Explaining mathematics

Videos are available from 2014-15, 2018-19, 2019-20 and 2020-21 editions of Foundations of Pure Mathematics (FPM)

The complete set of videos from the 2014-15 edition of Foundations of Pure Mathematics (FPM) is available on YouTube and iTunes. Since then, I have opened up some of the Echo360 recordings (also known as “Echoes”) from previous years. These have the (possible) advantage that you have two separate windows, one with the screen recording (the “screencast”) and one with the footage of me. These windows can be resized or hidden according to your taste! Another nice feature of these Echoes is that you can change the speed of the video if you find my pace either too slow or too fast. (This often varies from student to student, from lecture to lecture, and also within lectures). If you click on the settings cog near the bottom right of the video window, and click on the speed (default 1), there are plenty of options!

I don’t advise anyone to watch several versions of every class! But if there is a specific point you are interested in, then there is a possibility that I did say something different about it each year.

The 2018-19 edition of FPM is available at https://echo360.org.uk/section/4c490e8b-27f7-4fb8-b97f-251bad1ed2ad/public

The syllabus in 2018-19 was essentially the same as in 2014-15. But the syllabus then changed slightly in 2019-20. The main difference now is that the last topic from 2014-15 and 2018-19 (on countability and uncountability) is no longer in the syllabus for this module. Instead there is further coverage of equivalence relations and modular arithmetic, and some material on the Euclidean Algorithm for integers (See the new material in lectures 7b and 9b)

The 2019-20 edition of FPM is available at
https://echo360.org.uk/section/513af027-1220-409a-aa7a-711cb7567c33/public

Note that, because of industrial action, not all classes in 2019-20 were given live, so the set of videos is incomplete. However the new material is there, in lectures 7b and 9b.

In 2020-21, all of my teaching was online, due to the pandemic. I put together a set of lecture videos using my recordings from 2018-19 and 2019-20, and asked students to watch these, think about the questions asked in the videos, and attempt some Moodle quizzes to test their understanding. We then had online discussion/Q&A sessions on Teams, and we also held the Workshops online on Teams. The lecture videos are available from
https://echo360.org.uk/section/51b130f8-35dc-4f0e-b91a-3b75279d9d73/public

I have also made a TinyURL for this last set of videos: https://tinyurl.com/fpmvod20-21

Please let me know if there are problems with these links!