Course code Mate4011

Credit points 3

Applications of Mathematical Methods

Total Hours in Course81

Number of hours for lectures16

Number of hours for seminars and practical classes8

Number of hours for laboratory classes8

Independent study hours49

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

Course developer

author Matemātikas un fizikas institūts

Svetlana Atslēga

Dr. math.

Course abstract

In this study course probability, distributions, confidence intervals and hypothesis testing, linear correlation and linear regression, linear programming and graphical method are considered. The study course provides an understanding of modern concepts and problems of mathematical modelling. The study course promotes mathematical thinking, looks at different applications of mathematics in forest science. During the course, students acquire skills in working with appropriate application software, such as “Matlab”, “Excel”.

Learning outcomes and their assessment

By the successful completion of this study course, students will have
1. knowledge of probability, distributions, confidence intervals and hypothesis testing, linear correlation and linear regression, methods for solving linear programming problems. Knowledge is assessed during the tests.
2. skills to perform necessary calculations and operations, understanding of relevant concepts and regularities. Skills are assessed during practical and laboratory works.
3. Competence to perform intermediate results of calculations and professional evaluation and interpretation of final results. Competences are assessed during independent work.

Course Content(Calendar)

1. Probability. Total probability theorem. Bayes’ theorem. Bernoulli trial. Moivre-Laplace theorem and applications (5 h)
2. Discrete random variables and probability distributions (3 h)
3. Continuous random variables and probability distributions. Normal distribution and applications (3 h)
4. Confidence intervals for the mean and for the variance (2 h)
5. Hypothesis testing (3 h)
6. Test 1: Probability. Distributions. Confidence intervals. Hypothesis testing (1h)
7. Linear regression and correlation between two variables. Multiple regression and correlation (4 h)
8. Introduction to operations research. The concept of mathematical modeling (2 h)
9. Linear programming problems (3 h)
10. Graphical method for solving linear programming problems (5 h)
11. Test 2: Regression and correlation. Lineal programming problems (1h)

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. Probability
Independent work 2. Distributions
Independent work 3. Confidence intervals
Independent work 4. Hypothesis testing
Independent work 5. Correlation and regression
Independent work 6. Linear programming problems

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 the average mark of all tests

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).

Compulsory reading

1. Arhipova I., Bāliņa S. Statistika ekonomikā un biznesā. Risinājumi ar SPSS un Microsoft Excel. Mācību līdzeklis. 2. Izdevums. Rīga: Datorzinību Centrs, 2006. 364 lpp.
2. Krastiņš O., Ciemiņa I. Statistika. Rīga: Latvijas Republikas Centrālā statistikas pārvalde, 2003. 268 lpp.
3. James G., Witten D., Hastie T., Tibshirani R. An Introduction to Statistical learning. ISBN 9781461471370
4. Peck R., Olsen C., Devore J. Introduction to Statistics & Data Analysis. ISBN-13: 978-0-495-11873-2
5. Stewart J., Day T. Biocalculus. Calculus for the Life Sciences. ISBN-13: 978-1-133-10963-1

Further reading

1. Grīnglazs L., Kopitovs J. Matemātiskā statistika: Ar datoru lietojuma paraugiem uzdevumu risināšanai: Mācību līdzeklis. Rīga: Rīgas Starptautiskā ekonomikas un biznesa administrācijas augstkola, 2003. 310 lpp.
2. Uzdevumu krājums augstākajā matemātikā. / Dz.Bože, L.Biezā, B.Siliņa, A.Strence. Rīga: Zvaigzne, 2001. 332 lpp.
3. Bird J. Engineering Mathematics. ISBN 9781138673595

Notes

The study course is included in the compulsory part of the master’s study program “Forest Science”.