. "Applied Mathematics"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . "Mathematical analysis"@en . . "5" . "Understanding the key topics and problems of Mathematical Analysis. Also it is necessary to develop many skills between abstract entities according to certain rules and apply it into Geodesy. Demonstrate competences in theoretical principles, procedures of computing and visualising the surveying data.\nUnderstand mathematical methods and physical laws applied in geodesy and geoinformatics.\nApply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics.\nExercise appropriate judgements on the basis of performed calculation processing and interpretation of data obtained by means of surveying and its results.\nTake responsibility for continuing academic development in the field of geodesy and geoinformatics, or related disciplines,and for the development of interest in lifelong learning and further professional education. \n -Define and implement the tasks terms of mathematical logic, sets, sets of numbers and mathematical induction\n- Define, analyze and relate the concepts and properties of real functions of a real variable, as well as terms related to a sequences (limit of a sequence, limit of a function) \n - Define and apply the concepts tasks derivatives, indefinite and definite integrals\n- Define and apply the concepts tasks series of numbers, functional series and power series, as a Taylor series expansion and Mac Lauren series\n- Define, analyze and apply the tasks terms of functions of several variables, as well as Taylor and Maclaurin series for two variables, and to determine the extreme values of functions of two variables\n- Define the term and solve differential equations method of separation of variables" . . "Presential"@en . "TRUE" . . "Mathematics on computers"@en . . "1" . "The objectives of this course are\n- acquire the skills of independent use of mathematical software system (e.g. free open source Sage or similar) for tasks that require symbolic and/or numerical computation\n- solving of problems in the computer laboratory to support the teaching of mathematical courses (Analytic geometry and linear algebra and Mathematical Analysis). \nAt the program level, the course contributes to the following learning outcomes:\n- To use information technology in solving geodetic and geoinformation tasks.\n-To make conclusions on the basis of performed computational processing and interpretation of surveying data and obtained results.\n-To understand the mathematical methods and physical laws applied in geodesy and geoinformatics.\n-To apply the knowledge in mathematics and physics for the purpose of recognizing, formulating and solving problems in the field of geodesy and geoinformatics. \n -Use of a mathematical software system for solving equations and inequalities.\n-Use of a mathematical software system for computing with vectors.\n-Use of a mathematical software system for computing with matrices \n -Use of a mathematical software system for visualizing linear operator in plane and space.\n-Use of a mathematical software system for determining the eigenvalues and eigenvectors.\n-Use of a mathematical software system for determining the limits.\n-Use of a mathematical software system for symbolic and numerical deriving and integrating.\n-Use of a mathematical software system for testing properties and graphing functions of one two variables.\n-Using a mathematical programming system for drawing 2D and 3D graphs." . . "Presential"@en . "FALSE" . . "Vector analysis"@en . . "3" . "Understanding the key topics and problems of Vector Analysis. Also it is necessary to develop many skills between abstract entities according to certain rules and apply it into Geodesy. \n-Demonstrate competences in theoretical principles, procedures of computing and visualising the surveying data.\n-Understand mathematical methods and physical laws applied in geodesy and geoinformatics.\n-Apply knowledge of mathematics and physics for the purpose of recognizing, formulating and solving of problems in the field of geodesy and geoinformatics.\n-Exercise appropriate judgements on the basis of performed calculation processing and interpretation of data obtained by means of surveying and its results.\n-Take responsibility for continuing academic development in the field of geodesy and geoinformatics, or related disciplines,\nand for the development of interest in lifelong learning and further professional education. \n1) Define and implement the tasks of the term of the vector functions of one scalar variable\n2) Define and apply the concepts of tasks: line integral of the first and the second kind and their properties; determine the relationship between line integral of the first and the second kind, and define and apply Green formula\n3) Define and apply the concepts of tasks: double and triple integrals and their applications, with the introduction of the Jacobian for cylindrical and spherical coordinates \n 4) Define and apply the concepts of tasks: surface integrals and vector surface integrals. Describe the flux of a vector field through a surface\n5) Define and apply the concepts of tasks: scalar and vector fields and directional derivatives\n6) Telling the Green-Gauss-Ostrogradski theorem and Stokes' theorem and applying to the tasks" . . "Presential"@en . "TRUE" . . "Discrete mathematics"@en . . "5" . "Renew and expand the knowledge of basic mathematical concepts and methods used in computer engineering / informatics science.\nDevelop a sense of different degrees of mathematical rigor and formalism and learn to use them in problem solving tasks.\nDistinguish parts of mathematics that studies finite systems, i.e. deals with objects that can assume only a specific value.\nArgue the reasons why the characteristics of the computer are described within the framework of finite mathematical systems.\nBecome familiar with the language of computer science. recognize and apply basic types of mathematical reasoning;\ndefine and classify binary relations on sets knowing their properties and typical examples;\npronounce and apply the properties of relations in systems for data processing and for the development of functional algorithms;\n adopt basic combinatorial concepts and counting rules and recognize them when counting the elements of a finite set;\ndetermine the generating function of the starting sequence and identify and solve simple recurrence relations;\napply the theory of Boolean algebra to design logic circuits and networks; distinguish the basic concepts of graph theory;\nCompare and model certain combinatorial problems using graph theory (shortest path algorithm, nearest neighbor algorithm,…)." . . "Presential"@en . "FALSE" . . "Probability and statistics for data science"@en . . "8" . "This is a theoretical course covering fundamental \r\ntopics of probability and statistics in the context of \r\ndata science with its inherent challenges. This course \r\nwill start with a review of fundamental probability, \r\ncovering topics like random variables, their \r\ndistribution functions, expected values, conditioning \r\non certain events and independence. The students \r\nwill be acquainted with certain families of probability \r\ndistributions and then will learn how to estimate \r\ncertain quantities of interest from observations. \r\nA range of properties of estimators will be studied, \r\nincluding sufficiency, unbiasedness and consistency, \r\nwhich enable the evaluation of their quality with an \r\nemphasis in the framework of big datasets. \r\nThe students will also learn how to introduce \r\ndifferent types of hypotheses, how to construct tests \r\nfor their hypotheses, as well as how to compare \r\nbetween tests and how to construct confidence \r\nintervals for their estimators.