ST11815 Probability 1
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 aims
The aims of the modules are
 to introduce students to the nature of mathematics as an academic discipline;
 to develop mathematical comprehension and reasoning skills in a concepts and prooforiented setting;
 to develop communication skills in mathematics including proof writing;
 to develop systematic problemsolving skills;
 to lay the foundation for concurrent and subsequent modules in probability and statistics by introducing the key notions of mathematical probability;
 to introduce the techniques for calculating with probabilities and expectations.
 to build a foundation for independent learning including selfregulation and assessment literacy.
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 wellreasoned 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. Selfmotivated, setting and achieving goals, prioritising tasks.
Study time
Type  Required 

Lectures  30 sessions of 1 hour (20%) 
Seminars  9 sessions of 1 hour (6%) 
Private study  85 hours (57%) 
Assessment  26 hours (17%) 
Total  150 hours 
Private study description
Weekly revision of lecture notes and materials, wider reading and practice exercises working on problem sets and preparing for the examination.
Costs
No further costs have been identified for this module.
You do not need to pass all assessment components to pass the module.
Assessment group D
Weighting  Study time  

Weekly termtime assignments  20%  24 hours 
There will be weekly problem sets, of which up to six will contribute towards your module mark. Each problem set will contain a number of individual questions based on the material delivered in the lectures. Weekly problem sheets supported by seminars, including both analytical and computational tasks. 

Inperson Examination  80%  2 hours 
You will be required to answer all questions on this examination paper.

Assessment group R
Weighting  Study time  

Inperson Examination  Resit  100%  
You will be required to answer all questions on this examination paper.

Feedback on assessment
Individual feedback will be provided on problem sheets by class tutors. A cohortlevel feedback will be available for the examination. Students are actively encouraged to make use of office hours to build up their understanding, and to view all their interactions with lecturers and class tutors as feedback.
Courses
This module is Core for:
 Year 1 of USTAG302 Undergraduate Data Science
 Year 1 of USTAG304 Undergraduate Data Science (MSci)
 Year 1 of USTAG300 Undergraduate Master of Mathematics,Operational Research,Statistics and Economics
 Year 1 of USTAG1G3 Undergraduate Mathematics and Statistics (BSc MMathStat)
 Year 1 of USTAGG14 Undergraduate Mathematics and Statistics (BSc)
 Year 1 of USTAY602 Undergraduate Mathematics,Operational Research,Statistics and Economics