COURSE GOALS: After finishing this course students will be able to demonstrate knowledge and understanding of fundamental laws and principles of combinatorics, statistics and experimental data analysis and to implement them in their future education and work as teachers. Special attention is given to the basic distributions (Binomial, Gauss, log-normal) and to the implementation of the least square methods to various problems, since they are essential for their future education. Also, the students are expected to demonstrate knowledge and understanding of basic computer software from the field of statistics (Excel, Statistica, QPlot). After finishing the course they are expected to perform total statistical analysis of the experimental data, but also to perform statistical analysis of their pupils results. They should be able to perform this analysis not only qualitatively, but also quantitatively with the aid of different software.
LEARNING OUTCOMES AT THE LEVEL OF THE PROGRAMME:
1. KNOWLEDGE AND UNDERSTANDING
1.1. demonstrate a thorough knowledge and understanding of the fundamental laws of classical and modern physics;
1.2. demonstrate a thorough knowledge and understanding of the most important physics theories (logical and mathematical structure, experimental support, described physical phenomena);
1.3. demonstrate knowledge and understanding of basic experimental methods, instruments and methods of experimental data processing in physics;
1.4. demonstrate knowledge and understanding of new insights into contemporary physics teaching methods and strategies;
1.5. describe the framework of natural sciences;
2. APPLYING KNOWLEDGE AND UNDERSTANDING
2.1. identify and describe important aspects of a particular physical phenomenon or problem;
2.2. recognize and follow the logic of arguments, evaluate the adequacy of arguments and construct well supported arguments;
2.5. use information and communication technology efficiently (to foster active enquiry, collaboration and interaction in the classroom);
3. MAKING JUDGMENTS
3.1. develop a critical scientific attitude towards research in general, and in particular by learning to critically evaluate arguments, assumptions, abstract concepts and data;
4. COMMUNICATION SKILLS
4.2. present complex ideas clearly and concisely;
4.4. use the written and oral English language communication skills that are essential for pursuing a career in physics and education;
5. LEARNING SKILLS
5.1. search for and use professional literature as well as any other sources of relevant information;
5.2. remain informed of new developments and methods in physics and education;
5.3. develop a personal sense of responsibility for their professional advancement and development;
5.4. demonstrate professional integrity and ethical behaviour in work with pupils and colleagues;
LEARNING OUTCOMES SPECIFIC FOR THE COURSE:
1. Students are expected to be able to qualitatively solve problems from the area of combinatorics (combinations, permutations, variations).
2. They should be able to quantitatively solve problems from the area of basic distributions of experimental data (normal, log-normal, binomial and Poisson's distributions).
3. They should be able to qualitatively describe different types of errors that may come up during the experimental measurements.
4. They should be able to qualitatively determine basic parameters in the least square methods applied to the experimental data, and qualitatively know how and when to apply the method.
COURSE DESCRIPTION:
Course topics by the week:
1. Basic elements of statistics (population, sample, descriptive and inductive statistics, graphical and table methods, histograms).
2. Basic elements of combinatorics (permutations, combinations, variations).
3. Probability theory - basic concepts and definitions, set theory, mutually excluding or non-excluding events, geometrical probability).
4. Conditional probability and statistics, Bayes theorem.
5. Random variable, discrete and continuous, cumulative distribution function.
6. Characterization of random variable, scattering criterion, moments.
7. Binomial distribution.
8. Poisson distribution, concept of an integral, probability density function.
9. Normal (Gauss) distribution.
10. Multidimensional random variable and the theory of error.
11. Theory of error and linear regression.
12. Least squares method.
13. Choice of statistical computer software applicable to problems in science and technology.
14. Repetition and systematization.
REQUIREMENTS FOR STUDENTS:
Students are required to attend at least 75% of lectures and auditory exercises. Furthermore, they are required to attend two colloquiums (if the total score is above 50% they are not obliged to attend the practical part of the exam).
GRADING AND ASSESSING THE WORK OF STUDENTS:
If the students pass the colloquiums, they are not obliged to attend the written part of the exam and they have oral exam directly. Oral exam consists of several questions from the theory covered in the course. If the students do not pass the colloquiums, they have to attend the written part of the exam which consist of several numerical problems, and after passing that they have to attend the oral part of the exam. Active participation in the discussions during the lectures/auditory exercises is also highly valued and constitutes a part of the final grade.
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- Pavlić, Statistička teorija i primjena, Tehnička knjiga, Zagreb 1970.
Vranić, Vjerojatnost i statistika, Tehnička knjiga, III izdanje, Zagreb, 1970.
(selekcija prikladnih poglavlja, s napomenom "za internu upotrebu", već se nalazi u knjižnici Fizičkog Odsjeka)
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