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Compulsory Topics

topics are valid since SFE in June 2021

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

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