\n\nOutcome: Not Provided" . . "Presential"@en . "TRUE" . . "Mathematical methods for signal processing"@en . . "4" . "The main topics concern: general theory of Fourier analysis of analog signals (Fourier series, \r\nFourier transform); convolution; discrete sequences; discrete Fourier transform; introduction to \r\nsignal processing; linear time-invariant systems; discrete convolution operators; difference \r\nequations; signal analysis and processing with use of cross-correlation; circular convolution \r\ntheorem and cross-correlation theorem; numerical methods in signal studying and modelling \r\n(interpolation, least-squares method, numerical integration).\n\nOutcome: Not Provided" . . "Presential"@en . "FALSE" . . "Applied mathematical methods and data analysis"@en . . "6" . "The course lectures cover the theoretical basis of the following subject areas:\n• Essential linear algebra (matrices, eigenvalues, linear systems of equations)\n• Essential calculus (differentiation, integration, Taylor series)\n• Essential statistics (error analysis, correlation, significance)\n• Essential optimization (linear and nonlinear regression, parameter estimation, \ngradient methods)\n• Essential differential equations (ordinary and partial differential equations, phase \ndiagrams)\nIn the example classes students will learn how to apply this knowledge both analytically \nand numerically. In order to facilitate the latter, students will learn the basics of the Python programming language and how to use Python to solve real-world problems \nfrom the course’s topic areas\n\nOutcome:\nBasic knowledge in mathematical methods for data analysis and their application using \nthe Python programming language." . . "Presential"@en . "TRUE" . . "Control theory 1"@en . . "6" . "• Definition and features of state variables\r\n• State space description of linear systems\r\n• Normal forms\r\n• Coordinate transformation\r\n• General solution of a linear state space equation\r\n• Lyapunov stability\r\n• Controllability and observability\r\n• Concept of state space control\r\n• Steady-state accuracy of state space controllers\r\n• Observer\r\n• Controller design by pole placement\r\n• Riccati controller design\r\n• Falb-Wolovitch controller design\n\nOutcome:\n• Understanding and handling of state space methodology\r\n• Design of state space controllers with different methods\r\n• Observer design" . . "Presential"@en . "TRUE" . . "Numerical methods"@en . . "6" . "Course aim\r\nThe goal is to introduce the basic numerical methods and to learn how to apply these methods for solution of specific problems.\r\n\r\nDescription\r\nIn this course students learn the concepts of computer arithmetic, stability and computational complexity of numerical algorithms. Students learn numerical methods for solving nonlinear equations and systems of equations, direct and iterative methods for solving linear systems of equations, finite difference method for solving differential equations, interpolation and approximation methods, and numerical integration methods.\r\n\nOutcome: Not Provided" . . "Hybrid"@en . "TRUE" . . "Numerical methods for the environment"@en . . "9" . "The course introduces the students to the analysis, implementation and application of numerical methods for the solution of differential equations, ordinary ones (ODE) and partial differential equations (PDE) with applications to mechanics. Different approaches are presented (finite difference methods, finite volume methods, semi-implicit methods), with applications to hyperbolic equations (shallow water equations) linear parabolic (heat equation) and elliptic (Poisson) equations, and incompressible Navier-Stokes equations. An important part of the course is dedicated to a computer laboratory in which all methods are implemented in a computer program; some numerical methods will be subsequently used in the course Hydrodynamics." . . "Presential"@en . "TRUE" . . "Analytical and numerical methods"@en . . "5" . "The course aims to:\n\nProvide a basic introduction to calculus and basic statistical methods\nProvide an introduction to mathematical and computational methods for modelling applications\nIntroduce general conceptual frameworks for the problems and issues of developing forward and inverse models\nProvide practical analytical and numerical examples for both forward and inverse modelling, particularly linear v non-linear, approaches to solving and generic aspects of implementation\nProvide example applications of the techniques covered, including use of Jupyter Python notebooks\nCover generic issues arising in application of analytical and numerical approaches including the discretisation, detail vs computation time, stochastic processes etc.\nTo provide exposure to numerical tools that are used in a wide range of modelling applications, including an introduction to Bayes Theorem and Monte Carlo methods among others.\nThe module will provide an introduction to a range of fundamental concepts and principles for handling and manipulating data. The first half of the module (taught with CEGE) provides a basic introduction to stats and linear algebra, and important basic concepts; the second half covers slightly more advanced applications of methods and tools for data analysis. The module will cover:\n\nElementary differential and integral calculus and its applications (equations of motion, areas and volumes etc),\nLinear algebra and matrix methods, including computational issues (decomposition for eg) and generalised linear models\nDifferential equations and applications\nOverview of statistical methods including an intro to Bayes Theorem\nNumerical methods, model fitting, numerical optimization Monte Carlo and Metropolis-Hastings\nThe main sessions include:\n\nIntroduction to calculus methods\nIntroduction to linear algebra, matrices\nStatistics and further statistics\nLeast Squares and further least squares\nDifferential equations\nIntroduction to Bayes Theorem\nModel selection\nLinear & non-linear model inversion\nMonte Carlo methods and related numerical tools," . . "Presential"@en . "TRUE" . . "Differential equations, probabilities and statistics"@en . . "8" . "no data" . . "Presential"@en . "TRUE" . . "Mathematical methods of physics a"@en . . "5" . "LEARNING OUTCOMES\nAfter the course, the student will be familiar with basic concepts of group theory, group representation theory, and topology. The student can identify different common groups, study if their representations are reducible, irreducible or not, and knows why the theory of groups and their unitary representations is important in quantum physics of systems with various symmetries. The student also understands distinctions between nonhomeomorphic topological spaces and understands the use of topological invariants (such as homotopy groups) in their classification.\n\nCONTENT\nGroup theory: finite groups, continous groups, conjugacy classes, cosets, quotient groups\n\nRepresentation theory of groups: complex vector spaces and representations, symmetry tranformations in quantum mechanics, reducible and irreducible representations, characters\n\nTopology: topological spaces, topological invariants, homotopy, homotopy groups" . . "Presential"@en . "FALSE" . . "Mathematical methods of physics b"@en . . "5" . "LEARNING OUTCOMES\nAfter the course, the student will be familiar with basic concepts of calculus on differentiable manifolds and Riemannian geometry, which are mathematical tools used in physics e.g. in the contexts of general relativity and gauge field theories. The student will also be familiar with basics of Lie algebra representation theory, which is used e.g. in particle physics and condensed matter theory. The student can work with differential forms, express metrics in different coordinates and compute metric tensors of general relativity. He also understands basic representations of Lie algebras used e.g. in the theory of strong interactions.