ZP001

Mathematical Methods

 

Assist. Prof. Dr. Petra Grošelj

Year 1, Term 1

Credits: 6

Hours: 90

Syllabus

Introduction to mathematical methods

Precalculus for business and finance
Variables: discrete and continuous variables, tables, grouped data, frequency distribution, bar charts, pie diagrams, graphs, histogram, polygon, ogive, quartiles, deciles, percentiles, arithmetic mean, median, mode, geometric and harmonic means, standard deviation and some other measures of dispersion.

Real numbers: absolute values, quadratic, exponential and logarithmic equations, sequences and series, limits of sequences, number e, simple interest, compound interest, annuities, present value of annuity, law of natural growth.

Functions of one (two) real variable(s)

Elementary functions: equations, graphs and properties of linear, quadratic, rational, exponential, logarithmic, trigonometric and compound functions, continuity and limits of functions of one variable, supply and demand functions.

Derivatives: definition of the derivative, tangent to a curve, derivative formulas, higher order derivatives, relative minima and maxima, concavity, convexity, points of inflection, elasticity, elasticity of demand.

Integrals: definition of indefinite integrals, basic integration formulas, integration by substitution, definition of the definite integral, properties and calculation of definite integrals, area under a graph, area enclosed by two graphs, improper integrals, approximating the definite integral using trapezoids, average value of a function.

Functions of two real variables: partial differentiation, higher order partial derivatives, maxima and minima, least squares method, regression line, trend line.

Probability

Combinatorics: permutations, variations and combinations.

Introduction to probability: definition of probability, mutually exclusive and nonexclusive events, dependent and nondependent events, compound events, conditional probability, sequence of independent trials, Bernoulli’s formula, discrete probability distributions, binomial and Poisson distribution, continuous distribution, normal distribution, mean and variance.

Decision making: decision tree and its characteristics, decision making under uncertainty, optimistic and pessimistic rules, Laplace’s and Hurwicz’s rule, opportunity losses rule, decision making with risk, Bayes’ rule, the value of complete information.

Linear algebra

Matrices: definition of determinants, characteristics and calculating their value, definition of matrices and operations with them (product of two matrices, inverse matrix, rank of a matrix).

Vectors: operations with vectors, calculation of scalar, vector and scalar triple products, their geometrical significance, linear dependence and independence of vectors, systems of linear equations, solvability, elimination method, systems of linear inequalities, definition of a convex set.

Linear program: formulation of a linear program, a geometric approach to linear programming problems (production, diet, transportation, pollution problems) the use of computer programs and spreadsheets for solving seminar exercises.

Networks

Basic definitions, introduction to graph theory, maximum flow in a graph, critical path problems, super project computer program.

Assessment

A short seminar work (up to two pages); positive evaluation of the seminar work is a prerequisite for sitting the exams; there are two midterm exams covering calculations/exercises and theory; if the student does not pass the midterm exams, he/she has a written exam in both parts, exercises/calculations and theory.

Reading list

  • Grošelj Petra, 2017, Matematične metode za študente Biotehniške fakultete, 133 str., Univerza v Ljubljani, Biotehniška fakulteta, ISBN978-961-6379-44-1, https://repozitorij.uni-lj.si/IzpisGradiva.php?id=96293
  • ZADNIK STIRN, L., oktober 2012. Matematične metode za živilce na prosojnicah, 1.del (zapiski predavanj), Biotehniška fakulteta, Ljubljana, 329 str. (ISBN ni).
  • ZADNIK STIRN, L., november 2012. Matematične metode za živilce na prosojnicah, 2. del (zapiski predavanj), Biotehniška fakulteta, Ljubljana, 178 str. (ISBN ni).
  • ZADNIK STIRN, L., 2001. Metode operacijskih raziskav za poslovno odločanje. Visoka šola za upravljanje in poslovanje, Novo mesto. ISBN: 961-6309-07-2

Selected chapters:

  • Indihar S., Mastinšek M., Arih L. 1999. Matematika za ekonomiste. EPF, Maribor, 312 pp
  • Čibej J. A. 1985. Statistika, Zavod za šolstvo, Ljubljana, 73 pp
  • Čibej J. A. 1992. Poslovna matematika. Faculty of Economics, Ljubljana, 153 pp
  •  Jamnik R. 1985. Matematika, DMFA, Ljubljana.
  • Vadnal A. 1970. Elementarni uvod v verjetnostni račun, Mladinska knjiga, Ljubljana.
  • Cedilnik A. 1997. Matematični priročnik, Didakta, Radovljica, 462 pp.
  • Povh J., Pustavrh S. 2003. Matematične metode in poslovni račun; vaje z rešitvami. College of Management and Business Studies, Novo mesto, 28 pp.
  • Freund J.E., Simon G.A. 1992. Modern Elementary Statistics. Prentice, Engl. Cliffs, N.J.
  • Harshbarger R. J., Reynolds J.J. 1992. Mathematical Applications for Management, Life and Social Sciences. D.C. Health and Company, Lexington, 231 pp

Najnovejši članki objavljeni v znanstvenih in strokovnih revijah iz področja živilstva in prehrane.

Spletni viri:

Računalniški programi: Excel, MS Project in statistični podatki s spleta.