School for Viticulture and Enology

Mathematics with Statistic

This course is part of the programme:
Bachelor's programme in Viticulture and Enology (1st level)

Objectives and competences

Meet and complement the basic concepts and principles of mathematical analysis, algebra and statistics and their applications in science.

Prerequisites

Not required.

Content (Syllabus outline)

Lectures

Arithmetics and Algebra

1. Operations with sets

2. Natural, integer, rational and real numbers

3. Fractions and percenteges

4. Powers and roots

5. Logarithms

6. Linear and quadratc equations

7. Linear systems

8. Disequations

Geometry

1. Vectors in the space

2. Scalar, vectorial and mixed product

3. Lines and planes

4. Conics: circle, ellipse, hyperbola, parabola

Functions

1. Elementary functions (polynomials, rational functions, exponential and logarithmic functions, trigonometrical functions)

2. Limit of function

3. Rules and derivatives of elementary functions

4. Indefinite and definite integrals

Statistics

1. Basic concepts and algebra of events

2. Conditional probability

3. Statistical parameters (arithmetical mean, median, mode, dispersion, variance, standard deviation).

4. Mathematical hope

5. Quantiles

6. Correlation coefficient

7. Regression

8. Random sampling

9. Intervals of trust

Tutorials

Calculating exercises based on the course lectures.

Intended learning outcomes

Knowledge and understanding:

By the end of this course students will be able to:

-do operations with numbers and sets

-calculate logarithms, roots, powers

-solve linear and quadratic equations and systems

-solve problems with vectors, lines and planes in the space

-calculate limits, derivatives, integrals

-determine the probability of an event

-calculate statistical parameters (average, variance, median, mode, dispersion, variance, standard deviation, etc.)

Readings

1. Wrede, R.C., Spiegel, M. (2002). Advanced Calculus, 2nd Edition, Schaum’s Outlines Series

2. Zeliko, M. (2010). Izbrana poglavja iz matematike

3. Mizori Oblak, P. (2001) Matematika za študente tehnike in naravoslovja I, Fakulteta za strojništvo, Ljubljana.

4. Mizori Oblak, P. (2001) Matematika za študente tehnike in naravoslovja II, Fakulteta za strojništvo, Ljubljana.

5. Košmelj K. (2007) Uporabna statistika, Biotehniška fakulteta, Ljubljana

Assessment

Seminar work, homework tasks examination (20 %)/written examination (80 %)

Lecturer's references

Doc.dr. Irina Cristea is an assistant professor for Mathematics at University of Nova Gorica. She is employed in the research group Center for systems and information technologies.

Principal education and research areas: Mathematics, algebraic hyperstructures and connections with fuzzy sets and their generalizations; mathematical models based on cluster analysis (hard and fuzzy version).

Professional career: Doc. dr. Irina Elena Cristea received the PhD in Mathematics, with specialization in Algebra, in 2007, from the University of Constantza, Romania. She started the research career in 2003 at the University of Iasi, Romania, where she worked as Teaching Assistant for 4 years. After a post doctoral position at Udine University, Italy, since January 2012 she is employed at the University of Nova Gorica, as Assistant Professor in Mathematics, conducting research in Algebraic Hyperstructure Theory, being affiliated with the Centre for Systems and Information Technologies. She is currently teaching Mathematics at the School of Engineering and Management, School of Environmental Sciences, School of Applied Sciences.

Selected bibliography

CRISTEA, Irina, JANČIĆ-RAŠOVIĆ, Sanja. Composition hyperrings. An. Univ. “Ovidius” Constanţa, Ser. Mat. (Print), 2013, vol. 21, no. 2, str. 81-94. [COBISS.SI-ID 2850555]

ANGHELUŢǍ, Carmen, CRISTEA, Irina. On Atanassov’s intuitionistic fuzzy grade of complete hypergroups. J. mult.-valued log. soft comput.. [Print ed.], 2013, vol. 20, no. 1/2, str. 55-74. [COBISS.SI-ID 2623995]

CRISTEA, Irina, ZHAN, Jianming. Lower and upper fuzzy topological subhypergroups. Acta math. Sin., Engl. ser. (Print), 2013, vol. 29, no. 2, str. 315-330, [COBISS.SI-ID 2634747]

CRISTEA, Irina, JAFARPOUR, Morteza, MOUSAVI, Seyed S. On fuzzy preordered structures and (Fuzzy) hyperstructures. Acta math. Sin., Engl. ser. (Print), 2012, vol. 28, no. 9, str. 1787-1798, [COBISS.SI-ID 2490107]

CRISTEA, Irina, ŞTEFǍNESCU, Mirela, ANGHELUŢǍ, Carmen. About the fundamental relations defined on the hypergroupoids associated with binary relations. Eur. j. comb., 2011, vol. 32, no. 1, str. 72-81. [COBISS.SI-ID 2062587]

CRISTEA, Irina, DAVVAZ, Bijan. Atanassov’s intuitionistic fuzzy grade of hypergroups. Inf. sci. [Print ed.], 2010, vol. 180, no. 8, str. 1506-1517. [COBISS.SI-ID 2065915]

CRISTEA, Irina. About the fuzzy grade of the direct product of two hypergroupoids. Iranian journal of fuzzy systems, 2010, vol. 7, no. 2, str. 95-108. [COBISS.SI-ID 2061563]

University course code: 1VV100

Year of study: 1

Semester: 2

Course principal:

Lecturer:

Assistant:

ECTS: 8

Workload:

  • Lectures: 40 hours
  • Exercises: 50 hours
  • Individual work: 150 hours

Course type: lectures, tutorials

Languages: english and slovene

Learning and teaching methods:
lectures, tutorials, independent work