310-2121/01 – Mathematics III (MIII)

Gurantor department	Department of Mathematics and Descriptive Geometry	Credits	4
Subject guarantor	Ing. Petra Schreiberová, Ph.D.	Subject version guarantor	Ing. Petra Schreiberová, Ph.D.
Study level	undergraduate or graduate
		Study language	Czech
Year of introduction	2019/2020	Year of cancellation
Intended for the faculties	FS	Intended for study types	Bachelor

Instruction secured by
Login	Name	Tuitor	Teacher giving lectures
KAH14	Mgr. Marcela Rabasová, Ph.D.
SKN002	Ing. Petra Schreiberová, Ph.D.

Extent of instruction for forms of study
Form of study	Way of compl.	Extent
Full-time	Credit and Examination	2+2

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

Zápočet - absolvování 3 písemných testů Zkouška - složená z praktické a teoretické části Nutnou podmínkou pro absolvování zkoušky je uzavření předmětu Matematika II a udělený zápočet z MIII.

E-learning

http://mdg.vsb.cz/portal/m3/index.php

Other requirements

There are no more requirements.

Prerequisities

Subject code	Abbreviation	Title	Requirement
310-2112	MII	Mathematics II	Compulsory
310-2117	M1	Mathematics 1	Recommended

Co-requisities

Subject has no co-requisities.

Subject syllabus:

1. Combinatorics. Random events, operations with them, sample space. 2. Definitions of probability events - classical, geometrical, statistics. 3. Conditional probability, Bayes\' theorem. Bernoulli independent repeated trials. 4. Discrete random variable. Functions of random variables. Moment generating function. 5. Continuous random variable. Functions of random variables. Moment generating function, quantiles. 6. Discrete probability distribution. 7. Continuous probability distribution. 8. Statistics. Statistical methods, descriptive statistics 9. Interval estimators. 10. Statistical hypothesis testing – the testing process, interpretation, importance. Parametric tests. 11. Correlation and regression analysis.

Conditions for subject completion

Full-time form (validity from: 2024/2025 Winter semester)

Task name	Type of task	Max. number of points (act. for subtasks)	Min. number of points	Max. počet pokusů
Credit and Examination	Credit and Examination	100 (100)	51
Credit	Credit	35 (35)	15
Písemka 1	Written test	10	3	2
Písemka 2	Written test	10	3	2
Písemka 3	Written test	15	5	2
Examination	Examination	65 (65)	30	3
Praktická část	Written examination	55	20	3
Teoretická část	Written examination	10	5	3

Mandatory attendence participation: - participation is mandatory for every credit test

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Conditions for subject completion and attendance at the exercises within ISP: In order to complete the credit, students pass the credit test. On the basis of a successfully completed credit, they can take an exam.

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Occurrence in study plans

Academic year	Programme	Branch/spec.	Form	Study language	Tut. centre	Year	Type of duty
2024/2025	(B0715A040001) Transport Systems and Equipment		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0713A070002) Energetics and Environments		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B0715A270011) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2024/2025	(B0715A270011) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B1088A040001) Operation and management of air transport	(S01) Air Transport Technology and Management	P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B1088A040001) Operation and management of air transport	(S02) Aviation Operation Management	P	Czech	Ostrava	2	Compulsory	study plan
2024/2025	(B1041A040008) Intelligent transport and logistics		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0713A070002) Energetics and Environments		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0715A040001) Transport Systems and Equipment		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0715A270011) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B0715A270011) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2023/2024	(B1088A040001) Operation and management of air transport	(S02) Aviation Operation Management	P	Czech	Ostrava	2	Compulsory	study plan
2023/2024	(B1088A040001) Operation and management of air transport	(S01) Air Transport Technology and Management	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0715A040001) Transport Systems and Equipment		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0713A070002) Energetics and Environments		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0715A270011) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B0715A270011) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2022/2023	(B3712) Air Transport Technology	(3708R038) Aircraft Maintenance Technology	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B3712) Air Transport Technology	(3708R037) Aircraft Operation Technology	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B1088A040001) Operation and management of air transport	(S01) Air Transport Technology and Management	P	Czech	Ostrava	2	Compulsory	study plan
2022/2023	(B1088A040001) Operation and management of air transport	(S02) Aviation Operation Management	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0715A270011) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0715A270011) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2021/2022	(B0713A070002) Energetics and Environments		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B0715A040001) Transport Systems and Equipment		P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B3712) Air Transport Technology	(3708R037) Aircraft Operation Technology	P	Czech	Ostrava	2	Compulsory	study plan
2021/2022	(B3712) Air Transport Technology	(3708R038) Aircraft Maintenance Technology	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0715A270011) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0715A270011) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2020/2021	(B0713A070002) Energetics and Environments		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B0715A040001) Transport Systems and Equipment		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2341) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2020/2021	(B2341) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B2341) Engineering	(2301R003) Transport Equipment and Technology	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3712) Air Transport Technology	(3708R037) Aircraft Operation Technology	P	Czech	Ostrava	2	Compulsory	study plan
2020/2021	(B3712) Air Transport Technology	(3708R038) Aircraft Maintenance Technology	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B2341) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B2341) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2019/2020	(B2341) Engineering	(2301R003) Transport Equipment and Technology	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B3712) Air Transport Technology	(3708R037) Aircraft Operation Technology	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B3712) Air Transport Technology	(3708R038) Aircraft Maintenance Technology	P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B0713A070002) Energetics and Environments		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B0715A270011) Engineering		P	Czech	Ostrava	2	Compulsory	study plan
2019/2020	(B0715A270011) Engineering		P	Czech	Šumperk	2	Compulsory	study plan
2019/2020	(B0715A040001) Transport Systems and Equipment		P	Czech	Ostrava	2	Compulsory	study plan

Occurrence in special blocks

Block name	Academic year	Form of study	Study language	Year	W	S	Type of block	Block owner
Subject block without study plan - FS - P - cs	2023/2024	Full-time	Czech				Optional	FS - Faculty of Mechanical Engineering	stu. block
Subject block without study plan - FS - P - cs	2021/2022	Full-time	Czech				Optional	FS - Faculty of Mechanical Engineering	stu. block

Assessment of instruction