Barbara Ikica

Barbara Ikica

PhD Mathematician trained in evolutionary game theory and complex networks with a passion for data science, machine learning, and problem solving.

Teaching activities

During my PhD studies, I worked as a teaching assistant, which included preparing and conducting weekly tutorials, developing exam questions, and grading exams.

At the Department of Mathematics, University of Ljubljana:

2018/2019 Discrete structures (Undergraduate Financial mathematics, Year 1)

Topics (official syllabus):

  • Logic: propositional and predicate calculus, rules of inference;
  • Relations and ordered sets;
  • Graph theory: homomorphisms, trees, bipartite graphs, Eulerian and Hamiltonian graphs, digraphs and tournaments, connectivity, planar graphs, vertex and edge colourings.

2017/2018 Discrete mathematics 1 (Undergraduate Financial mathematics, Year 1)

Topics (official syllabus):

  • Logic: propositional and predicate calculus, rules of inference;
  • Relations and ordered sets;
  • Graph theory: homomorphisms, trees, bipartite graphs, Eulerian and Hamiltonian graphs, digraphs and tournaments, connectivity, planar graphs, vertex and edge colourings.

2016/2017 Discrete mathematics 1 (Undergraduate Financial mathematics, Year 1)

Topics (official syllabus):

  • Logic: propositional and predicate calculus, rules of inference;
  • Relations and ordered sets;
  • Graph theory: homomorphisms, trees, bipartite graphs, Eulerian and Hamiltonian graphs, digraphs and tournaments, connectivity, planar graphs, vertex and edge colourings.

2015/2016 Combinatorics & Combinatorics 2 (Undergraduate Mathematics, Master's programme)

Topics (official syllabus):

  • Twelvefold way;
  • Generating functions: ordinary and exponential generating functions and their applications;
  • Formal power series: formal power series, formal Laurent series, Lagrange inversion;
  • Pólya theory;
  • Principle of inclusion and exclusion;
  • Incidence algebra: incidence algebra, Möbius function, Möbius inversion.

2015/2016 Discrete Mathematics 2 (Undergraduate Mathematics, Year 3)

Topics (official syllabus):

  • Partially ordered sets;
  • Dilworth's, Hall's, Sperner's theorem;
  • Design theory;
  • Pólya theory;
  • Graph theory: symmetry properties of graphs, cartesian product of graphs;
  • Ramsey theory.

At the Department of Computer and Information Science, University of Ljubljana:

2016/2017 Discrete structures (Undergraduate Computer and Information Science, Year 1)

Topics (official syllabus):

  • Induction principle;
  • Logic: propositional and predicate calculus, rules of inference;
  • Set theory and relations;
  • Number theory: extended Eucledian algorithm, linear Diophantine equations, modular arithmetic;
  • Permutations;
  • Graph theory: homomorphisms, trees, bipartite graphs, Eulerian and Hamiltonian graphs, connectivity, planar graphs, vertex colouring;
  • Logic: propositional and predicate calculus, rules of inference;
  • Linear recurrence relations.

As a Master's student, I assisted in marking weekly assignments at the Department of Physics, University of Ljubljana:

2011/2012 Mathematics III (Undergraduate Physics, Year 2)

Topics (official syllabus):

  • Gamma and Beta special functions;
  • Multiple integrals;
  • Inner product spaces;
  • Fourier series;
  • Differential equations: ordinary differential equations, systems of differential equations, existence theorems;
  • Line and surface integrals;
  • Calculus of variations.

2011/2012 Mathematics IV (Undergraduate Physics, Year 2)

Topics (official syllabus):

  • Partial differential equations;
  • Fourier transforms;
  • Holomorphic functions;
  • Differential operators;
  • Legendre polynomials.