About these notes. Many people have written excellent notes for introductory
courses in probability. Mine draw freely on material prepared by others in presenting this course to students at Cambridge. I wish to acknowledge especially Geoffrey
Grimmett, Frank Kelly and Doug Kennedy.
The order I follow is a bit different to that listed in the Schedules. Most of the material
can be found in the recommended books by Grimmett & Welsh, and Ross. Many of the
examples are classics and mandatory in any sensible introductory course on probability.
The book by Grinstead & Snell is easy reading and I know students have enjoyed it.
There are also some very good Wikipedia articles on many of the topics we will consider.
In these notes I attempt a ‘Goldilocks path’ by being neither too detailed or too brief.
• Each lecture has a title and focuses upon just one or two ideas.
• My notes for each lecture are limited to 4 pages.
I also include some entertaining, but nonexaminable topics, some of which are unusual
for a course at this level (such as random permutations, entropy, reflection principle,
Benford and Zipf distributions, Erd˝
os’s probabilistic method, value at risk, eigenvalues
of random matrices, Kelly criterion, Chernoff bound).
You should enjoy the book of Grimmett & Welsh, and the notes notes of Kennedy.
Printed notes, good or bad? I have wondered whether it is helpful or not to
publish full course notes. On balance, I think that it is. It is helpful in that we can
dispense with some tedious copying-out, and you are guaranteed an accurate account.
But there are also benefits to hearing and writing down things yourself during a lecture,
and so I recommend that you still do some of that.
I will say things in every lecture that are not in the notes. I will sometimes tell you when
it would be good to make an extra note. In learning mathematics repeated exposure
to ideas is essential. I hope that by doing all of reading, listening, writing and (most
importantly) solving problems you will master and enjoy this course.
I recommend Tom K¨
orner’s treatise on how to listen to a maths lecture.