This week we will be taking a look at the module MA352 Real Analysis 1, which those of you studying for the Mathematics BSc and MMath, Mathematics and Statistics BSc, Mathematics with Secondary Education BSc and the Financial Mathematics BSc will take in the Autumn.

Real Analysis 1 is all about real numbers, as well as sequences of real numbers and functions or a real variable. The course is taught by Dr Marina Iliopoulou, who in this video will give you a little preview of the sort of exciting problems you will be able to solve. She will be imagining a doomed expedition to the Antarctic only saved by the Intermediate Value Theorem!

Before you watch the video, here is a short explanation of what the Intermediate Value Theorem is about. Consider a *continuous* function *f* (which means you can draw its graph without needing to take your pencil off the paper), such that *f(x)* is defined for any *a ≤ x ≤ b*. Then the function *f* must reach any value between *f(a)* and *f(b)*, as shown in the figure below.

Now without further ado, here is the video.

If it feels like it was ages ago that you studied for your A levels, or if you missed out on some content due to Covid-19 disruption, here are some online resources to prepare you for this course. Obviously, we don’t expect you to complete all of it, but do look at it to see if there is anything that triggers your curiosity!

HELM Workbooks were written by universities with content ranging from the start of A-Level to the end of your degree. There are many worked examples and exercises for you to practise. Of particular relevance to MA352 are

- Chapter 2, Basic functions;
- Chapter 11, Differentiation;
- Chapter 12, Applications of differentiation (the first 2 bullet points only);
- Chapter 13, Integration;
- Chapter 16, Sequences and Series (with less emphasis, as you won’t be seeing series in this course).

Mathcentre has a course named “Mathematics and Statistics” which covers a wide range of topics with revision resources developed by universities. You can also test yourself as much as you want using randomly generated questions. For MA352 the most useful content are the three chapters on different proof methods.

__Note:__ Some of the tests are “flash” files that are outdated; please __only__ use the “Numbas” or “DEWIS” tests!

You may also like to keep and use the SMSAS A-Level Formula Sheet throughout your degree!

We hope you enjoy the video and the revision material, and we are looking forward to seeing you in September!