Introductory description

It is a special module for the students returning from TWD in January to help them to integrate into the new curriculum framework.

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.

• Continuity
• Uniform continuity
• Discrete and continuous probability spaces
• Conditioning and independence, Bayes' theorem
• Random variables
• Moment generating functions

Learning outcomes

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

• learn the properties of continuous and uniformly continuous functions
• describe and interpret experiments with random outcomes using mathematical probability
• know and apply the theory of probability distributions, expectation, variance, and covariance associated with random variables

Indicative reading list

M. Hart, Guide to Analysis, Macmillan.
M. Spivak, Calculus, Benjamin. R.G Bartle and D.R Sherbert, Introduction to Real Analysis (4th Edition), Wiley (2011)
L. Alcock, How to think about Analysis, Oxford University Press (2014)
Richard Durrett, (2009), Elementary Probability for Applications, Cambridge University Press, New York
Geoffrey Grimmett; D. J. A. Welsh, (2014), Probability - An Introduction, Oxford University, Oxford.
Geoffrey Grimmett, (2020) One Thousand Exercises in Probability. Third Edition, Oxford University Press.

Subject specific skills

Demonstrate facility with advanced mathematical and probabilistic methods.  

Gain working knowledge of continuous and uniformly continuous functions.

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 skills: The module requires students to solve problems presenting their conclusions as logical and coherent arguments.

Written communication: Written work requires precise and unambiguous communication in the manner and style expected in mathematical sciences. 

Verbal communication: Dialogue with class tutors around problems prepared for each class.

Teaming working and working effectively with others: Students are encouraged to discuss and debate formative assessment and lecture material within small-group tutorials sessions.

Professionalism: Students work autonomously by developing and sustain effective approaches to learning, including time management, organisation, flexibility, creativity, collaboratively and intellectual integrity.