment.

Dynamic geometry as a means for exploring properties and relationships, verifying conjectures, presenting solutions, and finding counterexamples. Dynamic constructions as a basis for tasks that promote visual reasoning and spatial imagination. Interactive projections, transformations, and constructions. Automatic determination of geometric loci. Experimental discovery of geometric conjectures. Use of symmetry. Connections with analytic geometry.

The role of technology in education, with emphasis on the possibilities, pitfalls, and limitations of using symbolic computation and dynamic geometry in teaching. Critical evaluation of accuracy, reliability, and impact on the understanding of mathematical content. Pedagogical appropriateness and integration into coherent instructional design.

J. Boehm, I. Forbes, G. Herweyers, R. Hugelshofer, G. Schomacker: The Case for CAS. T3 Europe, 2004, ISBN 3-934064-45-0, 134 str. Dostopno na http://www.t3ww.com/pdf/TheCaseforCAS.pdf.
priročniki za sisteme za dinamično geometrijo
priročniki za sisteme simbolno računanje

The student develops an understanding of the role of symbolic computation and dynamic geometry in mathematics education and the ability to use them meaningfully and with didactic justification. They become skilled in designing tasks and materials that leverage technological possibilities to deepen mathematical understanding, and they develop a sensitivity to the appropriateness and limitations of using such tools in different instructional contexts. Particular emphasis is placed on the critical evaluation of technology’s impact on the learning process.

The student is able to use symbolic computation systems and dynamic geometry tools to explore mathematical content, test conjectures, design tasks, and prepare instructional materials. They can evaluate the didactic value of these technologies and adapt their use to instructional goals. They understand the limitations and risks of inappropriate use and are able to critically assess the impact of technology on the understanding of mathematical concepts.

lectures, exercises, homework, consultations.

Homework assignments, project work, written and/or oral exam. The weighting of individual assessment methods is adjusted according to the students and the selected content.
grading: 5 (fail), 6-10 (pass) (according to the Statute of UL)

Andrej Bauer:
• LUKŠIČ, Primož, HORVAT, Boris, BAUER, Andrej, PISANSKI, Tomaž. Practical E-Learning for the Faculty of Mathematics and Physics at the University of Ljubljana. Interdisciplinary journal of knowledge & learning objects. 2007, vol. 3, str. 73-83. [COBISS-SI-ID 14269529]
• BAUER, Andrej. Five stages of accepting constructive mathematics. Bulletin (new series) of the American Mathematical Society. 2017, vol. 54, no. 3, str. 481-498. [COBISS-SI-ID 18066265]
• MASSRI, Besher M., PITA COSTA, João, GROBELNIK, Marko, BRANK, Janez, STOPAR, Luka, BAUER, Andrej. A global COVID-19 observatory, monitoring the pandemics through text mining and visualization. Informatica : an international journal of computing and informatics. [Tiskana izd.]. Mar. 2022, vol. 46, no. 1, str. 49-55. [COBISS-SI-ID 107602179]
• HASELWARTER, Philipp Georg, BAUER, Andrej. Finitary type theories with and without contexts. Journal of automated reasoning. Dec. 2023, vol. 67, iss. 4, article no. 36, 87 str. [COBISS-SI-ID 168229379]

Damjan Kobal:
• KOBAL, Damjan. Reciprocally related primes. Mathematical Gazette. Nov. 2024, vol. 108, iss. 573, str. 450-459. [COBISS-SI-ID 234185219]
• KOBAL, Damjan. Analogy and generalization as a driving force of learning mathematics - the case of a matrix analog of a zero of a polynomial. PRIMUS 2024, vol. , iss. , 13 str. [COBISS-SI-ID 227129603]
• KOBAL, Damjan. A mathematical promenade along parallel paths. Mathematical Gazette. Nov. 2023, vol. 107, iss. 570, str. 445-453 [COBISS-SI-ID 234174211]
• KOBAL, Damjan. Matrix zeros of polynomials. Mathematical Gazette. Mar. 2020, vol. 104, iss. 559, str. 27-35. [COBISS-SI-ID 234171395]

Matija Pretnar:
• LUKŠIČ, Žiga., PRETNAR, Matija. Local algebraic effect theories. Journal of Functional Programming, ISSN - 1469-7653, 2020, vol. 30, E13, 27 strani [COBISS-SI-ID – 53281795]
• FORSTER, Y., KAMMAR, O., LINDLEY, S., PRETNAR, M. (2019). On the expressive power of user-defined effects: Effect handlers, monadic reflection, delimited control. Journal of Functional Programming, ISSN - 1469-7653, 2019, vol. 29, E15, 43 strani [COBISS-SI-ID – 18852441]
• LOKAR, Matija, PRETNAR, Matija. A low overhead automated service for teaching programming. Koli Calling '15: Proceedings of the 15th Koli Calling Conference on Computing Education Research, 2015, 132–136 [COBISS-SI-ID – 17536089]