\n\nCONTENT\nDifferentiable manifolds and calculus on manifolds: differentiable manifolds, manifolds with boundary, differentiable maps, vector fields, 1-form fields, tensor fields, differentiable map and pullback, flow generated by a vector field, Lie derivative, differential forms, Stokes' theorem\n\nRiemannian geometry: metric tensor, induced metric, connections, parallel transport, geodesics, curvature and torsion, covariant derivative, isometries, Killing vector fields\n\nSemisimple Lie algebras and representation theory: SU(2), roots and weights, SU(3), introduction to their most common unitary irreducible representations" . . "Presential"@en . "FALSE" . . "Numerical methods in scientific computing"@en . . "10" . "LEARNING OUTCOMES\nYou will learn to know the most common numerical methods and algorithms\nYou will understand the strenghts and weaknesses of these algorithms\nYou will be able to apply these algorithms using\nself-made programs\nnumerical libraries\nnumerical programs.\nCONTENT\nTools, computing environment in Kumpula, visualization\nBasics of numerics: floating point numbers, error sources\nLinear algebra: equations, decompositions, eigenvalue problems\nNonlinear equations: bisection, secant, Newton\nInterpolation: polynomes, splines, Bezier curves\nNumerical integration: trapeziodal, Romberg, Gauss\nFunction minimization: Newton, conjugate gradient, stochastic methods\nGeneration of random numbers: linear congruential, shift register, non-uniform random numbers\nStatistical description of data: probability distributions, comparison of data sets\nModeling of data: linear and nonlinear fitting\nFourier and wavelet transformations: fast Fourier transform, discreet wavelet transform, applications\nDifferential equations: ordinary and partial differential equations" . . "Presential"@en . "FALSE" . . "Mathematics for computer science"@en . . "6" . "Description:\nBrief description of the course:\n1. Language of mathematics and Set theory: Boolean algebra: logical operators, truth tables, logic laws. Set theory: sets, set operations. number sets\n2. Functions: mappings between sets, injection, surjection, bijection, computability and big O notation.\n3. Probability theory: Elementary counting principles, permutations, combinations, events and probabilities, random variables and distributions.\n4. Number theory: Divisibility, GCD, Euclidean algorithm, Bezout identity, prime numbers, congruences, Euler φ- function,\nChinese Remainder Theorem\n5. Group theory: Groups basic definitions and properties, types of groups (cyclic, dihedral, symmetric), subgroups, homomorphism, isomorphism, Lagrange theorem, quotient groups, product groups.\n6. Ring theory: Rings basic definitions and properties, polynomial rings, ring homomorphism, ideals, quotient rings, fields\nLearning outcomes:\nAfter completing this course, the student:\n- understands mathematical texts at undergraduate level;\n- uses standard mathematical notation and terminology in academical writing;\n- writew and evaluatew correct, clear and precise mathematical proofs in an applicable level of detail;\n- recalls definitions and theorems in mathematical areas, which are covered in the course." . . "Presential"@en . "FALSE" . . "Discrete mathematics"@en . . "6" . "Description:\n Sublinear time algorithms, w/ proofs,\nLower bounds for sublinear time algorithms,\nCommunication Complexity\nData stream (sublinear space) algorithms. Data stream algorithms w/ proofs\nLower bounds\nDiscrete probability (needed for the proofs)\nInformation theory\nQuantum computing basics\n\nLearning outcomes:\nThe student knows the foundations of discrete mathematics and is able to use it in the context of cryptography research." . . "Presential"@en . "FALSE" . . "Numerical modeling fundamentals"@en . . "5" . "LEARNING OUTCOMES OF THE COURSE UNIT\n\nThe graduate is able to:\n- understand principles of selected optimization techniques and choose appropriate method for selected problem, formulate the fitness functon,\n- understand principles of basic numerical methods,\n- use these methods for simulation and design of various structures.\n.\nCOURSE CURRICULUM\n\n1. Optimalization - basics, optimality conditions, aggregation methods, gradient methods\n2. Optimalization - global single-objective methods\n3. Optimalization - global multi-objective methods\n4. Numerical differentiation and integration\n5. Finite elements method\n6. Finite differences method\n7. Simulation of electromagnetic phenomena\n8. Microwave lines and antennas\n9. Simulation of mechanic phenomena\n10. Elasticity, strength, stress\n11. Simulation of thermal phenomena\n12. Multi-physics modeling - MEMS\n13. Multi-physics modeling - thermal effects of EM fields\nAIMS\n\nThe subject aims to learn students about tools of numerical analysis for modeling and design of microwave circuits and mechanical structures. Obtained knowledge will be applied to design these structures with the help of CAD modeling." . . "Presential"@en . "FALSE" . . "Selected lectures on mathematics"@en . . "5" . "LEARNING OUTCOMES OF THE COURSE UNIT\n\nAfter completing the course, students should be able to independently solve problems associated with mathematical modeling, verification and testing of designs for space applications.\n\nCOURSE CURRICULUM\n\nLectures:\n1. Vector algebra and analysis\n2. Differential geometry\n3. Differential calculus of a function of two or more variables (including extrema)\n4. Integral calculus of functions of two and more variables (double, triple integrals; use in geometry and physics)\n5. Transformation: Z-transformation, KLT, SVD, FFT.\n6. Relationship of impulse char, and LTI transfer functions. FIR filters\n7. Basics of probability and statistics. Random variable. Moment characteristics.\n8. Theory of estimation in general: BLUE, ML, LS. Estimation quality criteria.\n9. Theory of estimates and testing (point and interval estimation, testing of moment characteristics).\n10. Reliability of systems.\n11. Random processes. Stationary, ergodic.\n12. Spectral analysis of stochastic signals. Autocorrelation.\n13. Detection of signals hidden in noise.\n\nExercises\n1. Vector algebra and analysis\n2. Examples from the field of differential geometry\n3. Differential calculus of a function of two or more variables (including extrema)\n4. Integral number of functions of two or more variables\n5. Modeling and use of KLT, SVD, FFT transformations in Matlab.\n6. Design of filters and modeling of the relationship between impulse response and transfer function of the system.\n7. Test or individual work\n8. Modeling of a random variable and calculation of their characteristics.\n9. Work with estimates and measurement of their quality.\n10. Hypothesis testing: simulation, numerical analysis and testing in Matlab.\n11. Simulation of random processes.\n12. Spectral analysis of stochastic signals. Autocorrelation.\n13. Detection and testing of signals hidden in noise. ROC curve.\nAIMS\n\nThe aim of the course is to present to students a specialized mathematical-statistical apparatus, which is important for understanding and interconnecting the principles of electrical and mechanical systems and practical verification of acquired skills." . . "Presential"@en . "TRUE" . . "Calculus I/mathematical analysis 1"@en . . "12" . "Knowledge\nThe student who wish to pass the exam must have developed a solid control of logic and mathematical reasoning, and must have deeply understood what are a mathematical statement and a mathematical proof. The specific contents of the course are the notion of limit (of a sequence or of a series), the fundamental result of differential calculus in one variable, as well as some elements of the theory of ordinary differential equations. The student must be able to discuss all the proofs explained during the lessons." . . "Presential"@en . "TRUE" . . "Dynamics of solids and fluids"@en . . "5,5" . "This course provides students with an understanding of basic concepts and mathematical solutions of fluid and solid dynamics\nwith applications to atmosphere, oceans and the Solid Earth, preparing them for in-depth study of processes in specific Earth\ncomponents. Students will learn how to derive the governing equations of fluid dynamics and solid dynamics, to explain how\nthese are applied and simplified for flow and solid dynamics in the atmosphere, ocean and the solid Earth. Students will also\ncarry out exercises as group assignments using python notebooks and model codes that exemplify simple models built on these\ngoverning equations. After completing this module, students will be able to:\nDistinguish flows and deformation in different parts of the Earth system (atmosphere, ocean and solid Earth). \nPerform dimensional analysis of flows in different media and explain appropriate approximations to the equation of motion.