Undergraduate Course: Essentials in Analysis and Probability (MATH10047)

Course Outline
School	School of Mathematics	College	College of Science and Engineering
Credit level (Normal year taken)	SCQF Level 10 (Year 4 Undergraduate)	Availability	Available to all students
SCQF Credits	10	ECTS Credits	5
Summary	Random events, sigma-algebras, monotone classes. Measurable spaces, random variables - measurable functions. Measures, probability measures, signed measures. Borel sets in R^d, Lebesgue measure. Sequences of events and random variables, Borel-Cantelli lemma. Distributions of random variables. Independence of random variables. Integral of measurable functions - mathematical expectation,. Moments of random variables, L_p spaces. Convergence concepts of measurable functions. Limit theorems for integrals. Week and strong laws of large numbers. Completeness of L_p spaces. Conditional expectation and conditional distribution of random variables. Fubini's theorem.
Course description	Not entered

Entry Requirements (not applicable to Visiting Students)
Pre-requisites	Students MUST have passed: Honours Complex Variables (MATH10067) AND Honours Differential Equations (MATH10066) AND Honours Analysis (MATH10068)	Co-requisites
Prohibited Combinations		Other requirements	None

Information for Visiting Students
Pre-requisites	None

Course Delivery Information

Academic year 2015/16, Available to all students (SV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info)	Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 5%, Examination 95%
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Exam Information
Exam Diet	Paper Name		Hours & Minutes
Main Exam Diet S1 (December)	MATH10047 Essentials in Analysis and Probability		2:00

Academic year 2015/16, Part-year visiting students only (VV1)		Quota: None
Course Start	Semester 1
Timetable	Timetable
Learning and Teaching activities (Further Info)	Total Hours: 100 ( Lecture Hours 22, Seminar/Tutorial Hours 5, Summative Assessment Hours 2, Programme Level Learning and Teaching Hours 2, Directed Learning and Independent Learning Hours 69 )
Assessment (Further Info)	Written Exam 95 %, Coursework 5 %, Practical Exam 0 %
Additional Information (Assessment)	Coursework 5%, Examination 95%
Feedback	Not entered
No Exam Information

Learning Outcomes
1. To provide the students with the basic notions and results from measure theory and integration, motivating them by fundamental concepts of probability theory. 2. To prepare a firm ground for further studies in analysis, in modern probability theory and in their applications.