Probability and Combinatorics is a comprehensive mathematics course that explores the mathematics of counting, chance, and uncertainty. Students develop a deep understanding of how probabilities are calculated, how large numbers of possible outcomes can be counted efficiently, and how mathematical models can be used to predict and analyse uncertain events. Beginning with the foundations of probability and systematic counting techniques, the course progresses through combinatorics, probability distributions, Bayesian reasoning, simulations, and real-world applications. Throughout the course, students develop logical reasoning, analytical thinking, and problem-solving skills that are essential across mathematics and many scientific disciplines.
Students investigate theoretical and experimental probability, conditional probability, permutations, combinations, random variables, expected value, probability distributions, and advanced topics such as Bayes' Theorem, Markov processes, and Monte Carlo simulation. They also examine practical applications in finance, computer science, engineering, artificial intelligence, cryptography, genetics, and decision making under uncertainty. By combining rigorous mathematical techniques with authentic real-world examples, students gain a strong foundation for further study in mathematics, statistics, computer science, economics, engineering, actuarial science, and data science.
- Giáo viên: Mr. Young