\nCharacterise and derive the physical equations that underlie advection, diffusion, convection, conduction, elasticity, brittle and\nductile deformation, and consider their application in models of Earth System components. \nApply the physical equations to examples of flow and deformation in different media using python notebooks. \nAnalyse and compare the behaviour of flow and deformation phenomena in the Earth System using simple python models." . . "Presential"@en . "TRUE" . . "Numerical methods for engineering"@en . . "6" . "Learning outcomes\n\n\nThe course aims at making the students familiar with the principal calculation methods concerning applied mathematics: equations resolution; linear algebra problems; systems solutions; calculation of eigenvalues and eigenvectors, functions approximation and interpolation, numerical integration." . . "Presential"@en . "FALSE" . . "Higher mathematics"@en . . "6" . "Obligatory base module 1 \nLearning outcomes\nAfter passing this cource the student should come to:\n* identify, transform and use elementary functions, especially in their common applications;\n* understand, compute and estimate derivatives algebraically, graphically, numerically, and verbally;\n* understand and use basic methods of integral calculus, including analytical, graphical and numerical techniques of integration;\n* apply techniques of slicing and summing to a variety of physical problems in geometry, physics and economics;\n* use common functions like polynomials and sinusoidal functions as building blocks in approximations of more complicated functions;\n* understand and use simple differential equations to model and analyze problems in biology, geology and other scientific fields;\n* distinguish between convergent and divergent series and integrals;\n* understand and appreciate the interplay between discrete and continuous variables;\n* understand of the concepts and methods of linear algebra;\n* use matrix algebra fluently, including the ability to put systems of linear equation in matrix format and solve them using matrix multiplication and the matrix inverse.\nMore general goals include developing students' abilities to\n* improve logical thinking and think critically;\n* apply knowledge of mathematics to identify, formulate, and solve problems, particularly problems related to the environment;\n* work effectively in heterogeneous teams;\n* communicate effectively, especially by writing precisely about technical things;\n* use technological tools such as graphing calculators and equation editors in an appropriate manner; and\n* engage in life-long learning.\nBrief description of content\nIn this course, we will engage in the full mathematics process, which includes searching for patterns, order and reason; creating models of real world situations to clarify and predict better what happens around us; understanding and explaining ideas clearly; and applying the mathematics we know to solve unfamiliar problems. Some classical mathematical concepts and methods from different branches of advanced mathematics (mathematical analysis, linear algebra and analytic geometry) are studied. Main topics include functions, limits, differentiation, sequences, integration, differential equations, matrix algebra and determinants." . . "Presential"@en . "TRUE" . . "advanced mathematical methods"@en . . "6" . "I. Tensor calculus 1) tensor algebra, 2) tensor analysis: covariant derivative, parallel transport, 3) Lie derivative, Killing vectors, differential forms II. Complex analysis 1) Cauchy-Riemann conditions, 2) Cauchy theorem, 3) residua and its applications, 4) contour integration, 5) Green functions. III. Elements of group theory 1) introduction to discrete and continuous group, 2) basics of representation theory, Schur lemmae, 3) elements of Lie group and Lie algebra theory." . . "Presential"@en . "TRUE" . . "Mathematics"@en . . "6" . "1. Apply information and communication skills in representing and solving maximisation problems in a relevant financial context. 2. Demonstrate information and communication processing skills to use statistical and probability tools to solve complex realistic scenarios. 3. Demonstrate evaluation skills in solving statistical and probability scenarios applied to sampling, estimation theories and significance testing. 4. Demonstrate enquiry and evaluation skills in solving problems in familiar game theory context" . . "Presential"@en . "TRUE" . . "Vector integral &"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "Mathematics"@en . . "5" . "Linear and euclidean spaces: linear independence,\nbasis, linear mappings, nullspace and range, matrix\nrepresentation, transitional matrix, rank,\neigenvalues and eigenvectors, scalarproduct, norm,\northogonality, Gram-Schmidt orthogonalisation,\northogonal projection (vector of best\napproximation), Fourier coefficients, least squares method, overdetermined systems, normal system,\nregression line.\nNumerical linear algebra: numerical computation\nand errors, linear systems, matrix decompositions:\nLU, QR, SVD.\nGraph theory: matrix presentation, isomorphism,\npath, cycle, walk, spanning tree, Hamiltonian and\nEulerian cycle, the shortest path problem, weighted\ngraph, algorithms of Kruskal and Dijkstra.\nOrdinary differential equations: linear DE of order n,\nLDE with constant coefficients, linear systems of DE\nof first order, matrix solution of initial problem,\nboundary value problem.\nBasics on partial differential equations: equations of\nmathematical physics, vibrating string, d'Alembert\nsolutions. learning outcomes: basic knowledge and understanding of linear\nalgebra and mathematical analysis\n• mastering of basic computational skills\n• the achieved mathematical knowledge is used\nby the engineering courses\n• mathematics is essential for technical studies\n• ability of abstract formulation of practical\nproblems\n• capability of critical judgement of data and\nobtained numerical results\n• capability of systematical, clear and precise\nformulation of problems\n• ability of reasoning from general to special and\nvice versa\n• skills in using literatur" . . "Presential"@en . "TRUE" . . "Theory of stochastic processes"@en . . "10" . "no data" . . "Presential"@en . "FALSE" . . "Mathematics 1"@en . . "6" . "no data" . . "Presential"@en . "TRUE" . . "Mathematics 2"@en . . "6" . "The course aims to provide students with knowledge and under-\nstanding of basic concepts and theorems of mathematics, particu-\nlarly mathematical analysis, and to master elementary calculus\nskills with a range of knowledge including: real numbers, number\nsequences and number series; differential and integral calculus of\nfunctions of one real variable and ordinary differential equations.." . . "Presential"@en . "TRUE" . . "Mathematics 3"@en . . "4" . "The course aims to provide students with knowledge and under-\nstanding of basic concepts and theorems of mathematics, particu-\nlarly mathematical analysis, and to master elementary calculus\nskills including: differential and integral calculus of real functions of\nmany variables; vector analysis; calculus of probability and ele-\nments of mathematical statistics." . . "Presential"@en . "TRUE" . . "Mathematics 4"@en . . "5" . "Probability calculus. Basic probability distributions and their appli-\ncations. Mathematical statistics and its application in experimental\nresearch. Using numerical methods in probability calculus and sta-\ntistics." . . "Presential"@en . "TRUE" . . "Control theory"@en . . "5" . "Basic concepts of control theory. Time and frequency characteris-\ntics of basic elements. Control system structure. Basic quality indi-\ncators used to evaluate control systems. Stability of linear systems.