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Compulsory topics for NIE study program

topics are valid since SFE in June 2024

NIE-SPOL-1Group theory: Groupoids, semigroups, monoids, and groups. Subgroups, cyclic groups and their generators.NIE-MPI
NIE-SPOL-2Fields and rings: Basic definitions and properties. Finite fields. Rings of polynomials, irreducible polynomials.NIE-MPI
NIE-SPOL-3Multivariate functions: gradient, Hessian matrix, positive- and negative-(semi)definite and indefinite matrices. Extremal values and optimization (without constraints and with equality constraints).NIE-MPI
NIE-SPOL-4Integration of multivariate functions.NIE-MPI
NIE-SPOL-5Numerical mathematics: representation of numbers in a computer, errors due to floating number computations, problem conditioning and stability of numerical algorithms.NIE-MPI
NIE-SPOL-6Testing statistical hypotheses. T-tests, Goodness-of-fit tests, independence testing.NIE-VSM
NIE-SPOL-7Basics of information theory. Coding, entropy.NIE-VSM
NIE-SPOL-8Discrete-time Markov chains and their asymptotic properties.NIE-VSM
NIE-SPOL-9Continuous-time Markov chains and their relation to discrete-time chains and the Poisson process.NIE-VSM
NIE-SPOL-10Queuing theory. Asymptotic properties and relation to continuous-time Markov chains.NIE-VSM
NIE-SPOL-11The importance of the NP and NPH complexity classes for practical computations.NIE-KOP
NIE-SPOL-12Experimental evaluation of algorithms, especially randomized ones.NIE-KOP
NIE-SPOL-13Principles of local heuristics, the concept of local/global optima, techniques to avoid local optima.NIE-KOP
NIE-SPOL-14Principles of genetic algorithms, importance of selection pressure for their functionality. Controlling the selection pressure.NIE-KOP
NIE-SPOL-15Principles of simulated annealing, the importance of its parameters and systematic ways of their control.NIE-KOP
NIE-SPOL-16Performance evaluation of parallel algorithms, PRAM model, APRAM model, scalability.NIE-PDP
NIE-SPOL-17Shared memory programming, OpenMP programming model, data and task parallelism, thread synchronization, multi-threading algorithms (polynomial multiplication, matrix-matrix and matrix-vector multiplication, sorting).NIE-PDP
NIE-SPOL-18Distributed memory programming, MPI programming model (multi-threaded processes, communicators, 2-point blocking and non-blocking communication operations, collective operations), parallel multiplication of dense matrices, parallel power method.NIE-PDP
NIE-SPOL-19Direct orthogonal and hypercubic interconnection networks for parallel computers (definitions, properties, embeddings).NIE-PDP
NIE-SPOL-20Parallel reduction, parallel prefix sum, and segmented parallel prefix sum on PRAM, in orthogonal, hypercubic, and general topologies, applications.NIE-PDP

📄 The table is available also in CSV (semicolon-separated values). 🔙 History of changes is on GitLab.