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Path to formal methods
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Problem
It is not uncommon to see students starting their PhDs with only a limited background in mathematics and the formal aspects of computer science. Obviously it will be very difficult for such students to become theoretical computer scientists, but it would be good if they could become savvy with using formal methods and reading papers that contain formal methods.
What is a good short term path that starting PhD students could follow to gain the expose required to get them reading papers involving formal methods and eventually writing papers that use such formal methods?
In terms of context, I'm thinking more in terms of Theory B and formal verification as the kinds of things that they should learn, but also classical TCS topics such as automata theory.
What is a good short term path that starting PhD students could follow to gain the expose required to get them reading papers involving formal methods and eventually writing papers that use such formal methods?
In terms of context, I'm thinking more in terms of Theory B and formal verification as the kinds of things that they should learn, but also classical TCS topics such as automata theory.
Solution
In the preface of his book “Mathematical Discovery, On Understanding, Learning, and Teaching Problems Solving” George Pólya writes:
Solving problems is a practical art, like swimming, or skiing, or
playing the piano: you can learn it only be imitation and practice.
This book cannot offer you a magic key that opens all the doors and
solves all the problems, but it offers you good examples for imitation
and many opportunities for practice: if you wish to learn swimming you
have to go into the water, and if you wish to become a problem solver
you have to solve problems.
I think there is no short path, especially for reaching the state of writing papers. It requires practice, a lot of it.
Some pointers:
If “limited background in mathematics and the formal aspects” means “has never conceived a proof and written it down” then something like this might be a start.
If something on the Theoretical Computer Science Cheat Sheet makes the student feel uneasy, then a refresher course of the according branch of mathematics would be advisable.
There are many sources for mathematical writing: The lecture notes of the 1978 Stanford University CS209 course perhaps. Or this article by Paul Halmos.
Solving problems is a practical art, like swimming, or skiing, or
playing the piano: you can learn it only be imitation and practice.
This book cannot offer you a magic key that opens all the doors and
solves all the problems, but it offers you good examples for imitation
and many opportunities for practice: if you wish to learn swimming you
have to go into the water, and if you wish to become a problem solver
you have to solve problems.
I think there is no short path, especially for reaching the state of writing papers. It requires practice, a lot of it.
Some pointers:
If “limited background in mathematics and the formal aspects” means “has never conceived a proof and written it down” then something like this might be a start.
If something on the Theoretical Computer Science Cheat Sheet makes the student feel uneasy, then a refresher course of the according branch of mathematics would be advisable.
There are many sources for mathematical writing: The lecture notes of the 1978 Stanford University CS209 course perhaps. Or this article by Paul Halmos.
Context
StackExchange Computer Science Q#386, answer score: 15
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