\nOverview of basic control laws. Design of controllers. Theory of\nstate estimators and observers. Control from state vector using" . . "Presential"@en . "FALSE" . . "Machine learning, application of mathematics"@en . . "no data" . "N.A." . . "Presential"@en . "TRUE" . . "Vector-based gis (qgis)"@en . . "no data" . "no data" . . "Presential"@en . "TRUE" . . "Vector-based gis (arcgis)"@en . . "no data" . "no data" . . "Presential"@en . "TRUE" . . "Topics in applied mathematics"@en . . "5" . "no data" . . "Presential"@en . "FALSE" . . "Engineering mathematics and programming (core)"@en . . "no data" . "This module aims to develop the ability to understand and apply fundamental methods of engineering mathematics. It introduces the use of programming in engineering to improve the skill to represent and solve problems algorithmically." . . "Presential"@en . "TRUE" . . "Engineering mathematics and programming"@en . . "no data" . "N.A." . . "Presential"@en . "TRUE" . . "Mathematical methods in environmental processes modelling"@en . . "4" . "The study course provides basic knowledge and acquired skills in the use of mathematical techniques in the modelling of processes in the environment. Theoretical knowledge on model development principles, stages, methods for collecting and processing input data is supported by practical work, problem management and self-research. Course implementation in practical handling and clarifying of work or environmental problems. The aim of the course is to provide basic knowledge and skills in the use of mathematical techniques in the modelling of processes in the environment. Course Tasks: 1. to learn the basic principles for the development of models (typology, development phases), 2. to learn the methods of collecting and processing entry data; 3. to provide knowledge and practical skills in the practice of using mathematical models. 4. give students an interest in using modeling techniques to address environmental problems. The course includes lectures, seminars and practical works. Languages of instruction are Latvian and English.\nResults Knowledge 1. Understands the principles of empirical and numerical methods. 2. Distinguishing the methods for extracting and processing input data, classifying, ranking and prioritizing raw data. Skills: 3. In particular, are able to define modeling objectives, impacting processes and variables. 4. Compare and critically assess modelling results. Competence: 5. Interpret the modelling results and take decisions on the choice of the most appropriate empirical method or mathematical approximation." . . "Presential"@en . "FALSE" . . "Mathematical methods in physics"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "Numerical methods"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "Discrete mathematics"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "applied mathematics for earth sciences"@en . . "no data" . "no data" . . "no data"@en . "TRUE" . . "Numerical modeling of space structures"@en . . "6" . "Orbital observation. Visual and radiofrequency observables, and relevant instrumentation required. Reference frames \nand time scale. A reminder of the orbital dynamics. Orbital parameters and their relation with kinematic parameters. \nClassical problems in orbit determination (Gibbs, Laplace, Lambert). Orbit representation: Two-Line Elements (TLE). \nOrbit determination in LEO and GEO. Ground-based and on-board orbit determination. GNSS-based and image-based \norbit determination. Applications to lunar missions. Tracking of deep-space probes. Surveillance networks." . . "Presential"@en . "FALSE" . . "Mathematical methods of physics II"@en . . "9" . "Complements of complex variable function theory. Logarithmic indicator and Lagrange's formula. Mittag-Leffler and Sommerfeld-Watson expansions. Infinite products and expansions by Weierstrass. Asymptotic developments. Laplace method and saddle point methods. Ordinary differential equations. Green's functions. Sturm-Liouville problems. Series and transformed Fourier and Laplace. Special functions. Gamma, Beta and Zeta functions. Hypergeometric functions. Bessel functions. Notes on elliptic functions. Partial differential equations. Well-posed problems and fundamental solutions. Solution of boundary problems. Distributions and their applications to Differential Equations. Linear operators on Hilbert spaces. Riesz's theorem. Spectral theory. Punctual, residual, continuous spectra. Examples of operators in elle2, differential operators, and integral operators. Null modes and the alternative theorem." . . "Presential"@en . "TRUE" . . "Mathematics"@en . . "3" . "Basic terms and theorems of mathematics, mathemati\u0002cal analysis, ordinary differential equations, integral calculus of functions of several real variables, elements of theory of probability." . . "Presential"@en . "TRUE" . . "Fundamentals of mathematics (10 crédits ects)"@en . . "10" . "MA414E - Theory of distributions for signal processing\nMA405E - Probability/Statistics\nMA406E - Stochastic Processes\nIP405E - Programming and C language" . . "Presential"@en . "TRUE" . . "Numerical modeling"@en . . "3" . "Numerical modeling in Python and Fortran" . . "Presential"@en . "TRUE" . . "Fundamentals of mathematics"@en . . "no data" . "no data" . . "Presential"@en . "FALSE" . . "Mathematical methods"@en . . "6" . "Not found" . . "Presential"@en . "TRUE" . . "Engineering mathematics 1"@en . . "10.00" . "Unit Information\nDescription There are five main sections: Algebra (vectors, complex numbers, matrices as transformations, solving equations using matrices, eigenvalues and eigenvectors); Analysis (Sequences, series, functions, curve sketching, introduction to fourier series, introduction to numerical analysis); Calculus (differentiation and integration of functions of one variable, taylor series, numerical root finding, introduction to partial differentiation); Differential Equations (concepts, separation of variables, linear first and second-order equations, systems, numerical solutions); and Probability (basic concepts, events, random variables, empirical discrete and continuous distributions).\n\nAims The principal aim of this faculty-wide unit is to bring students entering the Faculty of Engineering up to a common standard in mathematics. The unit contains the well recognised elements of classical engineering mathematics which universally underpin the formation of the professional engineer.\n\nYour learning on this unit\nTo gain familiarity with the basic mathematics needed for engineering degree programmes.\nTo be able to manipulate and solve mathematical problems involving algebraic and analytic concepts such as matrices, vectors, complex numbers, differentials, integrals, and sequences.\nTo be able to link such algebraic and analytical concepts to geometric concepts in the form of graphs.\nTo gain a basic understanding of how data is represented and manipulated in computations deterministically and using the laws of probability applied to a single random variable.\nTo understand the relevance of these concepts to representation and solution of engineering problems." . . "Presential"@en . "TRUE" . . "Engineering mathematics 2"@en . . "10.00" . "Unit Information\nThis is the second of the two units that cover the basic mathematics requirements of engineering degree programmes. It comprises four elements: Vector Calculus, Applied Statistics, and Linear Systems & Partial Differential Equations.