. "Algebra"@en . . "6" . "Objectives and Contextualisation\nThis is a basic introduction to linear algebra, emphasizing the most functional and instrumental aspects of linear techniques.\nA fundamental objective is to achieve an agile and efficient transition between the three following levels of knowledge:\n\nAbstract knowledge of mathematical concepts related to linear phenomena.\nDeepened knowledge of the same concept from its practical manipulation \"by hand\".\nDeepened knowledge of the same concept from its practical manipulation with a computer.\nThe most important fundamental objective is to learn to design efficient strategies to apply specific techniques to solve\ncomplex problems.\n\n\nCompetences\nElectronic Engineering for Telecommunication\nCommunication\nDevelop personal work habits.\nLearn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.\nPerform measurements, calculations, estimations, valuations, analyses, studies, reports, task-scheduling and other similar work in the field of telecommunication systems\nWork in a team.\nTelecommunication Systems Engineering\nDevelop personal work habits.\nDevelop thinking habits.\nLearn new methods and technologies, building on basic technological knowledge, to be able to adapt to new situations.\nLearning Outcomes\nAnalyse measurements in the area of engineering, using statistical tools to extract and understand information.\nAnalyse measures in the area of engineering, using statistical tools to extract and understand information.\nApply, in the problems that arise in engineering, knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.\nApply, to the problems that arise in engineering, knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial derivative equations, numerical methods, numerical algorithms, statistics and optimisation.\nCommunicate efficiently, orally and in writing, knowledge, results and skills, both professionally and to non-expert audiences.\nDevelop scientific thinking.\nDevelop the capacity for analysis and synthesis.\nManage available time and resources.\nModel systems and analyse their features.\nResolve the mathematical problems that can arise in engineering.\nWork autonomously.\nWork cooperatively.\n\nContent\nMatrices\nMatrices. Operations with marices. Special matrices: symmetric, Toeplitz, circulant, invertible, hermitian, orthogonal.\nElemental transformations by rows. Gauss-Jordan's normal form of a matrix. Rank of a matrix. Invertibility and calculation of inverse matrices.\nSystems of linear equations and linear varieties. Gauss method. Direction and dimension of linear varieties. Rouché's Theorem.\nVector Spaces\nDefinition of vector space and examples. Linear combinations of vectors. Subspaces. Generating systems.\nLinear maps. Matrix associated to a linear map. Composition of linear maps. Kernel and Image of a linear map. Isomorphisms.\nLinear dependence of vectors. Linear dependence criterion.\nBases, dimensions and coordinates. Working with coordinates. Base changes.\nDiagonalization of matrices and inner products.\nDeterminant of a square matrix. Properties of the determinant.\nEigenvalues and eigenvectors of a square matrix. Diagonalization criteria.\nApplications of diagonalisation: calculation of matrix powers and resolution of systems of linear differential equations with constant coefficients." . . "Presential"@en . "TRUE" . . "Algebra"@en . . . . . . . . . . . . . . . . . . . . . "Bachelor in Telecommunication Systems Engineering"@en . . "https://www.uab.cat/web/estudiar/ehea-degrees/general-information/computer-engineering-telecommunication-systems-engineering-1216708259085.html?param1=1345654047869" . "327"^^ . "Presential"@en . "The fast-paced technological evolution and advances in globalisation have made the information and communication technologies (ICTs) present in almost all of our personal and also professional activities. The union of concepts such as information technology, internet and telecommunications is a reality demanding the knowledge of professionals capable of working in all three areas. For this reason, the UAB offers a double degree in which students can receive integrated training leading to two diplomas in five years.\n\nStudents of the double degree in Computer Engineering (Specialisation in Information Technologies) + Telecommunication Systems Engineering will receive training in both the subjects belonging to each degree and interdisciplinary training to help successfully face the professional challenges of the ICTs and acquire a highly valued versatility with which to stand out from other professionals in the sector.\n\nThe close relation with advanced technological and research centres of both local and international prestige, and with leading companies from the ICT sector, facilitates student participation in high quality work placements and a successful entry into the labour market."@en . . . . "5"@en . "FALSE" . . . "Bachelor"@en . "Both" . "1199.90" . "Euro"@en . "Not informative" . "Recommended" . "no data"@en . "no data" . "FALSE" . "Midstream"@en . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .