Extended data for Mathematics I.

Stored data
bibliography hu
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.
bibliography en
Mathematics I - digital lecture note containing theoretical knowledge, worked examples, and exercises and their solutions. The lecture note is available on the Moodle interface of the course.
courseContent hu
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.
courseContent en
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 Probability variable, expected value, standard deviation. Discrete probability variable, distribution table. Expected value and standard deviation. Binomial and hypergeometric distribution. Geometric distribution.
assessmentMethod hu
The course ends with an examination. A mark may be awarded on the basis of the tests taken during the semester.
assessmentMethod en
The course ends with an examination. A mark may be awarded on the basis of the tests taken during the semester.