The lecture notes for Monday's Lecture 2 (Combinatorial analysis) are now available. I will always make notes available shortly before the lecture.
You should already be able to do Questions 1, 2 on Examples Sheet 1. These questions require no more than use of the definition of classical probability.
I give you course notes so that you can dispense with some tedious copying-out, you can listen better, and you are guaranteed to have an accurate account. But I know there is a danger that this might induce complacency. Writing during a lecture helps to keep engaged, and so I hope you will still do some of that. I think Tom Korner makes a good point when he writes "many mathematicians find it easier to learn from lectures than from books ... We learn more by watching a house being built than by inspecting it afterwards." (See page 3 of his treatise In Praise of Lectures.) In Lecture 1 I told you how Probability IA can prepare you for a well-paid career, mentioned my treasonable conversation about the Lottery with HM, and emphasised repeatedly what I most wanted to you to remember: the definition of classical probability. Can you complete this sentence? Classical probability is concerned with situations in which ...
I hope you experience a process of a building of the theory of Probability and understand why Probability is subject I enjoy; I always intend to say some things that are not in the notes, and elaborate explanations of things that are.
For most of us, learning mathematics requires repeated exposure to ideas. So I hope that a combination of reading, listening, writing and solving problems will work well for you in this course.
You should already be able to do Questions 1, 2 on Examples Sheet 1. These questions require no more than use of the definition of classical probability.
I give you course notes so that you can dispense with some tedious copying-out, you can listen better, and you are guaranteed to have an accurate account. But I know there is a danger that this might induce complacency. Writing during a lecture helps to keep engaged, and so I hope you will still do some of that. I think Tom Korner makes a good point when he writes "many mathematicians find it easier to learn from lectures than from books ... We learn more by watching a house being built than by inspecting it afterwards." (See page 3 of his treatise In Praise of Lectures.) In Lecture 1 I told you how Probability IA can prepare you for a well-paid career, mentioned my treasonable conversation about the Lottery with HM, and emphasised repeatedly what I most wanted to you to remember: the definition of classical probability. Can you complete this sentence? Classical probability is concerned with situations in which ...
I hope you experience a process of a building of the theory of Probability and understand why Probability is subject I enjoy; I always intend to say some things that are not in the notes, and elaborate explanations of things that are.
For most of us, learning mathematics requires repeated exposure to ideas. So I hope that a combination of reading, listening, writing and solving problems will work well for you in this course.
Logging you in...
S. Holmes · 585 weeks ago
While procrastinating example sheets with more pressing deadlines, I found myself doing q13 on the first probability example sheet, and despite the fact it was an interesting problem with what I thought was quite a surprising solution, what struck me most was the names used.
And so I come to this blog with one question and one question only, that has been plauging me since I did the problem: were the names 'John' and 'Mary' Sherlock inspired, or is it but a complete coincidence? If yes, then can I say congratulations on adding a bit of joviality to what otherwise may have been a dry Sunday. If it is but a happy coincidence, then alas, but at least my procrastination was aided ever so slightly by writing this comment.
I eagerly await your reply to this question which has been debated fiercely amongst my friends and I ever since I did problem 13.
Thank you kindly,
S. Holmes
PS: Keep up the good work with the lecturing! (but turn on the microphone please, that was the noise last time I think!)
Richard Weber 35p · 585 weeks ago
You will probably notice that tripos and examples sheet questions in probability are of two types: those that look pure mathematics questions (mathematics symbols, identities, inequalities and limits), and those that are set in the context of a story (sometimes trying to relate to real life or a real physical process). Think how you might rephrase the John and Mary question in the former way, leaving out the words, "John", "Mary" or "coin". Would it be as memorable?