Faculty of Education · Secondary School Mathematics Education · Undergraduate
Course Objective
The aim of this course is to equip prospective primary school mathematics teachers with the fundamental concepts of probability theory, counting methods, random variables, and significant probability distributions, enabling them to apply these concepts in mathematical modeling and problem-solving.
Course Content
The basic principle of counting; Permutation concept and applications; Combination concept and applications; Binom's theorem; Concept of probability; Basic concepts of probability and probability axioms; Conditional probability and Bayes' theorem; Geometric probability problems; Random variable concept; Probability function; Probability density function; Expected value and variance of random variables; Moment generating functions and moments; Some discrete distributions; Bernoulli, binomial, geometric, hypergeometric, Poisson distributions; Some continuous distributions; Uniform distribution; Exponential distribution; Normal distribution and properties.
Required Resources
Özdemir, A.,Ş.,(2016), Eğitim İstatistiği, Marmara Üniversitesi Yayımevi
Akdeniz, F. (2017). Olasılık ve istatistik (19. bs.). Nobel Akademik Yayıncılık.
Course Learning Outcomes
- They can perform calculations based on the basic principles of counting, permutations, and combinations.
- They can apply the axioms of probability and the concept of conditional probability to problems.
- They can define and distinguish between discrete and continuous random variables.
- They can calculate the expected value, variance, and moments of random variables.
- They can recognize standard probability distributions (Binomial, Poisson, Normal, etc.) and apply them to real-life problems.
Core Area Distribution
Teaching Methods
Assessment & Evaluation
ECTS / Workload
| Activity | Quantity | Duration (h) | Total Workload |
|---|---|---|---|
| Course Duration (Including Exam Week) | 16 | 2 | 32 |
| Out of Class Study Period | 16 | 2 | 32 |
| Midterm | 1 | 5 | 5 |
| Quiz | 0 | 0 | 0 |
| Assignment | 0 | 0 | 0 |
| Practice | 0 | 0 | 0 |
| Final | 1 | 6 | 6 |
Course Schedule
| Week | Subject | Preparation |
|---|---|---|
| 1 | Counting Methods I: The basic principle of counting (multiplication and addition rules), the concept of permutations, applications of circular and repetitive permutations. | A preliminary study on the relevant chapter |
| 2 | Counting Methods II: The concept and properties of combinations, the binomial theorem and its expansion, and its relationship with Pascal's triangle. | A preliminary study on the relevant chapter |
| 3 | Introduction to Probability: Sample space, types of events, definition of probability (classical, frequency, axiomatic), axioms of probability, and fundamental theorems. | A preliminary study on the relevant chapter |
| 4 | Conditional Probability: Definition of conditional probability, multiplication rule, independent events, the exact probability theorem, and Bayes' Theorem. | A preliminary study on the relevant chapter |
| 5 | Geometric Probability and Random Variables: Geometric probability problems (length, area, volume). Introduction to the concept of random variables. | A preliminary study on the relevant chapter |
| 6 | Probability Functions: Discrete and continuous sample spaces. Probability mass function (PMF) and Probability density function (PDF). Cumulative distribution function (CDF). | A preliminary study on the relevant chapter |
| 7 | Measures of Central Tendency and Dispersion: Expected value, variance, and standard deviation of random variables. | A preliminary study on the relevant chapter |
| 8 | Moments: Moment generating functions (MGF), moments with respect to the origin and the mean. | A preliminary study on the relevant chapter |
| 9 | Midterm Exam | Midterm Exam |
| 10 | Discrete Probability Distributions: Bernoulli, Binomial, Geometric, Hypergeometric, and Poisson distributions; their properties and applications. | A preliminary study on the relevant chapter |
| 11 | Introduction to Continuous Probability Distributions: General properties of continuous distributions, general examples other than uniform distributions. | A preliminary study on the relevant chapter |
| 12 | Uniform Distribution: Discrete and continuous uniform distributions, graphs, expected value and variance calculations. | A preliminary study on the relevant chapter |
| 13 | Exponential Distribution: Definition of the exponential distribution, its relationship to the Poisson process, and its memory property. | A preliminary study on the relevant chapter |
| 14 | Normal Distribution I: Definition and properties of the normal (Gaussian) distribution, standard normal distribution (using Z-table). | A preliminary study on the relevant chapter |
| 15 | Normal Distribution II: Applications of the normal distribution, convergence of binomial and Poisson distributions to the normal distribution (introduction to the Central Limit Theorem). | A preliminary study on the relevant chapter |
| 16 | FINAL EXAM | Final Exam |