Handout Zero: Memorandum of Understanding File 220.4KB PDF document
What is the course about? What is expected from the students? What are the expectations of the students from a course like this one on mathematics? I feel that for issues such as these to be meaningfully examined, the stage is best set by agreeing to some kind of broad mutual understanding right at the start of the course. "Memorandum of Understanding" as I have called this document, is meant to do just that. I hope it does.
This piece attempts to lay down the basic idea that has led to the introduction of this course.
A very good introductory presention of the basic ideas and history of representational measurement theory.
In addition to his seminal monograph, `Algebra of Probable Inference', this paper of his is an equally important contribution in the theory
of probability. Relate what i have tried to convey in the lectures to the ideas put forth here.
A very lucid and readable presentation of the significance of Cox's approach in the general context of characterizing measurable attributes of what we perceive of the world.
A good paper that should be read with Cox's book.
Boolean algebra is commonly understood to have many separate applications. It is used in the design of logic circuits. It is the backbone of probability theory, and so on. It is time that you looked at boolean algebra within a broader framework, that of posets and lattices. More on this in the lectures. For the present try to absorb what Knuth has to say.
Related to logic, boolean algebra, probability theory, this is another of Kevin Knuth's (Do not confuse him with Donald Knuth) very engaging paper. Do take a look.
An interesting discussion on how to structure proofs. I first noticed this paper in 1985.
Could we make proofs more human? Proofs are generally terrifying, and the thought of having to go through them unpleasant. The way they are commonly presented, they seem to be rigid and unresponsive to the readers queries, cold and take-it-or-leave-it stuff. On the whole machine-like.
Turning to logicians is of no help. Actually there are no logicians left; they have all taken to fabricating machines -- turing machines, generalized turing machines, and maybe 3-phase turing machines.
So, can we on our own do something to ease the situation, at least for the purposes of teaching? Could we make proofs more `human', combining pleasure with learning? Are there some general guidelines that we could follow in this endeavour? Leron's suggestions might be of help.
A `tongue-in-cheek' slogan: Rigour dehumanizes, and absolute rigour dehumanizes absolutely'
In talking about a system as a black box, I mentioned in one of the lecture that the idea is linked with the philosophical position known as pragmatism. This paper expands this viewpoint.
Weekly outline
22 July - 28 July
As I have tried to convey to you in my Handout Zero, writing is an integral part of your daily activities.These notes are very helpful in this connection. I am sure you are familiar with the pioneering contributions of Knuth. If you are not, then do look him up on the net.
This is a pdf version of the hand written notes with the same title.
Aside: Music of the Week: I recommend Vishwa Mohan Bhatt on Guitar, or rather on Mohan veena (a hybrid of guitar and veena,
innovated by him). You can start with his youtube recordings, titled `Galaxy of Strings', which starts off with raga bageshari,
and hansdhwani.
29 July - 4 August
5 August - 11 August
12 August - 18 August
19 August - 25 August
26 August - 1 September
2 September - 8 September
9 September - 15 September
This is a template assiginment sheet. Do all the problems.
16 September - 22 September
23 September - 29 September
This set of problems is rather an unconventional one. Some of the problems are for `doing', so to say. Loke Exercises 1 to 7. The rest are like notes that i would like you to go over, and check for their correctness. You will find Axler a good support in doing that.
30 September - 6 October
7 October - 13 October
14 October - 20 October
21 October - 27 October
28 October - 3 November
4 November - 10 November
11 November - 17 November
18 November - 24 November
25 November - 1 December