Welcome to Real Analysis (MT3502).
Most of the information on this course, tutorial sheets etc., can be downloaded from
Moodle via MySaint (the course notes will be there and material will be made available in advance of the corresponding lectures, but the notes will be released in stages).
The official description of this course is here.
This course follows on from MT2502, so before taking it make sure you have revised the material in MT2502
- there is a short summary of that on the MT3502 Moodle page, which you should look at.
Lectures: Tue, Thur and "Even" Mon* 11am-12pm Lecture Theatre B
Tutorials: Tuesday 2pm-3pm in Theatre D, Thursday 3pm-4pm in Theatre A
*which means Monday of weeks 2, 4, 7, 9 and 11.
Contact Information
Lecturer: Mike Todd
Office: 320, Mathematical Institute
Email: m.todd -at- st-andrews.ac.uk
Course webpage: https://mtoddm.github.io/MT3502.html
Tutorials
The tutorials will primarily focus on the tutorial sheet questions for that week.
Each student should attend one tutorial per week, starting in week 2.
The School admin team will send emails explaining the process for you to sign up to either the Tuesday
or the Thursday slot, this will happen at some point before the end of Week 1.
Tutorial Sheets
There will be tutorial questions set for each week. These are not assessed, but you are strongly encouraged to
work through them each week prior to your tutorial. There will also be opportunities to get feedback on
work, the process for this will be announced in class: this will be voluntary and not part of assessment for the course.
Class test
There will be a class test 11am-12pm on Monday 28th October. This counts for 10% of your final mark.
Note that students entitled to extra time will be contacted by the admin team and their tests will be arranged around 11am-12pm on 28th Oct.
Recording
In line with University policy, and technology permitting, recordings of lectures and tutorials will be made available.
Topics covered
Countable and uncountable sets, including standard examples, basic properties, methods for showing sets are countable or uncountable.
Introduction to standard notions in metric and normed spaces, examples of such spaces and properties of them such as convergence and continuity.
Riemann integration, definition in terms of lower and upper sums, basic properties, integrability of continuous and monotonic functions; integral of the uniform limit of a sequence of functions; Fundamental Theorem of Calculus.
Power series, radius of convergence, differentiation and integration of power series.
Assessment
90% by two hour examination
10% by class test
Textbooks
John M. Howie, Real Analysis, Springer, 2016.
Robert G. Bartle & Donald R. Sherbert, Introduction to Real Analysis, 4th Edition, Wiley, 2011.
Kenneth Ross, Elementary Analysis, 2nd edition, Springer, 2014.
David Brannan, A First Course in Mathematical Analysis, CUP, 2006.
Wilson A. Sutherland, Introduction To Metric And Topological Spaces, Oxford 2010.
Robert Magnus, Metric spaces—a companion to analysis, Springer 2022.
DJH Garling, A Course in Mathematical Analysis, Vol.1, CUP, 2014. (More advanced)