\n\nUnit aims: To enhance and develop the student's understanding of and ability to use the language of mathematics in engineering problems.\n\nYour learning on this unit\nOn successful completion of this unit, students will:\n\nunderstand basic principles of vector calculus\nbe able to apply vector calculus methods to problems in engineering\nunderstand and apply transform methods to engineering problems\nbe able to classify simple partial differential equations, and understand the different qualitative behaviour of their solutions\nbe able to apply elementary techniques to solve simple partial differential equations\nappreciate the importance of the real world of applied statistics\nbe able to formulate hypothesis tests, and understand their use for making inferences and obtaining confidence intervals,\nuse applied statistics techniques such as goodness of fit, correlation and regression for simple data and models" . . "Presential"@en . "TRUE" . . "Advanced numerical methods for aerodynamics"@en . . "10.00" . "An overview of content\nThe unit will cover the following areas:\n\nthe various physics included and mathematical formulations used in fluid modelling and CFD codes, and where each is applicable, particularly density-based and pressure-based solvers, representation of viscous effects and how turbulence models work;\nfundamental mathematical techniques used in data modelling, surrogate modelling, and data-space interpolation, and their application to aerodynamic data;\nmathematical formulation of various optimisation methods, including application of constraints;\ntechniques used in aerodynamic shape optimisation and design using CFD codes, including links with the optimisation approach, surface and volume control, optimisation objectives and constraints, and application to typical aerodynamic examples;\nmathematical techniques used in coupled fluid-structure problems, including force and displacement transformations, time integration and system reduction;\nthere will be occasional demonstrations of key concepts using simulation codes.\nLearning Outcomes\nOn successful completion of the unit, students will be able to:\n\nanalyse the various techniques applied in aerodynamic design and optimisation by comparing, contrasting and differentiating between different technical options;\nevaluate and critique various techniques to select the most suitable for a specific problem, by identifying and balancing advantages and disadvantages of each;\nreview state-of-the-art literature in relevant areas, including identification of possible limitations;\npropose possible extensions to methods in state-of-the-art literature, including identifying alternative application areas for the adopted numerical techniques." . . "Presential"@en . "FALSE" . . "Stochastic aerospace systems"@en . . "3.00" . "Course Contents The course AE4304 covers ONLY the first five chapters of the lecture notes, the practical assignment AE4304P covers chapters\nsix to eight. Chapter 9 (Etkin's 4 point model) serves as background reading.\nSo, the lecture AE4304 (and its exam) covers:\n1. Introduction (aircraft do respond to atmospheric turbulence, effects on flight control system design).\n2. Scalar stochastic processes (probability theory, joint probability density functions, covariance and correlation functions,\nstochastic processes, ergodic processes).\n3. Spectral analysis of stochastic processes in continuous time (Fourier analysis, power spectral densities, analysis of dynamic\nlinear system responses in frequency domain).\n4. Spectral analysis of stochastic processes in discrete time (discrete time Fourier transform, Fast Fourier Transform, spectral\nestimates-smoothing).\n5. Multivariable stochastic processes (covariance function matrix and spectral density matrix, multi-variable system responses in\nthe frequency and in the time domain).\nThe practical assignment AE4304P (Matlab or Python) covers:\n6. Description of atmospheric turbulence (physical mechanisms, stochastic models of atmospheric turbulence, the two\nfundamental correlation functions, von Karman en Dryden spectra, models in the time domain).\n7. Symmetric aircraft response to atmospheric turbulence (symmetrical aerodynamic forces and moments due to turbulence, gust\nderivatives, equations of motion of aircraft\nflying in symmetrical atmospheric turbulence).\n8. Asymmetric aircraft response to atmospheric turbulence (elementary two-dimensional fields of turbulence, asymmetrical\naerodynamic forces and moments, asymmetrical gust derivatives, equations of motion).\nStudy Goals Introduction to stochastic processes, spectral analysis, understanding the physics of aircraft responses to atmospheric turbulence,\nderivation of equations of motion of symmetrical and asymmetrical responses to atmospheric turbulence." . . "Presential"@en . "TRUE" . . "Stochastic aerospace systems practical"@en . . "1.00" . "Course Contents Application of MATLAB or Python software to aircraft specific turbulence responses:\n1. Calculation of aircraft time-histories due to both symmetrical and asymmetrical, longitudinal, lateral and vertical turbulence\ncomponents.\n2. Calculation of analytical transfer functions, frequency response functions, and auto- and cross Power Spectral Density (PSD)\nfunctions of state- and output variables (e.g.\nacceleration levels).\n3. Numerical calculation of frequency response functions, and auto- and cross Power Spectral Density (PSD) functions of stateand output-variables.\n4. Calculation of (co)variance- and correlation-functions of aircraft state-and output-variables.\n5. The effects of Automatic Flight Control Systems on the aircrafts responses on atmospheric turbulence.\nStudy Goals Introduction to both time- and frequency-domain identification and simulation techniques using MATLAB or Python. The\ntechniques are applied to example aircraft (amongst others Cessna Citation 500)." . . "Presential"@en . "TRUE" . . "Stochastic processes and simulation"@en . . "4.00" . "Course Contents This course introduces various stochastic processes and Monte Carlo simulation to model and analyze aerospace engineering\nsystems under uncertainty. The topics covered in the course are as follows:\n1. Markov chains: Markov property, Chapman-Kolmogorov equations, ergodicity, transition probability matrix, Monte Carlo\nsimulation.\n2. Discrete-Time Continuous-State stochastic processes: linear difference equations, Monte Carlo simulation.\n3. Continuous-Time Markov chains: Q-matrix, stationarity, Monte Carlo simulation.\n4. Poisson processes: properties, time discretization, Monte Carlo simulation.\n5. Brownian motion: properties, Monte Carlo simulation.\n6. Stochastic differential equations, Monte Carlo simulation.\nThe stochastic processes above are illustrated by means of applications in air transportation such as, for instance, aircraft\nmaintenance and airport operations under uncertainty.\nStudy Goals The aim of this course is to provide students with a working understanding of a variety of stochastic processes that are of\nrelevance in aerospace engineering. At the end of the course, the students should be able to:\n1. State the defining properties of various stochastic processes.\n2. Model various applications in air transportation using appropriate stochastic processes.\n3. Evaluate the performace of various stochastic models in air transportation by conducting an analytical analysis or by means of\nMonte Carlo simulation.\n5. Explain the difference in results between the Monte Carlo simulation and the analytical results.