Kurzus nemzetközi vendég- és részidős hallgatóknak
- Kar
- Gazdaságtudományi Kar
- Szervezet
- Gazdaságtudományi Kar
- Kód
- GTI91AN102EN
- Cím
- Matematika I.
- Tervezett félév
- Őszi
- Meghirdetve
- 2024/25/1
- ECTS
- 6
- Nyelv
- en
- Oktatás célja
- The aim of the course is to provide students with mathematical knowledge, concepts and proceduresnecessary for them to complete their studies successfully and for their future work. The course and the assessment focus on practical application rather than theoretical knowledge.
- Tantárgy tartalma
- Functions. Function transformations and their meanings: scaling graphs. Linear function, slope. Quadratic functions, graphing, method(s) of finding extreme values. Exponential and logarithmic processes: interest rate, decay, decibel, pitch. Continuous interest, the number e. Change of functions, average rate of change over a given interval. Combinatorics. Calculating elementary probability. Counting, application of principles, permutation, combination, variation. Classical probability. Event algebra. Subsets of events, operations: and, or, exclusion events. The inclusion–exclusion priciple. Formula for two events (probability of union) Meaning of conditional probability, calculation. Independence. Total probability theorem and Bayes theorem. Linear algebra. Matrices, vectors. Geometric meaning of vectors. Matrix operations and their meaning. Matrix form of systems of linear equations. Linear combination and independence. Concept of the determinant, its application. Meaning of inverse matrix. Solution of system of linear equations by inverse. Eigenvalues, eigenvectors. Graphic solution of LP problems with two variables. Markov chains Representing transitions between states: diagram, tree diagram. Transition matrix. Transition to the next generation. Initial distribution, multigeneration distribution. Calculate stationary (stable) distribution. Long run behaviour for stable distribution Random variables, expected value, standard deviation. Discrete random variables, distribution table. Expected value and standard deviation. Binomial and hypergeometric distribution. Geometric distribution.
- Számonkérés és értékelés
- The course ends with an examination. A mark may be awarded on the basis of the tests taken during the semester.
- Irodalomjegyzék
- Mathematics I - digital lecture notes containing theoretical knowledge, worked examples, and exercises and their solutions. The lecture notes is available on the Moodle interface of the course.