Lecturer chooses amongst the following topics:
Selected topics in analysis (oscillator and resonance, contiuous and discrete Fourier transform with applications, sygnal analysis, heat and wave equation, image compression),
Selected topics in number theory with applications (modular arithmetics, Euler totient, RSA, testing primality),
Selected topics in algebra (semigrupus and automata, finite fields),
Selected topics in discrete mathematics (extremal combinatorics, latin squares, algebraic combinatorics)
Other mathematical topics of lecturer’s choosing.
Topics in mathematics
2018/2019
Programme:
Interdisciplinary University Study Programme Computer Science and Mathematics
Year:
2 year
Semester:
second
Kind:
mandatory
ECTS:
5
Language:
slovenian
Course director:
Lecturer (contact person):
Hours per week – 2. semester:
Lectures
2
Seminar
0
Tutorial
2
Lab
0
Content (Syllabus outline)
Readings
E. Kreyszig: Advanced Engineering Mathematics, 9th ed., Weiley (2006)
S. Coutinho: The Mathematics of Ciphers: Number Theory and RSA Cryptography, A.K. Peters ltd.,1999
T. W. Judson: Abstract Algebra Theory and Applications (2013), http://abstract.ups.edu/
Objectives and competences
Students familiarise with the selected mathematical problems and learn how to idependently solve them.
Intended learning outcomes
Knowledge and understanding:
Students learns and understands the topic of the course.
Learning and teaching methods
Lecture and exercises.
Assessment
Written exam with oral defense
Lecturer's references
Sergio Cabello:
CABELLO, Sergio. Many distances in planar graphs. Algorithmica, ISSN 0178-4617, 2012, vol. 62, no. 1-2, str. 361-381. [COBISS-SI-ID 15702873]
CABELLO, Sergio. Finding shortest contractible and shortest separating cycles in embedded graphs. V: 20th Annual ACM-SIAM Symposium on Discrete Algorithms, January 4-6, New York. SODA 2009 : special issue, (ACM transactions on algorithms, ISSN 1549-6325, Vol. 6, iss. 2). New York: Association for Computing Machinery, 2010, article No.: 24 (18 str.). [COBISS-SI-ID 15572057]
CABELLO, Sergio, KNAUER, Christian. Algorithms for graphs of bounded treewidth via orthogonal range searching. Computational geometry, ISSN 0925-7721. [Print ed.], 2009, vol. 42, iss. 9, str. 815-824. [COBISS-SI-ID 15160409]
Primož Potočnik:
POTOČNIK, Primož. Tetravalent arc-transitive locally-Klein graphs with long consistent cycles. European journal of combinatorics, ISSN 0195-6698, 2014, vol. 36, str. 270-281. [COBISS-SI-ID 16862041]
POTOČNIK, Primož, SPIGA, Pablo, VERRET, Gabriel. Cubic vertex-transitive graphs on up to 1280 vertices. Journal of symbolic computation, ISSN 0747-7171, 2013, vol. 50, str. 465-477. [COBISS-SI-ID 16520537]
POTOČNIK, Primož. Edge-colourings of cubic graphs admitting a solvable vertex-transitive group of automorphisms. Journal of combinatorial theory. Series B, ISSN 0095-8956, 2004, vol. 91, no. 2, str. 289-300. [COBISS-SI-ID 13087321]