\n6. Identify the advantages and limitations of Monte Carlo simulation" . . "Blended"@en . "TRUE" . . "Numerical analysis"@en . . "6.00" . "no data" . . "Presential"@en . "FALSE" . . "Advanced numerical methods"@en . . "6.00" . "no data" . . "Presential"@en . "FALSE" . . "Monte carlo simulation and stochastic processes"@en . . "5.00" . "no data" . . "Presential"@en . "FALSE" . . "Spacecraft control theory"@en . . "6.00" . "Learning Outcomes\nAfter successful completion of this module, students will be able to analyze and design spacecraft control algorithms for spacecraft with,\nmagnetic control actuators, reaction wheels, fluid-dynamic actuators, and a combination of the aforementioned actuators. They will be\nfurther able to work with tethered spacecraft.\nFor the aforementioned cases the students will be able to determine stability of the developed control algorithms using Lyapunov's second\nmethod.\nContent\n- Equation of motion for rigid-body spacecraft with a combination of redundant configurations of magnetic actuators, reaction wheels, and\nfluid-dynamic actuators.\n- Application of fluid-dynamic attitude control for the implementation of highly agile attitude control maneuvers on small satellites.\n- Analysis of the stability of complex attitude control systems using Lyapunov's second method.\n- Passive attitude stabilization with booms and tethered spacecraft.\n- Orbit control using tethered spacecraft" . . "Presential"@en . "FALSE" . . "Probability theory and physical statistics"@en . . "4.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Numerical methods for simulating manufacturing processes"@en . . "5.00" . "Learning Outcomes\nThe learning objectives are to pore over students in the field of the mathematical description of the manufacturing processes with material removal or plastic deformation, using finite element methods (FEM). By the conduct of this course, the students will gain the possibility to study, analyze and calculate critical technological and material parameters using modern analytical tools to solve such intractable problems. In this way, students will gain self-reliant research background in the field of material machining.\nGeneral Competences\nApply knowledge in practice\nRetrieve, analyse and synthesise data and information, with the use of necessary technologies\nMake decisions\nGenerate new research ideas\nCourse Content (Syllabus)\nMathematical description of the materials' removal process and plastic deformation using finite elements method (FEM) simulation techniques. Stress – strain fields determination during the plastic deformation. Simulation of high accuracy shear cutting, deep drawinm, sheet and tube bending etc.." . . "Presential"@en . "TRUE" . . "Numerical methods in vibration"@en . . "5.00" . "General Competences\nApply knowledge in practice\nRetrieve, analyse and synthesise data and information, with the use of necessary technologies\nAdapt to new situations\nMake decisions\nWork autonomously\nWork in teams\nWork in an international context\nWork in an interdisciplinary team\nAdvance free, creative and causative thinking\nCourse Content (Syllabus)\nAnalytical Dynamics: generalized coordinates, motion constraints, principle of virtual work, Lagrange’s equations, Hamilton’s principle, Hamilton’s canonical equations.\nNumerical solution of systems of linear and nonlinear algebraic equations (determination of static response, kinematics of mechanisms, direct determination of periodic steady-state motions).\nNumerical integration of the equations and equations of motion of mechanical systems and structures (systems of differential equations and differential-algebraic equations).\nEvaluation of natural frequencies and modes of complex structures.\nApplications from the area of rigid body dynamics and machine dynamics (mass balancing of reciprocating engines, power flow smoothing – flywheels, application of multibody dynamics software)." . . "Presential"@en . "TRUE" . . "Mathematical methods – vector, tensor and complex analysis"@en . . "7.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Mathematical methods – differential equations"@en . . "8.0" . "Description in Bulgarian" . . "Presential"@en . "TRUE" . . "Engineering mathematics I"@en . . "6.0" . "This module refreshes the mathematics skills required to describe the engineering principles in this course. It commences with a review of the concept of functions and then discusses the basic concepts of limits, differentiation and integration followed by applications of the differential and integral calculus. The course ends with an introduction to complex numbers, vectors and matrices that prepare the students for other modules in Year 1 and provides a strong foundation in mathematics." . . "Presential"@en . "TRUE" . . "Engineering mathematics II"@en . . "6.0" . "This module provides an extension of the basic concepts of differentiation and integration learned in Engineering Mathematics I which builds the foundation for the advanced engineering modules in this course. It covers operations of functions with multiple variables, advanced applications of differential and integral calculus, as well as series and ordinary differential equations" . . "Presential"@en . "TRUE" . . "Engineering mathematics III"@en . . "6.0" . "This module completes the series of mathematics modules in the course and focuses on the computational solution of important problems of matrix algebra, eigenvalues and mathematical modelling. The topics covered include matrix algebra, eigenvalues and eigenvectors, mathematical modelling, numerical integration and differentiation to describe complex engineering phenomena." . . "Presential"@en . "TRUE" . . "Mathematical methods in physics"@en . . "20.0" . "#### Prerequisites\n\n* (Foundations of Physics 1 (PHYS1122) OR Physics for Geoscientists (GEOL1121)) AND ((Single Mathematics A (MATH1561) and Single Mathematics B (MATH1571)) OR (Calculus I (MATH1061) and Linear Algebra I (MATH1071))).\n\n#### Corequisites\n\n* None\n\n#### Excluded Combination of Modules\n\n* Analysis in Many Variables II (MATH2031).\n\n#### Aims\n\n* This module is designed primarily for students studying Department of Physics or Natural Sciences degree programmes.\n* It supports the Level 2 modules Foundations of Physics 2A (PHYS2611) and Foundations of Physics 2B (PHYS2621) by supplying the necessary mathematical tools.\n\n#### Content\n\n* The syllabus contains:\n* Vector algebra.\n* Matrices and vector spaces.\n* Vector calculus.\n* Line and surface integrals.\n* Fourier series.\n* Fourier transforms.\n* Laplace transforms.\n* Higher order ODEs.\n* Series solution of ODEs.\n* PDEs: general and particular solutions.\n* PDEs: separation of variables.\n* Special functions.\n\n#### Learning Outcomes\n\nSubject-specific Knowledge:\n\n* Having studied this module students will be familiar with some of the key results of vectors, vector integral and vector differential calculus, multivariable calculus and orthogonal curvilinear coordinates, Fourier analysis, orthogonal functions, the use of matrices, and with important mathematical tools for solving ordinary and partial differential equations occurring in a variety of physical problems.\n\nSubject-specific Skills:\n\n* In addition to the acquisition of subject knowledge, students will be able to apply the principles of physics to the solution of predictable and unpredictable problems.\n* They will know how to produce a well-structured solution, with clearly-explained reasoning and appropriate presentation.\n\nKey Skills:\n\n#### Modes of Teaching, Learning and Assessment and how these contribute to the learning outcomes of the module\n\n* Teaching will be by lectures and tutorial-style workshops.\n* The lectures provide the means to give concise, focused presentation of the subject matter of the module. The lecture material will be defined by, and explicitly linked to, the contents of recommended textbooks for the module, making clear where students can begin private study. When appropriate, the lectures will also be supported by the distribution of written material, or by information and relevant links online.\n* Regular problem exercises and workshops will give students the chance to develop their theoretical understanding and problem solving skills.