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" Invitation to simple modeling of complex phenomena" by Tadashi Tokieda

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_.

Tuesday 21st

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

PDF document icon lecture_tue21aug.pdf — PDF document, 3.51 MB (3683004 bytes)

Wednesday 22nd

2nd Modeling lecture: Waves

PDF document icon lecture_wed22aug.pdf — PDF document, 3.99 MB (4179481 bytes)

Thursday 23rd

3rd Modeling lecture: Final firework, Sound & light

PDF document icon lecture_thu23aug.pdf — PDF document, 9.51 MB (9970622 bytes)

Helpful Numbers

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.

PDF document icon helpful_numbers.pdf — PDF document, 103 KB (106457 bytes)

Practice in Educated Guessing

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.

PDF document icon problems.pdf — PDF document, 95 KB (97917 bytes)

In fact... (Part 1/3)

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

PDF document icon solutions1.pdf — PDF document, 102 KB (105041 bytes)

In fact... (Part 2/3)

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

PDF document icon solutions2.pdf — PDF document, 93 KB (95979 bytes)

In fact... (Part 3/3)

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.

PDF document icon solutions3.pdf — PDF document, 102 KB (104558 bytes)

Suggested Further Reading

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

PDF document icon suggested_reading.pdf — PDF document, 68 KB (69875 bytes)