MATH42120: Probability

• Complex Analysis and Analysis in Many Variables and Probability.

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• To build a logical structure on probabilistic intuition, and to cover such peaks of the subject as the Strong Law of Large Numbers and the Central Limit Theorem, as well as more modern topics.

• Introductory examples.
• Coin tossing and trajectories of random walks.
• Discrete renewal theory.
• Limit theorems and convergence.
• Order statistics.
• Non-classical limits and their applications.
• Stochastic order.
• Additional topics in advanced probability.

Subject-specific Knowledge:

• By the end of the module students will: be able to solve complex, unpredictable and specialised problems in Probability.
• have an understanding of specialised and complex theoretical mathematics in the field of Probability.
• have mastered a coherent body of knowledge of these subjects demonstrated through one or more of the following topic areas:
• Random walks.
• Convergence theorems.
• Discrete renewal theory.
• Advanced applications of probability.

Subject-specific Skills:

• In addition students will have highly specialised and advanced mathematical skills in the following areas: Modelling, Computation.

Key Skills:

• Students will be able to study independently to further their knowledge of an advanced topic.

• Lectures demonstrate what is required to be learned and the application of the theory to practical examples.
• Subject material assigned for independent study develops the ability to acquire knowledge and understanding without dependence on lectures.
• Assignments for self-study develop problem-solving skills and enable students to test and develop their knowledge and understanding.
• Formatively assessed assignments provide practice in the application of logic and high level of rigour as well as feedback for the students and the lecturer on students' progress.
• The end-of-year examination assesses the knowledge acquired and the ability to solve complex and specialised problems. The Subject material assigned for independent study will form part of the examined material.

Eight written or electronic assignments to be assessed and returned. Other assignments are set for self-study and complete solutions are made available to students.

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