THE UNIVERSITY of EDINBURGH

DEGREE REGULATIONS & PROGRAMMES OF STUDY 2013/2014 -
- ARCHIVE as at 1 September 2013 for reference only
THIS PAGE IS OUT OF DATE

University Homepage
DRPS Homepage
DRPS Search
DRPS Contact
DRPS : Course Catalogue : School of Mathematics : Mathematics

Undergraduate Course: Essentials in Analysis and Probability (MATH10047)

Course Outline
SchoolSchool of Mathematics CollegeCollege of Science and Engineering
Course typeStandard AvailabilityAvailable to all students
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) Credits10
Home subject areaMathematics Other subject areaSpecialist Mathematics & Statistics (Honours)
Course website https://info.maths.ed.ac.uk/teaching.html Taught in Gaelic?No
Course descriptionRandom 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.
Entry Requirements (not applicable to Visiting Students)
Pre-requisites Students MUST have passed: Complex Variable & Differential Equations (MATH10033) AND Pure & Applied Analysis (MATH10008)
Co-requisites
Prohibited Combinations Other requirements None
Additional Costs None
Information for Visiting Students
Pre-requisitesNone
Displayed in Visiting Students Prospectus?Yes
Course Delivery Information
Not being delivered
Summary of Intended 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.
Assessment Information
Examination only.
Special Arrangements
None
Additional Information
Academic description Not entered
Syllabus Not entered
Transferable skills Not entered
Reading list Not entered
Study Abroad Not entered
Study Pattern Not entered
KeywordsEAP
Contacts
Course organiserDr Tom Mackay
Tel: (0131 6)50 5058
Email: T.Mackay@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
Navigation
Help & Information
Home
Introduction
Glossary
Search DPTs and Courses
Regulations
Regulations
Degree Programmes
Introduction
Browse DPTs
Courses
Introduction
Humanities and Social Science
Science and Engineering
Medicine and Veterinary Medicine
Other Information
Combined Course Timetable
Prospectuses
Important Information
 
© Copyright 2013 The University of Edinburgh - 10 October 2013 4:51 am