714-0368/01 – Mathematics III (MIII)

Gurantor departmentDepartment of Mathematics and Descriptive GeometryCredits5
Subject guarantorIng. Petra Schreiberová, Ph.D.Subject version guarantorMgr. Petr Otipka, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Year2Semestersummer
Study languageCzech
Year of introduction1999/2000Year of cancellation2008/2009
Intended for the facultiesFSIntended for study typesBachelor
Instruction secured by
LoginNameTuitorTeacher giving lectures
HOM44 PaedDr. Zdenka Homolová
NIK01 Ing. Marek Nikodým, Ph.D.
OTI73 Mgr. Petr Otipka, Ph.D.
PRA76 Ing. Pavel Praks, Ph.D.
RYH40 RNDr. Irena Rychtarová
STR78 Mgr. Jakub Stryja, Ph.D.
SVO19 Mgr. Ivona Tomečková, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 12+4

Subject aims expressed by acquired skills and competences

The goal of the course is to serve as a theoretical and practical base to understand the importance of the basic notions in probability, and teach the student statistical way of thinking as a mean of understanding real life processes, introduce basic methods of collecting and analysing statistical data, and show the student how to use these general methods in other courses of study and in professional career. The graduate of this course should be able: • understand and use basic notions in combinatorics and probability theory • formulate questions, which can be answered based on the given data, for this purpose learn the principles of collecting, processing data and presentation of relevant values and results • choose and use suitable statistical methods for data analysis • suggest and evaluate conclusions (inference) and predictions obtained from data

Teaching methods

Lectures
Seminars
Tutorials
Project work
Other activities

Summary

Probabilities of random events: axioms of probability, conditional probability, independence. Random variables: discrete random variables, continuous random variables, expected values. Important practical distributions of discrete and continuous random variables.Estimating of parameters of population. Testing of hypotheses. Exercises - EXCEL.

Compulsory literature:

Boháč, Zdeněk: Numerical Methods and Statistics, VŠB – TUO, Ostrava 2005. ISBN 80-248-0803-X

Recommended literature:

Harshbarger, R.J.-Reynolds, J.J.: Calculus with Applications. D.C.Heath and Company, Lexington1990, ISBN 0-669-21145-1 James, G.: Advanced Modern Engineering Mathematics. Addison-Wesley, 1993. ISBN 0-201-56519-6

Way of continuous check of knowledge in the course of semester

E-learning

Other requirements

Prerequisities

Subject codeAbbreviationTitleRequirement
714-0366 MI Mathematics I Compulsory
714-0367 MII Mathematics II Compulsory

Co-requisities

Subject has no co-requisities.

Subject syllabus:

Program přednášek ================= Náplň přednášek ------------------------------------------------------------------------------- 1 Kombinatorika. Náhodné jevy, operace s nimi, pojem neslučitelnosti a úplnosti, jevové pole. 2 Definice pravděpodobnosti jevů - klasická, geometrická, statistická. Podmíněná pravděpodobnost. Úplná pravděpodobnost. Bernoulliho posloupnost nezávislých jevů. 3 Náhodná veličina diskrétní a spojitá. Frekvenční a distribuční funkce.Charakteristiky náhodných veličin. 4 Základní typy rozdělení pravděpodobnosti diskrétní náhodné veličiny. 5 Základní typy rozdělení pravděpodobnosti spojité náhodné veličiny. 6 Náhodný vektor, rozdělení pravděpodobnosti, číselné charakteristiky. 7 Zpracování statistického souboru. 8 Náhodný výběr, bodové a intervalové odhady 9 Testování hypotéz - testy parametrické. 10 Testování hypotéz - testy neparametrické. 11 Lineární regrese. 12 Časové řady - složka trendová, sezónní a náhodná. 13 Prognózování. Program cvičení a seminářů + individuální práce studentů ======================================================== Náplň cvičení a seminářů ------------------------------------------------------------------------------- 1 Kombinatorika - kombinace, variace a permutace bez opakování a s opakováním, jevové pole. 2 Výpočet pravděpodobnosti. 3 První test - pravděpodobnost. Náhodná veličina - určování frekvenční a distribuční funkce, výpočet charakteristik. 4 Rozdělení alternativní, binomické, hypergeometrické, Poissonovo. 5 Rozdělení rovnoměrné, exponenciální, normální, Weibullovo. 6 Druhý test - náhodná veličina. Náhodný vektor - podmíněná rozdělení, charakteristiky. 7 Zpracování statistického souboru. 8 Zpracování statistického souboru - program. 9 Odhady parametrů základního souboru. 10 Testování hypotéz - hypotézy o střední hodnotě a rozptylu, testy shody. 11 Jednoduchá lineární regrese. 12 Časové řady - trendová, sezónní, náhodná složka, prognózování. 13 Třetí test - zpracování statistického souboru.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2006/2007 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Compulsory study plan
2006/2007 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (3708R028) Transport Technology (40) P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (71) P Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2301R013) Robotics (71) K Czech Ostrava 2 Compulsory study plan
2006/2007 (B2341) Engineering (2302R010) Design of Machines and Equipment (60) Design of industrial products P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R002) Transport Equipment P Czech Šumperk 2 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Šumperk 2 Compulsory study plan
2005/2006 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2005/2006 (B2341) Engineering (3904R016) Environmental Engineering K Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3901R003) Applied Mechanics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (71) Technological Management P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3902R001) Applied Informatics and Control (70) Applied Informatics and Control P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R002) Transport Equipment P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (20) Surface Transport P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3907R004) Energy Management P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3904R016) Environmental Engineering (70) Environmental Engineering P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R013) Robotics (70) Robotics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2301R023) Technical Diagnostics, Service and Management (70) Technical Diagnostics, Repairs and Maintenance P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R007) Hydraulics and Pneumatics P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R003) Transport Machinery and Material Handling P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (10) Machines for Mining and Treating Commercial Raw Materials P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (40) Design of Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (20) Production Machines and Equipment P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2302R010) Design of Machines and Equipment (30) Earth Moving and Building Machines P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (2303R002) Mechanical Engineering Technology (70) Mechanical Engineering Technology P Czech Ostrava 2 Compulsory study plan
2004/2005 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 2 Compulsory study plan
2003/2004 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan
2002/2003 (B2341) Engineering (2341R999) Bachelor Mechanical Engineering (00) Bachelor Machanical Engineering P Czech Ostrava 2 Compulsory study plan
2002/2003 (B2341) Engineering (3708R028) Transport Technology (30) P Czech Ostrava 2 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

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