Introductory description

This module is an introduction mathematical proof and its applications to probability. The module introduces the topics of set theory, counting, probability and expectation and looks at the methods of proof needed to produce fundamental results in these areas. At its core is the aim to allow students to develop logical arguments applied to sets and simple experiments involving probabilistic outcomes.

This module is core for students with their home department in Statistics and is not available to students from other departments. Students from other departments should consider ST120 Introduction to Probability. It is useful for all subsequent modules in probability or statistics.

Module web page

Module aims

Outline syllabus

This is an indicative module outline only to give an indication of the sort of topics that may be covered. Actual sessions held may differ.

This module covers the following topics: naïve set theory, logic, counting arguments, probability spaces and axioms, conditional probability, random variables, joint distributions, expectation.

Learning outcomes

By the end of the module, students should be able to:

• interpret mathematical notation accurately
• compare problem solving and visualisation techniques to compile concise, coherent and rigorous mathematical arguments
• calculate and interpret probabilistic computations
• know and interpret key notions relating to random variables and their distributions.

Indicative reading list

Ross, S. (2014). A first course in probability. Pearson;
Pitman, J. (1999). Probability, Springer texts in Statistics;
Suhov and Kelbert, Probability and Statistics by Example: Basic Probability and Statistics.

View reading list on Talis Aspire

Subject specific skills

• Demonstrate facility with advanced mathematical and probabilistic methods. 
• Select and apply appropriate mathematical and/or statistical techniques.
• Demonstrate knowledge of key mathematical and statistical concepts, both explicitly and by applying them to the solution of mathematical problems.
• Create structured and coherent arguments communicating them in written form. 
• Reason critically, carefully, and logically and derive (prove) mathematical results.

Transferable skills

• Problem solving: Use rational and logical reasoning to deduce appropriate and well-reasoned conclusions. Retain an open mind, optimistic of finding solutions, thinking laterally and creatively to look beyond the obvious. Know how to learn from failure.

• Self awareness: Reflect on learning, seeking feedback on and evaluating personal practices, strengths and opportunities for personal growth.

• Communication: Written: Present arguments, knowledge and ideas, in a range of formats.

• Verbal communication: Students will engage with their personal tutors and peers in mathematical dialogue concerning questions from the module.

• Professionalism: Prepared to operate autonomously. Aware of how to be efficient and resilient. Manage priorities and time. Self-motivated, setting and achieving goals, prioritising tasks.