\n* Students will be able to obtain further help in their studies by approaching their lecturers, either after lectures or at other mutually convenient times.\n* Student performance will be summatively assessed through an open-book examination and formatively assessed through problem exercises and a progress test. The open-book examination will provide the means for students to demonstrate the acquisition of subject knowledge and the development of their problem-solving skills. The problem exercises, progress test and workshops will provide opportunities for feedback, for students to gauge their progress and for staff to monitor progress throughout the duration of the module.\n\nMore information at: https://apps.dur.ac.uk/faculty.handbook/2023/UG/module/PHYS2611" . . "Presential"@en . "TRUE" . . "Mathematical methods in physics"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=509986" . . "Presential"@en . "FALSE" . . "Mathematical modeling"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=502162" . . "Presential"@en . "FALSE" . . "Stochastic processes and applications"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=502164" . . "Presential"@en . "FALSE" . . "Numerical analysis and simulation"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=502167" . . "Presential"@en . "FALSE" . . "Mathematical modeling of transport phenomena"@en . . "6.0" . "https://sigarra.up.pt/fcup/en/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=502179" . . "Presential"@en . "FALSE" . . "Stochastic decision making"@en . . "6.0" . "Any realistic model of a real-world phenomenon must take into account the possibility of randomness. That is, more often than not, the quantities we are interested in will not be predictable in advance but, rather, will exhibit an inherent variation that should be taken into account by the model. Mathematically, this is usually accomplished by allowing the model to be probabilistic in nature. In this course, the following topics will be discussed:\n\n(1) Basic concepts of probability theory: Probabilities, conditional probabilities, random variables, probability distribution functions, density functions, expectations and variances.\n\n(2) Finding probabilities, expectations and variances of random variables in complex probabilistic experiments.\n\n(3) Discrete and continuous time Markov chains and related stochastic processes like random walks, branching processes, Poisson processes, birth and death processes, queueing theory.\n\n(4) Markov decision problems.\n\n(5) Multi-armed bandit problems, bandit algorithms, contextual bandits, cumulative regret, and simple regret\n\nPrerequisites\nProbability & Statistics.\n\nRecommended reading\nProbability: A Lively Introduction by Henk Tijms; Reinforcement Learning by Richard S. Sutton and Andrew G. Barto (2nd ed.) (chapter 2); Bandit Algorithms by Tor Lattimore and Csaba Szepesvári\n\nMore information at: https://curriculum.maastrichtuniversity.nl/meta/464293/stochastic-decision-making" . . "Presential"@en . "FALSE" . . "Discrete mathematics"@en . . "6.0" . "Prerequisites\nNone.\n\nObjectives\nDevelop rigorous mathematical reasoning. Master the mathematical concepts and tools for algorithm and procedure analysis, focusing both on correctness and efficiency.\n\nProgram\nMathematical induction. Elementar number theory. Euclides and Saunderson algorithms. Fermat's little theorem. Chinese remainder theorem. Polynomials. Discrete Fourier Transform (DFT) and its efficient computation (FFT). Applications to RSA cryptography. Closed forms of infinite sums. Generating functions. Solution of finite difference linear equations. Graphs, subgraphs, cycles and circuits. Digraphs and networks. Planar graphs. Graph coloring. Deterministic and non-deterministic finite automata; regular languages, regular expressions and regular grammars. Pushdown automata. Context-free languages and grammars. Pumping lemmas. Programme correction. Hoare's calculus of partial and total correction of imperative programmes. Total correction of search and sorting algorithms.\n\nEvaluation Methodology\nExam/tests, possibly with minimum grade, complemented with continuous evaluation components.\n\nCross-Competence Component\nThe UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.\n\nLaboratorial Component\nNot applicable.\n\nProgramming and Computing Component\nNot applicable.\b\n\n\nMore information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938490003" . . "Presential"@en . "TRUE" . . "Probability and statistics"@en . . "6.0" . "Prerequisites\nDifferential and Integral Calculus I and II\n\nObjectives\nMaster concepts of statistical data analysis, probability theory and statistical inference to understanding and applying such concepts to solve real-life problems in engineering and science.\n\nProgram\n- Graphical representation of static and dynamic statistical data with R. - Basic concepts of probability theory. Conditional probability and total probability law. Bayes' theorem. Independence. - Random variables (discrete and continuous). Distribution function. Probability mass function and probability density function. Expected value, variance and quantiles. - Random pairs and linear transformation of random variables. Central limit theorem. - Statistical inference. Point estimation and interval estimation. - Hypothesis testing under normal populations. - Goodness of fit testing. - Linear regression.\n\nEvaluation Methodology\nExam/tests, possibly with minimum grade, complemented with continuous evaluation components (70%) + computational projects (30%). Oral evaluation for grades above 17 (out of 20).\n\nCross-Competence Component\nThe UC allows the development of transversal competences on Critical Thinking, Creativity and Problem Solving Strategies, in class, in autonomous work and in the several evaluation components. The percentage of the final grade associated with these competences should be around 15%.\n\nLaboratorial Component\nNot applicable.\n\nProgramming and Computing Component\nNot applicable.\n\nMore information at: https://fenix.tecnico.ulisboa.pt/cursos/lerc/disciplina-curricular/845953938490000" . . "Presential"@en . "TRUE" . . "Mathematics I"@en . . "20.0" . "https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=MATU9N1&_gl=1*1rqncef*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjAzODY1MC4wLjAuMA.." . . "Presential"@en . "FALSE" . . "Mathematics II"@en . . "20.0" . "https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=MATU9N2&_gl=1*kjdomz*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjAzOTA0NS4wLjAuMA.." . . "Presential"@en . "FALSE" . . "Mathematics I (matu9n1)"@en . . "20.0" . "https://portal.stir.ac.uk/calendar/calendar.jsp?modCode=MATU9N1&_gl=1*17xpbct*_ga*MTY1OTcwNzEyMS4xNjkyMDM2NjY3*_ga_ENJQ0W7S1M*MTY5MjAzNjY2Ny4xLjEuMTY5MjAzOTM5NC4wLjAuMA.." . . "Presential"@en . "FALSE" . . "Numerical methods in astronomy"@en . . "8" . "no data" . . "Presential"@en . "TRUE" . . "Mathematics I"@en . . "5" . "Introductory math course covering the basic principles of calculus and its applications. The material includes: Functions, limits and continuity. Derivatives, differentials, differentiation theorems, and applications of derivatives. Indefinite and definite integral, applications of integration. Sequences, series and power series. Complex numbers and introduction to statistics." . . "Presential"@en . "TRUE" . . "Mathematics II"@en . . "5" . "Introduction to the basic principles of linear algebra including vectors, matrices, determinants and their applications. Advanced subjects of calculus including: Equations of lines and planes in vector form, surfaces, multi-variable functions, parametric representation of surfaces, curvilinear coordinates, multiple integrals, line and surface integrals." . . "Presential"@en . "TRUE" . . "Mathematics III"@en . . "5" . "no data" . . "Presential"@en . "TRUE" .