Then and Now
I landed in the Netherlands at around 2300 on 23 October 2005. That means tomorrow will mark three months since I arrived. Looking back over this time, I am pleasantly surprised to see what a difference three months has made to me. In this article I record my mathematical development. I do this for two reasons. First, such an article will be nice to read a few years down the line. Second, it always feels nice to record progress.
Lets dive right in.
I used to struggle while reading several (mathematical) works, but now I am a whole lot more fluent with the same material. I used to barely mumble out sentences (at least that was my impression!), but now I find myself talking a lot more confidently about mathematics. I am less hesitant about asking questions and more willing to provide my opinions.
Earlier, I could barely understand certain fundamental mathematical concepts, and any proof which appealed to them was very hard for me to grasp. Now these same concepts (monotonicity anyone?) are second nature to me and thus a whole class of proof techniques and heuristics have been added to my mathematical toolkit.
My ability with formal program derivation has finally materialized. I now can read formal derivations and understand them and also perform my own derivations with a certain comfort. However I still have a long way to go and there are many techniques to learn and programs to create, but I have got a foothold on the cliff and I love the view from up here.
My appreciation of science, technology and mathematics has become more refined. Especially in the last few weeks I have been doing a lot of introspection about what I am studying and its utility in the production of software systems. I am now convinced more than ever that these methods and this training has potential to boost programmer productivity and software quality like nothing else. It really addresses the core concerns as far as I see. As a result of these insights I am more excited than ever about what I am doing and I have a stronger justification as to why it is worth it.
I have been exposed to mathematical writing the like of which I have never seen before. Wim Feijen and Netty van Gasterens book "On a Method of Multiprogramming" is probably the best book I have ever read (and this includes Dijkstra). They way it seperates concerns and utilizes mathematics to bridle the complexity in the extremely complex discipline of multiprogramming is a joy to behold. It is an inspiration. I can't contain a smile while reading it and often it induces me to let out a low whistle. Such is the beauty. Additionally, seeing Wim Feijen talk and work has allowed me to gain insight into the kind of discipline in thought that is required to write such a book. I have tried to pick up his habits up in the hope that one day I would also be able to produce writing of this standard.
So much for my mathematical development. I have more to write about personal and social development, but I will leave that for another time.
Lets dive right in.
I used to struggle while reading several (mathematical) works, but now I am a whole lot more fluent with the same material. I used to barely mumble out sentences (at least that was my impression!), but now I find myself talking a lot more confidently about mathematics. I am less hesitant about asking questions and more willing to provide my opinions.
Earlier, I could barely understand certain fundamental mathematical concepts, and any proof which appealed to them was very hard for me to grasp. Now these same concepts (monotonicity anyone?) are second nature to me and thus a whole class of proof techniques and heuristics have been added to my mathematical toolkit.
My ability with formal program derivation has finally materialized. I now can read formal derivations and understand them and also perform my own derivations with a certain comfort. However I still have a long way to go and there are many techniques to learn and programs to create, but I have got a foothold on the cliff and I love the view from up here.
My appreciation of science, technology and mathematics has become more refined. Especially in the last few weeks I have been doing a lot of introspection about what I am studying and its utility in the production of software systems. I am now convinced more than ever that these methods and this training has potential to boost programmer productivity and software quality like nothing else. It really addresses the core concerns as far as I see. As a result of these insights I am more excited than ever about what I am doing and I have a stronger justification as to why it is worth it.
I have been exposed to mathematical writing the like of which I have never seen before. Wim Feijen and Netty van Gasterens book "On a Method of Multiprogramming" is probably the best book I have ever read (and this includes Dijkstra). They way it seperates concerns and utilizes mathematics to bridle the complexity in the extremely complex discipline of multiprogramming is a joy to behold. It is an inspiration. I can't contain a smile while reading it and often it induces me to let out a low whistle. Such is the beauty. Additionally, seeing Wim Feijen talk and work has allowed me to gain insight into the kind of discipline in thought that is required to write such a book. I have tried to pick up his habits up in the hope that one day I would also be able to produce writing of this standard.
So much for my mathematical development. I have more to write about personal and social development, but I will leave that for another time.
posted by Apurva at
3:07 PM
1 Comments:
Indeed, I too have read A method of Multiprogramming, though it will be many more re-readings before I can say I have truly absorbed its teachings. My first introduction to concurrency/multiprogramming was through FSP and it is quite interesting how Feijen/van Gasteren's approach differs.
I must say, however that I feel a little uncomfortable with the semi-informal handling of progress, perhaps because my reasoning is not as honed as that of the authors but also because after spending so much time learning not to think operationally, suddenly we have to. Still, I think I need to study the book more before I can really decide what I think of this.
By
Eric, at January 23, 2006 12:32 PM
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