Mathematical models in chemistry

COURSE CURRICULUM 

1.

Course title

MATHEMATICAL METHODS IN CHEMISTRY

2.

Code

HM-332

3.

Study curriculum

Applied chemistry

4.

Organizer of the curriculum (institute, department)

Institute of Chemistry, Faculty of Natural Sciences and Mathematics

5.

Degree (BSc, MSc, PhD)

BSc

6.

Academic year/semester

II/III 

7.

ECTS points

4

8.

Lecturer

Prof. Dr. Igor Kuzmanovski

9.

Prerequisites

Mathematics I

10.

Course objectives (competences):
Students will be introduced to the basic, most frequently used mathematical methods/procedures in chemistry that will help students master part of the content of other subjects during their chemistry studies.

11.

Course content:
–    Elements of probability theory (statistical and theoretical probability, basic and other properties of probability, conditional probability, random variables, numerical characteristics of random variables);
–    Elements of statistics (descriptive statistics, normal distribution, statistical tests, first and second type errors);
–    Modeling of chemical data (correlation coefficient, linear regression, calculation of errors in the dependent variable, detection limit, multivariable linear regression, non-linear modeling methods);
–    Optimization and design of experiments (stochastic and systematic optimization, two-level factorial design, three-level factorial design, assessment of the factor effects, statistical assessment of the factor effects, проценка на ефектот на факторите, статистичка проценка на ефектот на факторите, sequential optimization - simplex optimization);
–    Factor-analytical methods (application of characteristic vector analysis,  noise reduction in data with factor-analytic methods, target factor analysis, characteristic vector regression, partial least squares regression).
–    Numerical exercises: Elements of probability theory (random events and probability, properties of probability, conditional probability); Elements of statistical inference (confidence intervals, comparison of mean values, comparison of variances, tests for extreme values, checking of correlation between two measured values); Optimization and design of experiments (estimation of the effect of factors in factorial designs at two or three levels); Characteristic vector analysis.

12.

Teaching methods: lectures, problem solving

13.

Total available time

120

14.

Time distribution

3+2+0 hours weekly (lectures: 45 hours;
problem solving: 30 hours)

15.

Teaching methods distribution

15.1.

Teaching - lectures

45 hours

15.2.

Practicals (laboratory, problem solving), seminars, team work

30 hours

16.

Other activities

16.1.

Projects

0 hours

16.2.

Independent work

10 hours

16.3.

Homework

35 hours

17.

Grading methods

17.1.

Tests

70 points

17.2.

Seminars/projects (written/oral presentation)

/ points

17.3.

Activity

 30 points

18.

Grading scale (points/mark)

< 50 points

5 (five) (F)

51 to 60 points

6 (six) (E)

61 to 70 points

7 (seven) (D)

71 to 80 points

8 (eight) (C)

81 to 90 points

9 (nine) (B)

91 to 100 points

10 (ten) (A)

19.

Criteria for taking the final exam

Attendance at lectures and completed exercises

20.

Course language

Macedonian

21.

Teaching quality control

Activity during lectures and practical work, assessment thorugh coloquia

22.

Literature

22.1.

Compulsory

No.

Author

Title

Publisher

Year

1.

I. Kuzmanovski

Chemometrics – application of mathematical and statistical methods in chemistry (reviewed unpublished textbook)

2.

M. Otto

Chemometrics: Statistics and Computer Application in Analytical Chemistry

Wiley-WCH, Weinheim

2007

3.

J.N. Miller, J.C. Miller

Statistics and Chemometrics for Analytical Chemistry

Prentice Hall, Harlow

2000

22.2.

Additional

No.

Author

Title

Publisher

Year

1.

Paul Gemperline ed.

Practical Guide to Chemometrics

Taylor & Francis

2006