Course code Mate2035

Credit points 2

# Mathematics IV

Total Hours in Course80

Number of hours for lectures16

Number of hours for laboratory classes16

Independent study hours48

Date of course confirmation19.02.2014

Responsible UnitDepartment of Mathematics

### Course developers prof.

## Natālija Sergejeva

Dr. math. Matemātikas katedra

## Svetlana Atslēga

Dr. math.

### Prior knowledge

Mate1029, Mathematics I

Mate1030, Mathematics II

Mate2034, Mathematics III

### Course abstract

The aim of the course is to deal with probability, laws of probability, distributions, statistical data, confidence intervals and hypothesis testing, linear correlation and linear regression. The study course is intended to acquire the mathematical knowledge and practical skills needed to study future special subjects, as well as to acquire skills for applying math techniques to study different problems related to Engineering science and related fields. During the course, students acquire skills in working with appropriate application software, such as “MS Excel”, “Matlab”.

### Learning outcomes and their assessment

Upon successful completion of this course:
1. Knowledge - students are able to manage and demonstrate knowledge and critical understanding of probability, laws of probability, distributions, statistical data, confidence intervals and hypothesis testing, linear correlation and linear regression. Students manage the application of the acquired topics in practical examples related to the specialty of the Engineering science and related fields – tests.
2. Skillis - students are able to show understanding of the corresponding concept and regularities, to perform necessary calculations and operations. Students are able to use appropriate software for calculations – laboratory works.

3. Competence - working in a group or doing work independently, student is able to apply the mathematical calculations corresponding to the specialty problem situation, to make a professional assessment and interpretation of the intermediate result of the calculations and the final results – independent works.

### Course Content(Calendar)

Full time intramural studies:
1. Introduction to probability (4 h)
2. Laws of probability (3 h)
3. Discrete random variables and probability distributions. (4 h)
4. Continuous random variables and probability distributions. (5 h)
5. Test 1: Probability. Distributions
6. Elements of mathematical statistics. Presentation of statistical data (4 h)
7. Confidence intervals for the mean and for the variance (3 h)
8. Hypothesis testing (3 h)
9. Linear regression and correlation between two variables (2 h)
10. Multiple regression and correlation (2 h)
11. Test 2: Elements of mathematical statistics. Confidence intervals. Hypothesis testing. Correlation and regression
Part time extramural studies:

All topics specified for full time studies are accomplished, but the number of contact hours is one half of the number specified in the calendar

### Requirements for awarding credit points

Assessment: Exam.

### Description of the organization and tasks of students’ independent work

In writing form and by using the appropriate software, the following independent work must be completed (all tasks are executed correctly) at times specified by the teaching staff:
Independent work 1. Definitions of probability. Laws of probability
Independent work 2. Bernoulli trials. Total probability. Bayes’ formula
Independent work 3. Discrete variables. Distributions
Independent work 4. Continuous variables. Distributions
Independent work 5. Mean, median, mode and standard deviation. Presentation of statistical data
Independent work 6. Confidence intervals
Independent work 7. Hypothesis testing

Independent work 8. Correlation and regression

### Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam if:
1. all independent works are completed at times specified by the teaching staff;
2. during the semester each test score is at least 4.
Failed tests can be repeated.
The student may overwrite unsuccessfully written test work during the study process, at times specified by the teaching staff. The student can rewrite the last test in the 1st week of the individual study and examination period at the time indicated by the teaching staff.
The accumulative exam mark is
- 90% of the average mark of all tests
- 10% for completed independent works.

The written exam can be arranged at the time indicated by the teaching staff, if all the independent works are defended (all tasks are performed correctly).

1. Vasermanis E., Šķiltere D. Varbūtību teorija un matemātiskā statistika. Rīga: Izglītības soļi, 2003. 186 lpp.
2. Krastiņš O., Ciemiņa I. Statistika: mācību grāmata augstskolām. Rīga: Latvijas Republikas centrālā Statistikas pārvalde, 2003. 267 lpp.
3. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 534 lpp.

4. Goša Z. Statistika: mācību grāmata. Rīga: Latvijas Universitāte, 2003. 334 lpp