Drop a stone into water. It makes a sound, "glop" for a big stone, "splitch" for a small stone. Can you predict the pitch of the sound from the size of the stone?
The usual teaching of mathematical theories is like a pyramid.
Young people tend to become passive (if passionate) admirers of a structure built by old people, and problems they are taught to solve make them walk straight up to the peak. But what if we want to explore a natural mountain range, whose peaks are invisible among clouds, whose trails among trees are unknown?
The problem of the sound of a stone falling into water is natural, so natural that every child knows the phenomenon and can wonder about it. The mathematics involved is extremely hard, so hard that it is not taught at any mathematics department in the world.
This course tries to teach how to make _some_ progress on _any_ natural problem, when we know _nothing_. We will use no theory more sophisticated than calculus*, which to a passive admirer may seem little, but the _way_ we use it is very robust and powerful and a bit magical, and allows us to solve for example the problem above. In short, we shall learn the first steps in _applied mathematics_.

1st Modeling lecture: 1) Dimensional analysis 2) Back of the envelope estimate 3) Solving

lecture_tue21aug.pdf
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3rd Modeling lecture: Final firework, Sound & light

lecture_thu23aug.pdf
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A table of helpful numbers, with which you can make sense of
the (almost) entire universe and the daily life around you. I
recommend that you memorize and use them.

helpful_numbers.pdf
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Set of problems, on which we worked together in the afternoons.
They are all simple and curious problems, which any child may
wonder about, but whose solutions will make all scientists think
and, I hope, learn something new about the universe (natural or
social) in which they live.

problems.pdf
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Sample solutions to 1)--6) of Practice in Educated Guessing,
plus extra problems and their solutions.

solutions1.pdf
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Sample solutions to 7)--12) of Practice in Educated Guessing,
plus extra problems and their solutions.

solutions2.pdf
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93 KB (95979 bytes)

Sample solutions to 13--18) of Practice in Educated Guessing,
plus extra problems and their solutions. Together with the
extras, the set of these sheets provide a total of 40 problems.

solutions3.pdf
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A list of suggested items for further study, to learn modeling with insight and enjoyment.

suggested_reading.pdf
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