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DEGREE REGULATIONS & PROGRAMMES OF STUDY 2019/2020

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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
Credit level (Normal year taken)SCQF Level 10 (Year 4 Undergraduate) AvailabilityAvailable to all students
SCQF Credits10 ECTS Credits5
SummaryThe central topic of this course is measure theory. Measure theory is the foundation for advanced topics in Analysis and Probability.
Course description The course will cover many of the following topics:
Random events, sigma-algebras, monotone classes.
Measurable spaces, random variables - measurable functions.
Measures, probability measures, signed measures.
Borel sets in R^d, Lebesgue measure. Caratheodory extension theorem.
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.
Weak 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: 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-requisitesNone
High Demand Course? Yes
Course Delivery Information
Academic year 2019/20, 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%
Feedback Not entered
Exam Information
Exam Diet Paper Name Hours & Minutes
Main Exam Diet S1 (December)2:00
Learning Outcomes
On completion of this course, the student will be able to:
  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.
  3. To provide students with further experience in constructing proofs for previously unseen results.
Reading List
None
Additional Information
Course URL https://info.maths.ed.ac.uk/teaching.html
Graduate Attributes and Skills Not entered
KeywordsEAP
Contacts
Course organiserProf Istvan Gyongy
Tel: (0131 6)50 5945
Email: I.Gyongy@ed.ac.uk
Course secretaryMrs Alison Fairgrieve
Tel: (0131 6)50 5045
Email: Alison.Fairgrieve@ed.ac.uk
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